Physics-
General
Easy
Question
In the figure shown, A & B are free to move. All the surfaces are smooth. ![open parentheses 0 less than theta less than 90 to the power of ring operator end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
- the acceleration of A will be more than g sin
- the acceleration of A will be less than g sin
- normal force on A due to B will be more than mg cos
- normal force on A due to B will be less than mg cos
The correct answer is: the acceleration of A will be more than g sin ![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
Related Questions to study
physics-
System is shown in figure. All the surfaces are smooth. Rod is moved by external agent with acceleration 9 m/s2 vertically downwards. Force exerted on the rod by the wedge will be:
![](data:image/png;base64,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)
System is shown in figure. All the surfaces are smooth. Rod is moved by external agent with acceleration 9 m/s2 vertically downwards. Force exerted on the rod by the wedge will be:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAADjCAYAAAAyjw7OAAAgAElEQVR4nO2dZ1hUV/f27xkGBhDpvQuCNCmCJUER0QRblGDDEqMxPGpswZJYUFEDRolRY6JRo8ZI1FijxoIN1NgBkV6UjvRep539fvAvr0bm0AaGcn7X5QeZNWuvM3PPPuvssjaLEELAwNDNYUs7AAaGjoAROkOPgBE6Q4+AETpDj4AROkOPgBE6Q4+AETpDj4AROkOPgBE6Q4+AEXo3RCQSgc/ng5n0/v9wpB0Ag2Th8Xior68Hm82GrKystMPpNDA9ejfjxx9/hLu7O/bv3w8ejyftcDoNjNAlAEVRoCiqU6QKOTk5iI6ORm5ubqeIp7PApC4S4MCBA3j58iU+/vhjfPTRR9IOp1UIBALIyMiAze6efR8jdAlw+vRphIeHQ1lZuUsJnc/n4+XLl3j27BmqqqowZcoUqKurSzusdoEReg8kPz8foaGhCA8PByEE/fr1w6BBg6CoqCjt0NoNRug9hJqaGoSFheH3339HVFQUJkyYAF9fX9jY2EBRURGysrJgsVjSDrPdYITezlAUherqalAUBUVFRcjJyTVq9/fff8POzg46OjpQUlJqs+jq6+uRk5ODV69eITQ0FA8fPoSBgQFmzZqFkJAQyMvLt8l/V4MRejtSWlqKW7du4datW6irq4OdnR2GDx8OR0fH9wQvLy8PHx8feHt7Y9GiRVBRUWlT2xEREQgODgabzcbQoUMxf/58GBkZdduHzaZghN5O1NbW4vDhwwgODkZhYSGMjY1x69YthISEYMKECViyZAm0tbUb7EePHo09e/bg7t27mD17dpuFbmpqisWLF8PGxgYcDvM198yfdwcQHR2NH374ATU1Ndi8eTPCw8MRFhaG4OBglJeX45NPPkFiYuI77xGX1rQGQ0NDWFhYMCL/P5hPoZ04efIkamtrERgYiIULFzaI2MLCAh9//DFiY2Oxc+dOLF++HP369evWD4KdAaZHbydqamrg4OAAT0/PRnvq/v37w9/fH5GRkUhLS2NmMdsZRujthL6+fpPiNTY2xsiRI5GdnY2MjIwOiux9KisrERMTg5qaGqnF0N4wQm8nvLy8QFEUUlJSaAWvq6uLAQMGIDU1FTk5OR0WH4/Hw6NHj+Dv7w9vb2/8/fff3XoRGJOjtxMODg5YunQpDh06BDMzM9jZ2Ym1VVZWxqhRo3D37l1ERES0a1y5ubk4duwYTp48CQUFBcyePRunTp2CsrJyt35w7b5XJmU4HA58fHzg6OiIe/fuQV9fn3YdCZvNxvLly3HlyhWJrSPn8/moqKhAfn4+nj17hjt37iA9PR0jR47EH3/8AVtbW8jIyEikrc4OI/R2xsrKClZWVs2yVVdXx/Tp0xsdgREKhSgqKoKysjJ69erVpK+kpCTs3bsX5eXlqK2thYGBAebNmwcXFxcoKCi0+Dq6OozQOxEFBQWgKArA6zF1DQ0NEEIQFRWFI0eOIDk5GcbGxli+fDlsbW1pfVVXV0NbWxseHh4wMzODpqZmjx7CZITeiVi+fDnCwsJgYmKC+fPnY86cOcjMzERAQACuXbsGiqIgLy8PDoeD7du3086eOjo6Ytq0aVBSUurAK+i8MKMunYgBAwbAzs4OR48exZw5cyAUCnHp0iVcvXoVhoaGiImJwdOnT1FSUoLo6GhaXxwOp8fk382BEXonIisrC4sXL4alpSUAICMjA3v27IGqqip27doFW1tbWFhYNAxHikQiKUfcdWCE3omIiYmBubl5w//379+P9PR0TJkyBW5ubgAAFosFNpsNgUDAzKa2AEbonQg5OTmEhYWhvLwc4eHhOHToEExMTDBlyhSoqqoCAEpKShAbGwttbW2JpCalpaX4888/sXHjRrx69arN/jorjNBbASEEAoEA0dHROHLkiMT8fv/999ixYwe0tLTg4eGBqqoqDB48GM7OzgBej4sfPXoUd+/ehaqqaqtGUSiKAo/HQ3h4OGbNmgUHBweEh4dj9OjR0NHRkdi1dDaYUZdmQAhBdXU18vPzkZWVhcjISERHR0MoFMLLy0ti7Tg6OuLixYvYs2cPcnJy4OHhgS+//BIqKipITExEYGAgioqK4OTkBDabDYqimrWRorKyEnl5eXj58iWioqLw7NkzKCsr49NPP8XevXuhrKwssWvorDBCp6GmpgZJSUl4/vw50tLSUFdXBwCwtbXFmjVrYGlpCS6Xi0OHDrXIb2xsLDQ1NaGnp/fO31ksFvr3748DBw689x5ra2uEhIQ0u43a2lpERUUhKSkJaWlp4PF4kJeXR//+/TFjxgz06dOnR42rM0L/DxRFIT4+HtevX8fjx4+hpqYGKysrDB06FH369IGxsXGbZxafPn2Kf/75B+bm5hg/fjwGDRok8dnKmzdvgqIo2NnZwcPDA6ampjAwMOhxe0XfwAj9LR48eAA/Pz8QQuDt7Y2AgAAYGRk1TNJIqgecOXMmJk6ciOvXr2P79u0oKirC5MmTMWvWLOjr60ukjY8++gibN2+GmpoaU4MRjNDfQVVVFXv37m3IgdsLLpcLLpeL6dOnY9q0aUhKSsKpU6fg7e0NOzs7jB8/Hg4ODtDQ0ICSklKrYlFQUEDv3r0Zkf8fjNDfwsbGpsPbZLPZsLGxQUBAAFatWoV///0X4eHhCA0Nha6uLvr27QsbGxtYWlo2azEXQ+MwQu9E9OrVC56enhg1ahRycnKQkJCAxMREPHv2DLW1tRgwYACGDx8Oc3PzHlu2orUwQu+EyMjIwMTEBCYmJvDw8EBZWRmys7MRFhaGpUuXQlVVFStXrsSAAQMk8txACEF+fj5UVVW77RJeRuithKIo8Pn8hmW17QWXy4Wuri50dXUxcOBALFu2DGFhYQ0nWrRG6CKRCDweD/n5+bh69SpOnDgBDQ0NHDhwgBE6w2uBFBYWIjs7G6mpqYiLi2u37WcCgaDRRVtvZmVlZWVblL7w+XwUFBQgOzsbCQkJiIuLQ35+PhwcHLBnzx7Y29t369WOjNCbQWFhISIiIhAdHY3S0lLIyMhAQ0OjobzcgwcPJNIORVFITU1FWFgY0tLSUF9f36hdRkYGFi9e3KS/NynJ06dP8fz5c5SXl4PD4UBfXx9TpkyBnZ1dmyuCdRUYoYuhoqIC9+/fx5UrV5Ceng5bW1s4OTlh9OjR0NfXh6ampsR786ioKHz99deIjY1FVVWV2NWJKioq+Oqrr2h9xcbGws/PD9nZ2XB0dISTkxMsLS1haGgIdXX1HjUrCjBCf48nT57gyJEjuHnzJmxsbPDZZ58hKCgIioqKkJGRaVeBfPfdd3jw4AFcXFwwZ84c6OrqvmdTUVGBc+fONRlHSUkJ5s2bhwkTJoDL5bZ77J0dRuhvcfHiRRw8eBBeXl7w9/eHvr5+h4ojLi4OQ4cOxW+//daw+aIxrK2tm0w53N3d4eXl1W0fLlsKI/S3+OSTTzBhwgSptT9x4kS8evUKBgYGtHYuLi49unduDcysw1tIWzxffvklFBUVER8fT7t7KCUlBbm5uR0YWdeH6dE7Ef369cPSpUsRFhYGBQWFRteJi0QiXL9+HY6OjjA2NpZClO1Ha+cFmgMj9DZAURQEAoHE/NXX1+PRo0cN5aTpRl1OnjzZprZEIhFqa2tRWVmJf//9F8nJyfD19X1vjXxHUV9fj6CgIGzevLld/DNCbwV1dXXIzMxEXFwcKisrJeb3r7/+gp+fHzgcDvr169fo2nGBQICqqqpWt1FZWYn09HTExMQgMjISmZmZsLGxwejRo6GhodGW8FtNXV0dDh06hL179zJClzZ8Ph+pqal49OgRYmNjISsrC2VlZQwYMEBibezduxcKCgqYP38+xo0b1+hxiHw+H+Hh4Q2bpZsbe0JCAh48eIDk5GRwuVyoq6vDzc0N9vb2MDc3l9rziVAoxLVr13D48GHU1dW1W/rCCL0JcnNzcfHiRdy4cQMcDgeDBw/GpEmTYGhoCC0tLfTq1Qs//vijRNrS1NSEsbExVq1aBTU1NbF2BgYG4HK5TfrLyMjA7du3cf36dSgoKMDV1RUzZsxomPDqDEOP0dHRWL16NTIyMtr1CEhG6P+BoihUVFTg8uXLOHLkCGJjYzFr1ixs2LAB/fv3b9f1ID4+Prh48WKTdgYGBk0K4vDhw7hw4QK8vb0RGBgIW1tbqY8q/Zfc3NyGIVXgde/eXjBCf4v4+HgcPHgQqampsLS0xNq1a+Hm5tZhu3QmTJiAwsJCREZGwt3dvdElBoQQPHjwAOrq6rC2thbry8vLCzt37uyUR54TQpCUlISZM2ciPz8fmpqa4PF47XriBiP0t2CxWBgzZgzWrVsnleqzFy5cQElJCQ4ePIjo6OhGH0YpikJ0dDRmzJhBK3R1dfVOkZo0RlJSElatWoWYmBiYmprC29sbp06dYoTeUdjY2EhlO90bTp06hdu3b0MkEuHChQuN/tAIIejVqxemTp0qhQjbTn5+PrZs2YJbt25BWVkZu3fvhoKCAk6fPt2u7TJC70T4+vrixo0bMDc3h6ura6M9clVVFaKioqQQnWTYsGEDTp8+DS6Xiz/++ANjx47F3bt3271dRuidiCFDhuCbb77BnDlzYGFhIdbuzp07Esu9BQIBKioqwOPxoKWlJdFDfd+mpqYGW7ZswcGDB6GqqorAwEB4enp22N5XRuithKIoFBcXo6SkRGI+tbS0sGTJkibHyO3t7du0Fp6iKOTm5iI5ORnJycnIycmBvLw8vvrqK2hpabXarzgqKirw888/Izg4GL1798ayZcswY8aMDi3FwQi9hVRXV+Px48d48OAB8vPzYW9vLzHfHA6n0TXo/4VujJ2OoqIiPHr0CPfv30d1dTW0tLRgbGyMiRMnwtLSsl1GaGpra3H06FHs2rULFEXhyy+/xKJFi1o04SUJGKE3Az6fj6ioKJw9exb37t2Dvb09PDw8MHnyZOjq6uLUqVPSDlEsFEXh33//xenTp5GQkAAHBwd4eHjAxsYG6urqUFZWbrf0gaIoXLp0CUFBQSguLsacOXOwYcOGDhc5wAi9UQQCAfh8PtLS0nD+/HlcuHABSkpKmDVrFtatWyeVL6qlZGRkIDAwEGfOnIGhoSG++OILbNmypcNiJ4QgIiICCxcuREVFBby8vPDbb79JbQM2I/S3KCkpQVRUFGJjYxEfH4/a2lp8+OGHOH78OCwsLLpU0aCXL1/C3d0dV69ehampaYfOCby5i/j4+KC6uhqenp744YcfpFplgBH6W7x48QK3b99uWBduZWXVrDUlnZGRI0fif//7X4dPGhFCcO/ePSxduhT5+flwdXXF5s2bYWZm1qFx/BdG6G9hZ2cHW1tb5sjCNvD8+XNs2LAB8fHxMDU1xY4dOyRWUawtMEJ/C2kX8SSEgMfjgc/no1evXl2uoFBRURHWrFmDe/fuQVVVFf/88w+sra2lLnKA2TMqVQghKC4uxpEjRzB27FiYmJigV69eUFFRgYqKCjw8PHDixAnk5eVJdCdTY9TV1bXpOMfS0lJ8/fXXuHbtGgwMDHDy5EnY2Nh0CpEDTI/eZtpyBGJSUhK+//57nD17FhRFQUdHB3379kVpaSnKysoQFhaGJ0+eYPjw4ViwYAHGjx8vUeFUVlYiOTkZ8fHx4PP5mDJlSqvG6PPz87F+/XocP34choaG+O677+Du7i6xOCUBI/RWQFEUsrKycOfOHRQXF7fKR3l5OZYvX4709HQsXrwYzs7O0NbWBofDQWVlJc6ePYuoqCjk5eXh6tWrSE1NhaysLEaPHt2m2AkhiIuLw61btxAfHw8lJSUYGxtjwIABrXpwLSkpwbZt2/DHH39AWVkZK1euxKRJk9ptKUFrYYTeAkpLS3H16lWcOXMGBQUF+OijjzBx4kRcuXKlxb6+//575Obm4rfffoOzs/N7InNxccGYMWNw8+ZNHD9+HL/++itmzpyJkJAQjBkzpsXt5eXl4cKFCzhx4gRkZGQwYcIELFmyBAYGBujdu3erhFlbW4t9+/bht99+A5/Px7p16zB//vxOeU4SI3QxiEQi1NXVoaamBk+fPsX58+cRGRmJQYMGYenSpXB1dW11r0UIwalTp7B3714MHTq0URtNTU2w2WzU1NQgMDAQo0ePxtKlS7Fy5Upoa2s3nD0qDh6Ph4KCAjx//hznzp1DQkIC3NzcsGvXLjg5ObUq7rcRiUQ4ffo0vv/+ewgEAixZsgQbNmxos9/2ghH6WxBCUFBQgPT0dKSkpCA1NRVpaWnQ1NTExIkTsX37donslBeJRCgpKcGwYcNoY2GxWIiJicGgQYMwbNgwPH78GH5+fggJCYGVlRXtKNGjR4+wdu1a6OnpYfr06RgyZIjEZkWFQiHOnz/fUJLj888/x9atWyXiu71ghP4WDx8+xPHjx6GkpARtbW0MHToUCxculHgNRg6HA3t7e/z+++9YsGDBe8OIhBBcvHgRKSkp74y2yMnJYfny5di9ezeSk5NpKxD069cPgYGBEp8VpSgKZ86cwdKlS1FdXY1JkyZh3bp1Uh+abQpG6G9hYmKC+fPnQ1tbG+rq6u26jNTX1xerVq1CcnIyFi5cCBMTEwiFQiQmJuL48eM4f/48RCLRe2I2MTGBpaUlsrKy4OTkJFbEb07JkKTICSG4cuUKNmzYgKKiIowYMQKbN2/uEhXDGKG/hYGBQZMFPiXFZ599hqdPn+Lnn3/Gnj17GrVZvnw5Bg8e/M7fOBwOrKyswOPxIBKJ2u3EjcZ49uwZ1q1bh9TUVOjr6yMkJERi56K2N4zQpQSLxcLmzZthYmKC06dPIycnp+HIFk1NTQwbNgxBQUGNvtfU1BQFBQVtGsNvKampqVixYgViY2Nha2uL8+fPdxmRA4zQpYqamhpWrFiBSZMmIS4uDtXV1VBUVISDgwOMjY3FrpZ8c1S7JHpzQgiys7ORm5uL/v37N7rO5+XLl1i6dCnCw8Nhb2+PXbt20W7164wwQm8D9fX1yMnJaZMPFouFPn36oE+fPs1+j4yMTJvXwZSVleHevXu4du0aCgsLMWzYsEbLZ2RlZTVM7ZuZmSEgIACurq5talsaMEJvBS9fvkRISAj++ecffPDBB9IOp9lQFIWnT5/i2LFjuH37NmxsbDB9+nS4u7tDUVHxvYmekpIS+Pv749q1a1BUVMTGjRvxySefdOhzgaToehF3MDweDxUVFcjLy8O///6L0NBQFBcXw9vbGydPnkSfPn3w0UcfSTvM9yCEoL6+HlVVVcjJycH169cRGhqK+vp6TJo0CZcvX6YdeqyoqMCOHTvw119/gcvlYvPmzZg9e3YHX4XkYITeCPX19cjIyEBqamrD6RLV1dWwsrLCxo0b4ejoKLEltLW1tcjPz4dAIIC5ubnEesukpCTs2rULubm5qKyshJ2dHb777jsMHDiwyRldPp+Pffv2Yc+ePVBUVMSKFSvg5+cnkbikBSP0tygoKMDly5cRHR0N4HX5CTMzM7i7u8PCwqLREyjaSkJCAoKDg5GXl4ezZ89KrNxEUVERVFRUMGLECNjY2EBLS6tZY+pCoRC7d+/G1q1bwWKxsHDhQixbtqzTLLdtLYzQ3yI+Ph65ubmYNGkS+vTpA3V19XbfbVReXo6nT58iPT0dfD5fYn6HDBkCX19f9O7du9nvoSgK+/fvR1BQEOrr6zF79mz4+fm1yEdnhRH6W3h4eMDDw0PaYUgEOTm5FqVBFEXh3LlzCAoKQkVFBUaNGoXt27e3uoZMZ4PZYcQAQghu376NgIAA5OfnY/jw4fj999+7jcgBRugMACIjI7F69WokJCRg5MiROHjwYJea9WwOTOrSw4mLi8PcuXMRFxeHDz/8EIGBgTA3N5d2WBKHEXorqampwe3btxETEyPtUFpNRkYGvvjiC8TFxcHMzAyBgYHd9lRqRujN4M25RiUlJUhOTsa9e/cQGRkJfX19zJgxA7dv35Z2iC3izfqWb775BlFRUdDS0sK2bds63YZmScIIXQxvSlEkJycjMTER2dnZKC0thYKCAgYNGoRFixbBwMAAbDYb27dvl3a4LaK0tBRBQUG4ePEitLW1sW3bNkyePFnaYbUrjND/Q319PR4+fIg7d+4gOzu7obSym5sbLCwsYGho2OUKC70Nn89HQEBAw679zZs3Y9asWdIOq91hhP4WYWFh8PPzg52dHcaMGYOZM2dCU1MTSkpKHVq0vr0QiUT49ttvceDAAXC5XKxcuRIzZ87sljn5f2GE/hbm5ua4ceNGu5z6IG34fD527tyJAwcOgMViYe7cuVi0aFGnPblO0jBCf4uusPexNdTX1yMkJAQ//fQTeDweZs2ahYCAgE6/oVmSMBNGUiAzM5P2dYqimrRpCZcvX8bWrVuRn5+PWbNmITg4uFvNejYHRuhSYOfOncjOzhb7+q1bt3D16lWJtHXv3j34+fkhLS0NkydPxpYtW7platYUjNDbACGkVacdp6Wlwdvbu9EKuTk5Ofjxxx8l0qM/f/4c48aNQ3Z2Ntzc3LBlyxYYGRm12W9XhMnRW0B9fT2KioqQl5eH58+f4/Hjx1BUVGyVr8jISHz33XdwcXFp+FtdXR1CQkIQFhYGR0fHNsWalJSE+fPno6qqCk5OTggKCoKlpWWbfHZlGKE3ASEEL168QGxsLJKSklBRUQE+nw9jY2PMnTsXjo6OmDBhQqv8Hjp0CKWlpQ1lK+7cuYP9+/eDx+O1Oe43R6337dsX27dv75IbmiUJI/RGIIQgJycHYWFhuH37NlgsFiwtLWFlZQVzc3MYGxtDVVW1zePPbyrcVlVVAXhdYTc/P79NPoVCIYDXw4mmpqY4cOBAt57aby6M0N+irq4OV65cwfHjx5GZmQkPDw8sWLAA/fr1g4KCArhcrsTrGL5dLuPFixdt8icQCHDjxg0AgIaGBnbt2oXhw4f3iAmhpmCE/hZXrlzBlStX8L///Q9Dhw5tt3Hmt6vaNlZti81mQ0VFpUU+KysrsWLFCqSnpwMAJk+ejBEjRnSpIyPbE0bobzFp0iRMmjSp3dtZtGgRQkNDUVhY2Ojr9vb2LYqjrKwMO3bswMmTJ8HhcKCtrQ19ff1Od+qENGF+7lJg8ODB2LRpU6N7OjU1NbF48WKYmpo2y1ddXR0OHz6MAwcOoK6uDitXrsSBAwcwbdo0RuhvwfToUmLOnDkICwvDqVOnGv7GZrPx0UcfwcvLq9mLyM6ePYugoCCUlZVh5cqV8Pf371FT+82F6dGlhLy8PFavXv1Oz21gYAA/P79mnapBURRu3LiBL774AuXl5Zg9ezZWr17NiFwMjNCliLW1NRYuXAglJSVwOBwsW7YMAwcObPJ9AoEA169fx2effQZCCMaPH49169ZBXV29A6LumjCpixSRl5eHj48P7ty5Ay6XiwULFjT5HpFIhHv37mH16tUNVXA3b97c5co4dzSM0KWMkZERNmzYAD09vWalHYmJiVi3bh3i4uJgZ2eHvXv3wtbWtgMi7dowQpcyLBYLgwYNatakTl1dHb744gtERESgT58+OHPmTI9ev9ISmBy9E9Ackefn52PcuHGIiIiAmZkZ9u3bh759+3ZAdN0DRuhdgKysLKxatQrh4eEwMDDAxo0b4e7uzsx6tgDmk+rkFBYWIjg4GOfOnYOsrCw2btyIyZMnM5NBLYTJ0TsxbwryHzp0CHw+H3v37sXs2bMZkbcCRuidFKFQiKNHj2LLli3gcDjYuHEjfH19mZWIrYQReiekvr4ef/75JxYvXgx5eXnMmzcPX331FSPyNsDk6J0MPp+PU6dOwd/fHxRFwdvbGytWrGjWsgAG8TBC70RQFIXr169jy5YtKCgowIgRIxAUFNRt6810JEzq0olITk7GsmXLkJaWBkdHR1y4cKHHVNJqb5gevZOQkpICHx8fZGZmYtCgQfjrr78YkUsQRuidgJiYGMybNw+xsbGwt7fHtm3bmFlPCcMIXcokJyfD398fDx8+hKGhIb777ju4uroys54Shvk0pUhhYSECAwNx9epVsFgs/Prrr/D09JRqiWqRSITnz583umm7K8MIXUrU1tYiODgYISEhUFRUxB9//IGxY8c265ABQgiqqqoQGxuLkydPNmlfVVWF+/fv4+DBgwgLC8OrV68a6r+8oaKiAmfOnIGrqysGDBgAiqJafW2dEWbURQpUVVVhx44d2LVrFzQ1NbFmzZpmH61SUVGBx48f4++//8aJEyfg4uICHx8fsfaJiYnYt28f0tLS8MEHHyAqKgqRkZHw9/fH2LFjweFwQAhBXFwcjhw5gtjY2G4ncoAReodTU1ODXbt2YevWrVBUVMSCBQswZ86cZqcr0dHRePz4MW7cuIHy8nJa27y8PCxYsAA1NTXYt28fnJycwGKxsGXLFmzatAna2toYPHgwWCwWXF1d8e233yI1NRWpqamSuNROBZO6dCB8Ph+//fYbdu/eDYFAgBkzZsDPz69FtcqdnJywZMkSjB8/vskfx7Fjx3D//n18+umncHFxAYfDgYyMDObNm4eqqir89NNPKC4ubrDv3bs3uFxuq6+vM8MIvYOgKAqXL19GYGAgysrK4Onpid27d7e4IL+ysjJUVVVhZ2dHu4qxvLwcFy9ehEgkwogRI95ZJ6OqqoqBAwfiwoULEu29CSGd9iGWSV06iPDwcKxYsQLl5eUYN24cTpw40a7LbdPT01FWVgYAMDMze+c1LpcLGxsbHD9+HOHh4fjwww/F+hEIBIiNjUVlZSXYbDZ69+4NQ0PDdw4TKCkpQWJiIkpLS8HhcKCrqwtLS0vIy8sDeL2DSton+TFC7wBu376NhQsXIjs7Gx9//DF++OGHdq+/kpmZ2ZDD/3dMXlZWFmZmZpCVlUVaWhqtH6FQiGPHjuHQoUOYOHEiPD09oaCg0CD03Nxc/Pjjj0hPT4enpyfKyspw4MABGBoaonfv3gAAS0tLeGWV1JIAAB1lSURBVHt7t7iepCRhhN7O3L9/H35+fkhNTcWQIUOwZcuWDpn1fPXqFSorK6GoqPiewFgsFpSUlMDlcpGVlUXrp7S0tOFQAT8/P+jr6ze89mY58YkTJ/D3339j0KBBqKurg6KiItavXw89PT3s3LkT2traUs/9mRy9HUlMTMTq1asRGxsLHR0d7NmzB05OTh0y68nn8yESiWBkZNSoyFgsFlgsFnJzc8X6KCwsxLfffotRo0YhKCjoHZEDr+8af/75Z0PteABQUFDAvHnzYG5ujpycHBBC4Ozs3JDGSAtG6O1EVlYWNmzYgPv370NXVxd//fUXnJ2dpbJ5QiQSvfc3iqJAUVSjrwGvhyaDg4Ph5OSERYsWNTrCU19fj9LSUsjIyLxzXb169YKNjQ34fD6io6MldyFtgBF6O1BcXIyAgACcO3cOpqam+OWXX+Dm5tahMXA4HLDZbAgEgvceBAkhqKioQH19PbS1tRt9/86dO3H16lU4OzuLTTve5OppaWmoq6tr+LtIJGp4eNXU1JTcRbUBRugS5k1V22PHjkFfXx/+/v4YN25ch8ehpaWFXr16IS8v770zkQQCAXJyciASiTBs2DCx78/IyMCuXbvE1nHX1taGq6sr8vLycP369YbhxSdPniA2NhaOjo4YO3asxK+tNTAPoxKkpqYG69evx4kTJ6CgoIClS5dixowZUtm1b21tDW1tbRQWFiI7O/udB2CBQID09HRwuVyxQpw7dy5evHiBY8eOISAgAHv37n0v7VJRUcHatWsbTtu4cuUKDA0NER4ejjFjxmDt2rUwNDRs1+tsLozQJcjRo0dRVVUFiqIwb948LF++XGrjxzY2NrCyskJ8fDwSEhLeEXp9fT0SEhJgYWEBHR2dRt+vqakJPz8/JCUlYf/+/bCxscGCBQveydXfnNinqKiIhw8fNjzcfv3119DT0+tUm7mZ1EUCEEJAURTy8/MhEokwb948fP/99+0q8qZmITkcDubOnQtNTU2Eh4e/c3jvs2fPkJKSgunTp8PAwOAdn29ja2uLb7/9FoaGhli7di1OnDjxzsNrQUEBfvjhB3C5XFRUVEBOTg4WFhaQkZFBYWEhCgsLJXKUpCRgenQJ8CaH5XK5+Pzzz7Ft27Z2HTcWiURIT0+HUChEZWUlcnNzoaOj895RMZ6entiyZQt++eWXhmMYCwoKsH79enh5eWHWrFnvbNfLy8tDRUUFACA1NRUWFhYYM2YMPvnkE+zbtw8//vgjjI2NMXToUHA4HFRVVSErKwsPHjzA3bt3YWho+E6axmaz4ezsjLlz54p96O0oZAICAgKkGkEX58yZMzh48CBEIhEmTpyIwMBAsemAJMjPz8fRo0eRlpYGLS0taGpqIj09HSwWC0ZGRu/cRdhsNhwcHGBiYoL79+/j1KlTDZM/s2fPbujNCSGIjIzE1atXISsrC3Nzc+Tn50NOTg6ampp4/vw5evXqBXV1dRQUFODly5fQ09ODrq4u6urqUFFRAW1tbYhEIqSlpSEtLQ05OTl48uQJHj9+DA6HAxcXF7HPKhkZGfj7779RWVmJjRs3ts8HRxhaTVhYGDE0NCQAiIaGBjl8+HCHtEtR1Hv/WvKe5vptqr38/Hyye/dukpyc3KhNUVERCQ4OJsOGDSMRERFi2w0LCyMmJiaEzWa34FNoGUyO3gooisKTJ0+wevVq5OTkwNbWFmFhYZg7d26HtP9mVvPtfy15T3P9NtXe6dOnER8fDx0dnUZtNDU1MW3aNDg6Okp9Dywj9FaQkpKC9evX48mTJ3BycsLvv/+O/v37SzusDoUQgu3bt+PFixd4/PgxioqK3nmY5fP5iI2NxfHjx6Gmpib1YUbmYbSF5OXlYcmSJbh9+zZsbW3xww8/wMXFRdphdTgsFgtTpkzBvn37sGjRIpiYmMDQ0BCqqqoQCoXIy8tDfX09vLy84OPjI/0Z0nZLirohpaWlZOTIkYTNZhMjIyNy7tw5IhQKpR2W1KiqqiKhoaFkwoQJhMvlEhkZGaKjo0Pc3d3J/PnzycOHDwmPx2vST0fk6EyP3kxKSkqwcuVK3LlzB6qqqlizZg0mTpwo9dxTmigpKeHjjz/Gxx9/DIFAAKFQCC6X2yk/E0bozaC8vBzBwcE4c+YMFBQU8M0338DX17dTfqHSQlZWVqr1aJqC+aaagBDSMOFCCMHatWvx9ddfvzc5w9C5YYTeBLt378b27dtRW1sLPz8/LFq0SOq7ZRhaDtMtiYGiKISEhGDVqlUAgM8++wx+fn4N+yAZuhZMj94IfD4ff//9N/z9/SEUCjFu3DgEBARAXV1d2qExtBJG6P+BoijcvXsXmzZtQnZ2NkaNGoXg4GDm1IkuDpO6/IekpCSsWrUKsbGxcHd3Z05o7iYwQn+LvLw8jBs3DpmZmXBwcMDu3bsZkXcTmNQFr4cQ09PTMXXqVGRmZsLS0hJBQUE9bv1Kd4YROl7XJ1mzZg0eP34MXV1dbNy4ER9//HGn2grG0DZ6vNDLy8sRFBSES5cuQUlJCTt27MCUKVOkXiuQQbL0eKEHBATg2LFjYLFY2LVrF6ZOncrMenZDeqzQ+Xw+Nm/ejN27d4PNZmP9+vWYOnUq05N3U3pk11VdXY1Dhw7h+++/h7y8PObPnw9fX1+p1wdkaD96XI9eX1+PU6dOITg4GHV1dZg1axZWrVrFzHp2c3pcj37r1i1s2rQJr169go+PD4KCgt4pas/QPelRQn/x4gVmz56N0tJSeHp6Yv/+/VBWVpZ2WAwdQI9IXSiKQmRkJIYPH46KigoMHz4cP/zwAyPyHkS3FzohBFFRUViyZAlevXoFBwcHbN68Gba2ttIOjaED6fZCT0lJwYYNGxAREQFdXV3s2LEDQ4cOZWY9exjdOkevrq7GmjVrcOPGDfTu3RsXL16Es7Mzs9ezB9Jtv/Hq6mosW7YM58+fh5qaGg4dOoSBAwcyIu+hdMsevbi4GIGBgTh8+DC0tbWxfv16jB49WtphMUiRbte9lZeX46effsLBgwchLy+PZcuW4bPPPnunPDJDz6NbCZ3H4+GPP/7Azz//jJqaGixduhRLliyR6kGuDJ2DbpO6EEIQGhqKtWvXoq6uDvPmzcO2bdukHRZDJ6FbCF0kEuHGjRv44osvIBQKMW3atGaLvKysDOXl5ZCRkYG6ujqUlJQatRMKhaitrQVFUWJ9ycnJQUFBoWHoUigUori4GHV1dVBSUoKmpiYzrCklurzQKYrC1atX8dVXX6GiogJjxozBxo0boaGhQfs+kUiEO3fuICQkBJmZmZCVlYWNjQ2WLFmCPn36vGcfGRmJP//8EzU1NWJ9Dh8+HFOnToW8vDxqampw9uxZPH36FPLy8uDxePD09ISHhwfzvCAFurTQCSG4c+cO/P39kZOTg4EDByIoKAiWlpZNvu/48eM4cOAATExMYGBggJs3b+LmzZuIi4vDX3/9BTU1tQb7uro6/PPPP9i3bx+EQmGjPuXk5GBiYtKwaSMsLAxHjx6Fr68v7OzskJ6ejt9//x0CgQATJkxghjk7mC4t9JSUFKxZswYxMTHQ1dXFiRMn0KdPnybTg7i4OBQUFODkyZMNPf/t27cxb948hIWFYfv27di6dWuDfUFBASIiIjBz5kxMmTLlvWpdoaGhCAkJwcCBAxuE/ssvv8DX1xdTp04Fm82GjY0NOBwOzpw5AxcXF6kXxu9xtFtB6nYmPz+feHp6EhaLRczNzUlMTEyz3sfn80lERATJzc195+8URZHdu3cTFotFZs6c+c5rDx8+JL/++isRiUTv+RMKhcTDw4O4ubmRoqIiQgghlZWVxNbWltTW1r5jm5eXR7766ivy/Pnzllxqt4c5w0gMWVlZWLhwIUJDQ2FhYYFdu3Y1e5GWrKwsBgwYAH19/Xf+zmKxMGzYMMjJyWHUqFHvvKampoaZM2c2mm4kJSXh33//hZubW8OpDjIyMpCVlUVRUdE7trW1tRCJRMyeVCnQ5YSem5uLdevW4fz589DX18f69esxatSoFuW84lKbmzdvYvTo0ZgwYcI7f+/Xr5/Y0Zjjx4+DxWLBy8ur4W+Kiopwd3fHwYMHUVZWBuC1yM+dOwd1dXXo6ek1O1YGydClhF5WVoZt27bhzJkzYLPZ8Pf3x5QpUySy1/PBgweora3FwYMHm72trri4GNeuXYO9vT0cHBzeeW3p0qVIT0/H7Nmz8fXXX2Ps2LEoKCjAwoULoaqq2uZ4GVpIuyVFEqauro5s3bqVyMnJEQDkyy+/JLW1tc06Y1McQqGQlJaWkpMnTxJTU1PSv39/EhUVRQQCQbPef+7cOaKtrU3279/f6OvV1dXk+vXr5ODBg+TevXttirU70xE5epcQOo/HI7/++itRUlIiHA6HsNlsIicnR+bMmUNu3LhBqqqqWuU3KyuLbN68mbi7uxNdXV3CZrOJmpoa+fPPPxt98Hyb+vp6snTpUqKlpUVKS0tb1T7DaxihE0IEAgHZt28fUVVVJb169SKzZ88my5YtI/r6+oTFYhFjY2Py3Xffkerq6lb5pyiKFBYWkhMnThAnJyfCYrHIsGHDSGpqKu37EhMTiaurK5k1a1ar2mX4//R4oYtEInLkyBGip6dHOBwO8fHxITk5OaSqqoo8ffqUzJgxg3A4HKKsrExmzpxJSkpKWt2WUCgkjx8/JmpqakRLS4ucOHFCrC1FUeTMmTNEVVWVXLhwodVtMrymxwv92rVrxNTUlAAgzs7OpLi4+J3XKyoqyLfffkvk5eUJi8UiI0aMIGVlZW1qc9q0aURHR4ecOnVKrE11dTX56quvSP/+/cmLFy/a1B5DDx9Hf/LkCdasWYOsrCwMHDgQFy5ceG/9irKyMjZu3IhNmzZBXV0d9+/fxzfffPPe+HVLcHFxgZaWFszNzcXalJaW4vr16xg+fDhTE6aL0CmFHhcXh+XLlyM6OhoffPABfvvtNxgYGDRqq6CggBUrVmDTpk1QUFDAyZMnceDAAdTW1ra4XR6Ph7i4ODg4ONCul7l37x5KSkowZMgQ5vCurkK73StaSWJiIvnwww8JAOLk5ETCwsKadQw5n88nwcHBRF5enhgYGJCnT582aicQCMjDhw9JaGjoO6M1RUVFJCAggDg4OIh9LyGv83N3d3cycOBAEhcX1/ILZHiPHpejZ2VlNaxf0dPTI5cuXWqWyN9QUlJC5s6dSwCQ8ePHN2qTl5dHpk2bRlRVVYm1tTVZunQpWbt2LRk1ahTx8fEhL1++pB1ajI+Pbxja5PP5Lb5GhvfpCKF3mkUXhYWFCAgIwM2bN9GrVy9s27YN48ePb5EPdXV1LFiwABEREfjnn39w+/ZteHh4vGOjra2NZcuWwdDQEC9fvoRIJIK+vj62b98OOzu7Jo/5jo+Px8SJEzFt2rROfSQ4w39ot59QC6iqqiKrVq0iXC6XaGlpkb1797bal1AoJCtWrCCysrLk008/bdEdgUE69IhRFx6Ph8DAQPzyyy9QUlLCt99+C19f31b7k5GRwaBBg6CkpIR79+4hOTlZgtEydFWkKnSRSISgoCDs3r0bLBYLCxYsgK+vb5uXsTo6OkJJSQm1tbWIjo6WULQMXRmpCV0kEuHXX3/Frl27wOPx4O3tjTVr1kikwq22tjZkZWVBURSKi4slEC1DV0cqD6NCoRBnz55FcHAwampqMH78eOzatQu9evWSiP/evXs3CL28vFwiPhm6NlLp0d+cOpGdnQ0vLy/s379fokersNlsyMjIgBAidjMzQ8+iw3v0R48eYcmSJXjx4gXGjh2LwMBA6OrqSrSNuro68Pl8sNlsZuaSAUAHCz0uLg4zZsxAeno6XFxcsGXLliZLU7SGyspKCIVCsNlsphwdA4AOEjohBMnJyVi8eDEyMjJgbm6Obdu2wcnJqV3aS0hIQG1tLWRkZCR+t2DomnRIjl5cXIygoCDcv38fJiYm2Llz53szlpJCIBDg2rVrKC8vh7q6OoYMGdIu7TB0LWh7dIqikJWVhZycnDY1Ul5ejqqqKujp6WHatGlQVVXFv//+2yaf4igrK8ODBw/A5/NhaWmJlJQUpKSktEtbDJIhOzsbTk5OMDMza5UuzMzM3itf8l9YhBAi7kUej4ft27dj7969LW78v9TX16Ourg4qKirtWo5NJBKhoqICfD4fSkpKYstUMHQeKIqCQCAAIaRVFR0CAgIwf/58Wpsmc3Q+n4+amhq8+T3QlXsjr1dDihWynJwc6urqmu2rKZs3dv+14XK54HK5ANDs2IHXH3hTP8KO9tWWz6G1viT5ObQ0LnFFXOnaEwgEtP6BJnp0iqKQnZ2NV69e4fnz5+jduzfMzMzEOqutrUVoaCi8vLxoL+7Zs2dQUVGh9VVaWoqUlBQ4OzuLXSXI4/EQHx8PIyMj2p0+L168AJ/Ph42NjVgbHo/XUMBIRkZGrF18fDyEQuF7dVz+y7Vr1+Dm5gZFRUWxNklJSQAAKysrsTYlJSXIzMyEjY2N2N5OJBIhIiICffv2pa0inJWVhVevXtE+txBCcOnSJQwfPpx2xCovLw9paWlwdXUVayMUCvH06VNYWlqKjYsQ0rCKtF+/fmJ9lZaWIi0tDf3792/oxN5gamradFGo5q7++vnnn8nXX39Na1NTU0MGDBhAMjIyaO3++OMPsmXLFlqbFy9ekCVLlpCXL1+KtamtrSWbN28mly5doq2ZcuPGDeLn50drw+PxyNixY0lUVBRtXDdv3iTe3t5N1miZPXs2uX//Pq3N+fPnyYYNGwiPxxNrk5KSQr755hvaqgRCoZAEBASQs2fP0rYXHR1NRo4c2eSKztmzZ9PumSXk9d6BiRMn0pYaqa+vJ/7+/uTixYtibSiKIhcuXCBbt26lreSQk5NDfH19SXZ2Nm1c4mh2suzh4YETJ07QblFTVFTEmDFjcPPmTVpfH3zwATIzM2nXoWhqakJVVRUvX74Ua6OgoABLS0skJCTQ3r5cXFyQmJiIqqoqsTZycnIYO3Ysjh07Rhu7q6srCgsLkZmZSWvn4eHR5IOVhYUFqqqqkJeXJ9bGyMgIMjIytO3JyMhgyJAhCAsLo23PxsYGhJAmF7rNmTMHp0+fprUxNDSEjo4OYmNjxdrIysqif//+iI2NFfv9sFgsWFhYoKSkBKWlpWJ96erqQkVFhbY9OpotdGtraxgbG+Pu3bu0dj4+Prhx4wbtyRAaGhrQ1NRsuHU3hrKyMkxNTZGQkAA+ny/WbsCAAYiPj6e1UVVVhYODA86ePUsb++TJk3Hq1CnweDyxNvLy8hg5ciTCw8NpfQ0aNAhpaWm0X56enh7k5ORoRSwvLw8bGxtERkY25KmN8eGHH+LJkye0HZGsrCw+/fRTnDx5kjb24cOHo6ioiDYuFouFwYMH4/Hjx2Jt2Gw2+vbti/LychQWFoq1Mzc3R11dHV69eiXWRkZGBh988AFCQ0NpYxcbS0uM//e//+HSpUu0IjY1NUXv3r1pRaykpAQTExMkJiaK9cVisWBra4vMzExUV1eL9WVubg42m434+Hja2D/55BMcOXKENnYdHR0MHDiwSRGPHTsWjx49ov1xaWhoQE1NDampqWJt1NTUYGRkhMTERNo1OYMGDUJ0dDTtXat3794YOnRokyL29vbGzZs3aU/uYLPZ8PDwaLJTs7e3R1ZWVkMh1cYwNjYGIQS5ublibeTk5ODs7Nxke66urnj48CFt7OJokdC9vLyQmpqKgoICsTZcLhc2NjZ49uyZWBtZWVn069cP2dnZqKioEGvXr18/lJeX0/7S2Ww2Ro0ahRMnTtDG7uLigsLCQrx48YLWbubMmQgNDaXtPfv06QMZGRnatEpVVRW6urpISUmBSCRq1IbFYsHR0RHx8fG0dxEzMzOw2Ww8f/6cNvZJkybh2LFjYtsDAH19fVhbW+Phw4e0vtzc3PDs2TPU19eLtXlzR8rIyBBr86Z6cEJCAu1n6urqivv379P+4HV0dGBpadlkatwYLRK6hoYGrKys8PTpU7E2HA4H1tbWePnyJe0vr2/fvigtLUVJSYlYG1VVVVhZWTXZw44aNQo3btyg7fm5XC6mT5+OS5cu0fpyc3PDq1evaPNmJSUlmJqa0t5F5OTk0K9fP6SlpdGmE/3790dBQQHy8/PF2nA4HIwePRqHDx+mjd3Z2RnV1dVNTpB9+umnuHXrFq3wzMzMQFEUbfqipaXVcNcSd6dks9kYOHAgIiIiaO+mZmZm4HK5iIiIoI198uTJTd61Go2jJcYsFqshF6Trpfr06YPa2lraL8/AwAAqKipNphweHh5NilNbWxv29va4desWrd0XX3yB69ev06YcysrK6NOnD+0Dm7y8PCwtLfHixQtaEdvY2CA7OxuVlZW07dnb2+PKlSu0sY8ZMwbnzp2jbY/L5cLLy6vJPPaDDz7Aq1evaO/Mampq0NLSov3RyMnJwdraGklJSbR3JCcnJ7x8+ZI2xeFwOBg3bhyOHj1KG7unpydiYmJoc/7GaPEUpa2tbZPphJGREQDQLh1gs9kYMmQI7ty5Q9uek5MTysvLkZiYKNaGxWLh888/x7lz52h7KSMjI+jq6tKmAHJycujfvz9iYmJof8zNuSMZGRlBSUmpyZECT09PnD17ljbl0NDQwPDhw5u8bU+dOhV3796lFZ6KigqMjIxoOxklJSWYm5sjJSWF1pe9vT1evHhBe/dWUlLCkCFD8Ndff9HG/sknn+Dy5cu0vuTl5eHu7o579+7R+vovLRa6rq4uFBQUkJ6eLtZGUVERVlZWiIqKohXeoEGDEBMTQ5uny8jIYOrUqQgJCaGNa8SIEcjKyqJ96AGAIUOG4PHjx2LjYrPZsLS0RElJCW2PZ2JiAqFQSPtjZrFYcHd3xz///EMbk4ODA2pqapq8u82bN6/JwQBDQ0NoamoiLi5OrI2ioiLMzc2bfAi2trbGq1evaL8fY2NjKCkpISoqijb2cePG4c8//6RtT01NDW5ubk3emT/99NMWr79qsdDV1dVhaGiIpKQk2qAHDx6MiIgI2l5KR0cH/fr1w+XLl2nbnDRpEq5fv95kDj5s2LAmx64dHR2Rnp7e5JdHURTtXUtJSQnW1ta0w2vA64esyMhI2mFGWVlZ+Pj4NDl2/WbYj+5LlpWVhb29PW0nIyMjg379+iE/P582nejbty9qa2ubvDOPGjWqydgdHBzA4/Fo78wA8Pnnn+PatWu0HaSLiwuMjY1p/bwXZ4us8fpDcnBwQEJCAu0Ted++fUEIafK27e3tjUOHDtHamJiYwNTUlPYhGHj9UPro0SPaYThDQ0Ow2WzahyxNTU3o6ekhLi6uyZGCplIvTU1N2Nvb4+rVq7R206dPx40bN5q8bTs5OeHJkydibTgcDmxtbZGenk77bGBmZoaqqiraSbtevXqhf//+TV7jm1SCbn+urKwsZsyYgQsXLtD6GjJkCEpLS5GdnS3W5s1Qakto1TJCR0dHZGRk0H6QsrKy+Oijj3D8+HFaXyNGjEB6ejqysrLE2rw5DOv27du0vt6cMUr3IWlra0NZWRlpaWm06YuzszOeP39Oe0eytraGQCCgTTlYLBZ8fHyaHP7U19eHhYUFIiMjae0+/PDDJu+Ub9IqupEjXV1daGpqIiEhgbY9d3f3Jh9u1dXVMXTo0CZ/zHPmzMGtW7doBwMUFBRga2tLOxggIyPT4irGMgEBAQEtegde9yw6OjpQVVWlXfhjaGgIgUBAezQii8WClZUV1NXV3zmt+b8YGRmBzWbDzMxM7IIxLpcLLS0taGpqit0ryuFwoKWlBVVVVWhra4v1paGhAVlZWVhYWIi1YbFYMDc3h6ysLLS1tcXGbmhoCJFIBDs7O9pVgSYmJlBWVqb1paqqCnV1dejq6oqtf6OoqAhlZWXo6+vTLlPW09ODoqIi7VpuDQ0NsNlsWFlZ0S5269u3L2RlZWFiYiLWRlFREVpaWtDX1xe7QI3FYkFHRwdKSkoS3R1Gu3qRgaG7IPWSdAwMHQEjdIYeASN0hh4BI3SGHsH/A9nYRpoCn79cAAAAAElFTkSuQmCC)
physics-General
Physics-
A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is
A stone is released from an elevator going up with an acceleration a. The acceleration of the stone after the release is
Physics-General
physics-
A ball is projected from point A with velocity 10m/sec. perpendicular to the inclined plane as in figure. Range of the ball on the incline is
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)
A ball is projected from point A with velocity 10m/sec. perpendicular to the inclined plane as in figure. Range of the ball on the incline is
![](data:image/png;base64,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)
physics-General
physics-
Three projectiles A, B and C are thrown simultaneously from the same point in the same vertical plane. Their trajectories are shown in the figure. Then which of the following statement is false.
![](data:image/png;base64,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)
Three projectiles A, B and C are thrown simultaneously from the same point in the same vertical plane. Their trajectories are shown in the figure. Then which of the following statement is false.
![](data:image/png;base64,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)
physics-General
Physics-
A soap bubble has radius R and thickness d
as shown. It colapses into a spherical drop. The ratio of excess pressure in the drop to the excess pressure inside the bubble is
![](data:image/png;base64,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)
A soap bubble has radius R and thickness d
as shown. It colapses into a spherical drop. The ratio of excess pressure in the drop to the excess pressure inside the bubble is
![](data:image/png;base64,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)
Physics-General
physics-
Equal volumes of two immiscible liquids of densities r and 2r are filled in a vessel as shown in figure. Two small holes are punched at depth h/2 and 3h/2 from the surface of lighter liquid. If v1 and v2 are the velocities of a flux at these two holes, then v1/v2 is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVIAAADxCAYAAACZKj8bAAAgAElEQVR4nO29d1hUV/f+fQ8zAwPSexUroqKC3QRFjQVNjKZqEitiT1GTJz5PzFdj1FiiMdFERaPR2BJNUaNi7JrYFcTeUZAmHYY2zMx+//DHvByBOXsKILI+1zWX15mz77XXHoc155y99l4SxhgDQRAEYTQWte0AQRBEXYcCKUEQhInIatsBU1AqlUhOTkZxcbHedhYWFnB3d4erqyssLOi3gyDKk52djcTERNF21tbWcHJygquraw14Vbeo04F08+bNmDVrFtLT0/W2k8lkCAsLw/bt2+Hs7FxD3hFE3eDLL7/Et99+K9rO09MToaGh2LFjRw14Vbeo04H05s2byMrKQufOnREUFFRpm/z8fBw7dgyHDx9GSUlJDXtIEM8+169fh1QqxQsvvIDmzZtX2iY7OxvHjh3DyZMna9i7ukGdDqQAIJfL8fbbb2PatGmVno+Pj8d7770netVKEPUVCwsLWFpaYtSoURgzZkylba5evYr33nsPmZmZNexd3aDOB1IAkEgkVT77tLCwgEQiqWGPCKLuIfZ3RFQNfToEQRAmQoGUIAjCRCiQEgRBmAgFUoIgCBOhQEoQBGEiFEgJgiBMhAIpQRCEiVAgJQiCMBEKpARBECZCgZQgCMJEKJASBEGYCAVSgiAIE6FAShAEYSIUSAmCIEyEAilBEISJUCAlCIIwEQqkBEEQJkKBlCAIwkQokBIEQZgIBVKCIAgToUBKEARhIhRICYIgTOS5KMesD61WC61WCwDYv38/nJycatkjgni2SEtLq20X6jzPfSDVaDS6QDp9+nSqz00QT5Gfnw+Z7LkPBdVKtX966enpiI6ORlFREbfGxsYG4eHhcHNzM7l/iUQCiUQCAPD09IRcLjfZJkE8Tzx48ABqtbq23ajTVHsgTUhIwIwZM5Camsqt8fHxQcuWLc0SSGUyGaRSKQDgyJEj8PLyMtkmQTxPDBgwAMePH69tN+o0dJ9LEARhItV+RdqqVSscOXKkwq3DDz/8gKioKEyYMAFTpkwRnJPL5WjYsGF1u0YQBGEWqj2QWltbo2XLloL3YmJisGXLFgDA5s2bERkZiY4dO1a3KwRBENVCjd/aJyUlYfz48VAqlQCAgoICTJo0CY8ePappVwiCIMxCjQbS0tJSLF++HJcuXRK8f+nSJXz//fdQqVQ16Q5BEIRZqNFAeuLECfzyyy/QaDSC99VqNbZt24Z///23Jt0hCIIwCzWWhZuZmYmVK1ciISGh0vMJCQn44YcfEBwcDGdn55pyqwJnzpwRrPTo2bMnHBwc9GrS0tJw5swZ3bG/vz+Cg4NF+9q1a5fgePDgwaKaU6dOIT09XXfcu3dv2NnZieri4uLw4MED3XGXLl3g6empV5OXl4ejR4/qjt3d3dGtWzfRvowZV2xsrOC70a1bN7i7u+vV5OTkCNJ2vLy80LlzZ9G+SktLsW/fPt2xvb09evXqJaqLjo4W3DXxjOvmzZu4deuW7jg4OBj+/v56NSUlJdi/f7/u2NHREWFhYaJ97d27VzCpy+NfYWEh3QmaA1ZDfPvtt0yhUDAAVb6srKzYsmXLuG1+9NFHTKFQsKVLl1bZ5v79+6xr164MAEtOTha1OXDgQIFPsbGxopo9e/YINOPGjePy/+nx89CnTx+B5vr161y6iRMnCnS7d+8W1cTFxQk04eHhXH0ZM64xY8YINPv37xfVnDt3TqAZPHgwV19ZWVkCXevWrbl0rq6uBo9r1qxZAs3atWtFNampqQJN+/btufqys7Mz2L+rV6+ywMBAZmVlxb777rsq2125coUFBQUxLy8vLrv1jRq5tb969SpmzZqF4uJive1KSkowe/ZsXL58uSbcIoh6T9lKP7VajejoaJw/f163pJowgOqO1CqVig0dOpT5+PgIXo6OjgwAc3R0rHBu2LBhrKSkRNR2dVyREkR9Izw8nFlbW7N169ZV2YauSPVTI89IlyxZUmGCaevWrfjss8/w6aef4t133xWck8lkuvXxBEEQzzrVHkjlcjl8fX0rvO/i4gIAcHZ2Fn34ThAE8SxDa+0JgiBMhAIpQRCEiVAgJQiCMBEKpARBECZCgdQARowYodtxX99r/PjxXPZ4bEkkEq6aOj/++COXrRYtWojaGj16NJetsWPHmnWcycnJeu0kJydz2+Jh7NixXLZGjx4taqtFixZctn788UdRW2lpaWYbp0qlwqlTp3Dz5k0olUoUFxejtLQUjDGuz4jggwq1EMRzTHFxMb755hv8/vvv8PLyQuvWrREUFISgoCD4+fnB3d0dhYWFte1mnadeBdL79+8jPz+/0nPu7u5wdHTUq4+IiED37t1F+wkMDOTyJyoqiqudvb29aJvQ0FAue2L7BgBPrkhfeOEF0XY8V7cA/zjFPn9HR0duWzyMHDkSXbp0EW0XEBAg2ubLL79Ebm6uaLvQ0FDRNvb29mYbp0KhQGRkJHr37i14v6SkBBkZGbC0tKR6TWagXgVSHx+fKjfq4CmK16tXL67NLXjhfQTAQ2BgIHcAF6Nnz57o2bOnWWwB5hunjY2NWT+zsLAwrs1AeBg6dKhZ7ABPNkM31zgtLS3Rv39/vW14fqgJ/dSrQGplZQWFQlHbbhBEjUKrBKsfmmwiCIIwEQqkBEEQJkKBlCAIwkQokBIEQZgIBVKCqMdQYr55qFez9jx89NFHOHnypO5469atonmE//77L6ZOnao7HjJkCD7//HPRvjp27Cg4vnDhgqhm8uTJOHfunO54x44daNy4sahuwYIF+P3333XHy5YtE82JvXPnDt555x3dcbdu3bBixQrRvowZ15w5c/DXX3/pjlesWCFaH+r69esYOXKk7jgsLAxLly4V7SsvL0+QV9mkSRNs375dVNenTx/k5OTojnnGtXr1asFqps8//xxDhgzRq8nKykK/fv10x4GBgdi8ebNoXz169BAk1/P4d+vWLSQlJYm2I/RDgfQp7t69i4sXL+qOeVZ95ObmCjTt27fn6qu8hpc7d+4IdGLlW8pISEgQ6MoHhKooKioSaNzc3Lj6MmZcDx8+FOjy8vJENQUFBQJNZfveVoZGozHqM4yLi0NGRgZX2zJSUlIEffHoS0tLBRreq8ZLly5VueCkKoqLi6FUKqFSqfDvv/9iyJAhtVp8sq5CgfQpwsLCBKt/nJycRDXe3t6CK7dOnTpx9VVew0uvXr0EAY03mbpjx46C/nx8fEQ1jo6OAk3btm25+jJmXF26dBEENC8vL1GNi4uLoK8OHTpw9WVpaSnQ8Qbg119/3eBA1aZNG0FfTZs2FdUoFAqBplGjRlx9vfnmm9w/CmU0a9YMfn5+SE5OhoeHB5RKJZycnCj31FBqq8ZJVFQUA8BWr15ttA2q2UQQpkM1m0yHJpsIgiBMhAIpQRCEiVAgJQiCMBEKpARBECZCgZQgCMJETE5/Ki0tRVJSEu7du4cOHTqIbs5bl7l69SpSUlJE2/n4+KBVq1ai7Q4ePMjVb1hYGCwtLfW2SUpKwvXr10Vt2djY4MUXX9Tb5tq1a6JlPwDzj7NHjx6wsrKq8nxJSQlOnDjBZatv376iba5fv86VjO7t7Y3WrVvrbXPy5EmunONWrVqJpp6pVCocP35c1BYgPk6NRoPExERotVo4OzvD3t4eFhZ0/WRuTAqkV65cwa5du3Dw4EGcO3cOR44cEV2NUpdZtGgR1wqTcePGYc2aNaLtyq9e0Udqaio8PDz0tomOjsa4ceNEbQUEBODWrVt623z99dfYuHGjqK2IiAisW7dOtB3vOJOSkuDt7V3l+czMTG5bjCOJfenSpVi/fr1ou1GjRmHDhg1620REROD27duittauXYvIyEi9bbKzs802zsLCQixduhSxsbHw9/eHv78/mjZtiqZNm6JZs2Zc+bqEOCYFUkdHRzRu3Bi3b982OBG4NoiLi6vySqthw4aiK3fmz5+PTz75RLQfFxcXLn927twpulyQIExBKpXC1dUVVlZWSE1NRXp6Oq5fvw5bW1vY2dnB29ubloiaAZMCqZ+fHzp27Ag/Pz+kpqaay6dqo127dib9Ajds2BANGzY0mz+DBw8226YRkZGRolc6vGzYsEH0CswQzDVGb29vs26ysW7dOq4rah7ErvINwcPDw2zjtLGxwezZs/W2OXXqFO7evWuW/uor9LCEIAjCRCiQEgRBmEi1BVKlUonExERoNJrq6oIgCOKZwKyBVK1W4+LFi4iMjISPjw+aNGmCAQMG4M6dO+bshiCIakStViMvLw/5+fl0IcSJWbfRO3nyJC5dugQfHx/MnDkTBw4cwJEjRzBjxgz89ttvlL9GEM8wRUVF2L9/P86cOYNHjx7BxsYGbm5u6NOnD2xtbWvbPSQnJyMmJgalpaW695ydnREaGgqpVArgSQrdpUuXoFKpIJPJ0Lt3bzRo0KDafTNrIL148SI+/fRTtG3bFpaWlggLC8O4ceOwZ88exMbGcu8XSRBEzaLRaPDLL78gPj4eycnJkEgkkEqlUKvV2LhxIwYPHgytVlurPioUCiQmJmL+/PlQqVRo3bo15s2bJ9g71dbWFlKpFPPnz8eECRMgk9XMlstmvUT84IMP0KlTJ1hZWUEikaBly5Zo1aoVSktLzZoeUp28/PLLkEgkutelS5eqbMsYQ0pKCqKiojBx4kQMGTIEs2bNwpUrV7huiW7duiXoi4e+ffsKNDdu3ODSTZo0SaArX9ajKi5fvizQDBgwgKuv8hrecUVERAg0f//9t6jm/PnzAg1vTm52drZAFxQUxKVzc3MzeFyzZ88WaMqXHamKtLQ0gYb3AsTe3t5g/zIyMlBYWKjbIT8pKQmMMWi1WpSWloIxhnv37iEqKoprVV9VPHjwAG+++SbCw8PRv39/3Wv48OE4f/48V7qXs7MzJk2ahC5duiA9PR1yuRyNGjUS3Ok6ODigadOmaNGiBQYNGqR3pZw5MWsglcvlgmOFQqG7rL569ao5u6p1srKy8M0332Dw4MH4559/YGlpiezsbCxfvhydO3fG0KFDcf/+/dp2kyD0kpCQgIcPH4q2KygoQHZ2ttH9NGrUCF9//TVsbGxw5swZHDhwAAcOHMCWLVswcOBALFy4EPHx8VwB9T//+Q/kcjnOnz9f6QXahQsXEBoaCk9PT6P9NZQaKzVS/rnGs8z48eMF65crWxddWlqKrVu3YsuWLVi/fj3atm0LCwsLpKSk4K+//sK8efPw+++/Q6lUYseOHbCzs6u0L3d3dyxbtswg/yZNmoSXX35Zdyy2dLSMt956Cy1atNAdi60dB54kwJf3j7fkhaFjAp6UJylfyiQwMFBU07BhQ0FfPGU8gCdJ6uV1vCvR5s2bh6KiIq62ZYSHhwvK1XTt2lVUY2dnJ/DP3d2dq6+FCxdCpVIZ5J+vry+cnJy4gqmpNG7cGFFRUdi4cSOWLVumW2WYkZGBmTNn4tChQ5g8eTIGDhwIa2vrKu106tQJXbp0wb///ovffvtNUMiwuLgYO3bsMOo7aApUs+kpBg8eLNomMTERUVFR6NatG4KDg3Xve3l5YcyYMVCr1ZgxYwYOHjyIzZs3Y9KkSZXacXJyElQf5eH11183qH0ZvXv3FnzheHB1dTXYPwBGafr27cu10Uh5PDw8jOrLysrKKN2ECRMM1nTr1s3g/SdsbGyM8m/y5MkGa9zd3bkmkiwsLHSPC7KysvCf//wHBQUFBvcHPNl8xt3dHdnZ2bofJsYYjh49iri4OAwbNgxff/11lcFUKpViwoQJOHnyJLZu3Yr58+frfqz27NmDZs2amXUFIg8USI3g6tWruHr1KsaMGVPhnFwux1tvvYWdO3fi4MGD+OWXXxAZGVnhsQdBPCvwZNOUn2gqLi7Gvn37kJuba3SfWq22wtUzYwyZmZnYsGEDJBIJli9fXuWz3m7duqFt27aIi4vDDz/8gM8//xwlJSVYuXIl1q1bV6mOMYaCggLEx8fD3t4e/v7+Rvv/NBRIjeDatWsAIKg2Wh43NzeEh4fj2LFjyMjIwKNHj7hqzxNEbSC2RSMAQWBycHDAnDlzUFJSYlR/aWlp+Pvvv3H58mVBMJXJZAgJCcHkyZMxcuRIvRNm3t7e6NevH65du4Y1a9Zg4sSJuHjxIoKCgir9W9NoNHj48CHWrVuHVatWYdmyZRg1apRR/lcGBVIj4HmeFBoaCrlcDpVKxVWjnSBqi7IUIYlEUuVkT4MGDXQBt0GDBhg/frxRfd24cQNz587FjRs3BEHU0tISU6ZMwdixYxEYGCh6lWxtbY0+ffpgy5YtSE1NxW+//YZ79+5VWQpcIpHAysoKgYGByMnJMcp3fVRrhnxpaanBD7/rAjy/xGW38tbW1qLb8xFEbWNpaYlOnTrBxsYGwJPAUxZgFQoF/vOf/5i8d+k///yD8PBw/Prrr4Lnqy1atMDBgwexcOFCtG7dWpdcL0ZoaCgCAgJQWlqKRYsWobCwUDChWh4LCwv4+PggPDy8WhYGmXRFmpmZiTNnziA1NRUKhQLXrl1Do0aN4O7uDpVKhZiYGNy7dw8KhQKpqamIj4+Ht7d3jeV2VTf6Aurt27eh0Wjg6+vLPetKELWFVCrF2LFj4eXlhR07duDBgwdwdXWFu7s7PvjgAzDGsGPHDqPtJycn48SJE4iIiBC87+TkhCFDhhg1OWRjY4NRo0bh2LFjSE5ORsuWLat83FZGda2uNCmQJiYmoqioCNOnTwfw5Ar09u3bcHJyglKpRHJyMoYNG4a3334bEokEsbGxcHBweG4CaXx8fKXvl5aW4vTp05DL5fj4449rbHUFQTwNYwwajQZSqVQ0SV8mk2HQoEEYNGgQ1Gq17j3A9Dxwb29vzJw50yQblTFkyBB88cUXsLW1xYsvvsh9NWtuTPoLDw4OFqT/lEehUGDo0KGmmH/miYmJQWFhoe52qIyzZ88iOjoa//3vf9GzZ88q9YmJiRg+fLhoPzt37hTkIlbG3r17sXjxYlFbvr6+2LJli942X331FdfKooEDB2LGjBmi7cLCwkTbAMDvv/8OV1fXKs9nZGTgjTfe4LLFU/No0aJF2Ldvn2i7/v3747PPPtPb5r333sOjR49EbX366aeCPODKyM7O5l6lJTbOwsJCLFq0CPHx8QgJCUH79u3Rrl070e9TXfnxd3R0xNSpUxEXF8dVP6y6qBuflpkoW/pWGYYsqyvj2LFjeP311/HNN9+gadOmkEgk2LdvHxYtWoR33nkHM2bM0PsLWVhYyFXMjec5c0pKCpetgIAA0Ta3b9/mstWsWTPRNgC4C9aJjVOlUnHb4oF3nDwZFxcuXOCq2TRixAjRNuYcp0ajwe3bt/Hnn39i+/btAJ7c3rZs2RJhYWEICwuDUqk0S1+1xZQpU5CSklKrd7r1KpDeunULWVlZlZ7z9vaGs7OzQfYiIyPx8OFDTJgwAa6urrCxsYFGo8HMmTPRr18/0V91W1tbvPrqq6L98HxB/P39uWzpKy5XRnBwMNdywKruRp6Gxy/gyV2M2HleWzwEBwdz2eMZZ+/evblWY/HkLlpZWZltnA0aNMC8efN0j98qo65vlSeXy2s8Af9p6lUgDQwMNGvVxM6dO2Px4sXIyMhAXl4e7Ozs4O/vz5187+Pjg127dpnFF2NWBlXF1KlTjVpZUxXmGqOzs7PZbAFPNtn54IMPzGJr1apVZrEDPLldNdc4pVKp6J2D2AQNIU69CqTVgYODA30RCaKeQzstG0HZc1ZHR8da9oQgCEMwZxXa8lAgNYKEhATIZDLuXYMIgqh9srKycPbsWchkMsTHx5t1xyu6tTcQxhgePnwIa2tr2oiEIOoQMpkM/v7+2LFjB1xdXbn2GOC2bTZL9YgdO3ZALpdzp/8QBFH72NvbIygoiLsigiFQIH2KGzduCFJ/2rVrJyieVVnph+zsbEHJDw8PD65Nhk+dOiU4fuGFF0Q1169fF2y6EBISoncT3DLu37+P1NRU3XHLli1Fk7ILCwsFpVYcHR25kp6NGdfdu3fx+PFj3XGrVq1En0ErlUpcvnxZd+zs7MyVgqRWq3Hu3DndsY2NDVeK0/nz5wUblPOMKzExEYmJibrjpk2bim7GXVpaivPnz+uObW1tBZteV8XZs2cFqUw8/hUXF9eZTdefaVgtERUVxQCw1atXG23jo48+YgqFgi1durTKNvfv32ddu3ZlAFhycrKozYEDBzIAuldsbKyoZs+ePQLNuHHjuPwvr+H9r+jTp49Ac/36dS7dxIkTBbrdu3eLauLi4gSa8PBwrr6MGdeYMWMEmv3794tqzp07J9AMHjyYq6+srCyBrnXr1lw6V1dXg8c1a9YsgWbt2rWimtTUVIGmffv2XH3Z2dkZ7N+VK1dYYGAgs7KyYt988w3TarVVtgsKCmJeXl5cdusbNNlEEPUYa2trSKVSaDQanDx5EpcvX662me3nGbq1f4q9e/carHn55ZeN+vIZozl48KDBGuBJwrihSeNt27atsXGtX78e69evN0jTqVMno/pycnIySpeenm6wZs6cOZgzZ45BGg8PD6P8M2bf26ZNm8LPzw/379/HwIED0a5dO4NtEJT+RBAEYTIUSAmCIEyEAilBEISJUCAlCIIwEQqkBEEQJkKBlCAIwkQokBrAmDFjoFAoRF+TJ0/mssdjS6FQCFb8VMVPP/3EZatNmzaitiIjI7lsTZgwwazjTElJ0WsnJSWF2xYPEyZM4LIVGRkpaqtNmzZctn766SdRW48fPzbbOEtKSnDw4EGcPXuWVjBVI/UqjzQvL6/K5ZQ2Njaimxio1WquUsxlhcPE4LEF8OVlajQaLns8ZUue1XEyxrht8WDOcapUKi5bPLvRm3OcJSUlWLduHf744w/Y2NigTZs2CAkJQUhICAIDA+Hi4oLi4mKz9FWfqVeBND8/v8pAKpVKRQPpW2+9xbWWOyQkhMufefPmcbWztbUVbdOxY0cuezxb/73xxhto3ry5aDve5G3ecdrb24ue57XFw2uvvYYmTZqItuNZ5z5t2jRkZmaKtuvYsaNoG1tbW7ONU6FQYPjw4ejSpYvg/ZycHMTFxcHPz48CqTmonZWpz+5ae4Kob4SHhzNra2u2bt26KtvQWnv90DNSgiAIE6FAShAEYSIUSAmCIEyEAilBEISJUCAlCIIwEQqkBFGP0Wg0tJGzGahXeaQ8zJo1CxcuXNAdf//996K5hufPn8fs2bN1x+Hh4fjwww9F+xo4cKDgeN++faKazz77TFBHKSoqCn5+fqK677//XmB/9uzZFXILnyY+Ph5TpkzRHXfo0AFz584V7cuYcS1btkywafXcuXMr1MZ6mtu3b2Pq1Km6465du2LWrFmifSmVSrz99tu644YNG2L16tWiumHDhgk2T+YZ16ZNm7Bt2zbd8UcffYT+/fvr1eTk5ODdd9/VHTdt2hQrVqwQ7euNN95AUVGRQf7du3cPycnJou0I/VR7IM3Pz0evXr0QGxsreL/sV3DSpEkVllR26NABhw4dEk3Qrg4uXryI6Oho3THPruOPHz8WaHx9fbn6Kq/h5fz58zh06JDuWKlUcumuXbsm6G/SpEmimvz8fIGG98rFmHFduXJFoPvoo49ENbm5uQINb3nd0tJSga5169ZcusOHDyMjI4OrbRl3794V9PX666+LakpKSgSa9u3bc/V18OBB5OfnG+SfUqlEXl4eSkpK8NdffyE8PBze3t4G2SBqIJDa2dnhu+++w6BBgwTVOctgjAn+QB0dHbF06dJaCaIAEBwcLFhGaWdnJ6pxdXVFnz59dMctW7bk6qu8hpenV02Vr3Cqj8DAQEF/bm5uohpbW1uBhqfSJmDcuFq1aiXQ8azAsre3F2h4V1rJ5XKBzt/fn0vXo0cPg8t5NGnSRNCXj4+PqMbS0lKg4S373bNnT8EVKQ8tW7ZE48aNkZqaiuDgYN3fo0QiMchOvaemMv8XLFjAZDJZhQqT5V9SqZR99dVX3DZpZRNBmA6tbDKdGptsioiIQN++ffW26devH9dOOwRBEM8SNRZI3d3d8f7778PT07PS856envjggw+4bjkJgiCeJWo0/alnz54YOnQoLCyE3UqlUgwdOhRhYWE16Q5BEIRZqNFAamNjg2nTpiEgIEDwfosWLTB16lTY2NjUpDsEQRBmocYT8v39/bFu3TpIpdInDlhYYM2aNWjUqFFNu0IQBGEWqj396cGDB/jll19QUFAgeD8oKAhxcXEICgrC/v37sX//ft05W1tbvP3222jcuLFZfYmJiYFWqzWrTYKo6zx+/BgajQaXLl1CQkICGjZsWNsu1TmqPZBevHgRixYtQk5OTqXnL1++jMuXLwvec3JyQtOmTc0eSJcuXYqjR4+a1SZBPC+sWLECbdq0QWRkJOWRGki1B1Jm5DpeY3X66NChQ5WPEFxcXEST73///fcKQb+qfl599VXRduWXlerj008/FU28j4mJwa5du0Rtubi4iC5f/fPPPwXLUKsiJCQEQ4YMEW3HO85PPvlE7/9Bfn4+lixZwmVrzpw5om127txZYcVdZQQHB+O1117T22b58uVcpUYGDx4sulKpoKAAixcvFrUFiI9TrVbj8uXLSE1NrfS8TCbDrVu3kJOTg5dffll0WS5RORJWHRGrHImJiVi7dm2FpWvHjx9HbGwsgoOD0bNnT8E5BwcHREREiN5iTJ06FVFRUZg/fz6mT59eaZv4+Hi8++67OHPmDJKTk+Hl5WXagAjiOWPAgAE4fvw4vv/+e0RERFTa5urVq3jnnXeQmZlJa/MrodqvSP38/PDll18K3jtw4ABWrVoFALh+/ToWLFiA8PDw6naFIAiiWqjxWfu7d+/iww8/1JWbValUmD59Ou7cuVPTrhAEQZiFGg2kxcXFWLJkSYWgeevWLXzzzTdUFpYgiDpJjQVSxhj+/vtv7Ny5swJNSMMAACAASURBVEIKklarxZ9//omDBw/SJrMEQdQ5aiyQpqWl4fvvv0daWlqV55cvX47Hjx/XlEsEQRBmocYC6apVq3D8+HG9bY4dO4YffvihhjwiCIIwDzUSSE+fPo2FCxeitLRUbzu1Wo1Fixbh5MmTNeFWpQwdOhQuLi6619WrV0U1Bw8eFGjKl7/QR3kNz0bGwJMd1strbt++zaX7+OOPBbq///5bVHPt2jWBpnx5Dn0YM64PPvhAoDly5IioJjY2VqAZPnw4V185OTkC3Ysvvsila968ucHjWrhwoUCzadMmUU16erpA06tXL66+/P39DfYvLS3N4F31iYpUe/pTSUkJVq9ejRYtWgjez8rKQlJSEnx8fODs7Cw4t3btWnTs2BFWVlbV7V4FlEolsrKydMdqtVpUo1KpBJrCwkKuvspreMnPzxfoNBoNl66wsFCgK18FoCo0Go1Aw/sHZ8y4CgoKBDqxH13gyf9NeQ1v2RXGmECXm5vLpcvJyTF4bEVFRQJNWbaKPrRarUDDuyt/dna2wUExOTkZSUlJ0Gg0ePjwIfLz87mqQhBCqj2QymQyfPfddxUmmDZu3Ijp06fj448/xqhRowTnLCwsIJPVTl2+oUOHCsp5eHh4iGqaNWuGmTNn6o47duzI1Vd5DS/vvvuuoGidq6srly48PFxwldK8eXNRjbu7u8BHHg1g3LheeeUVQa0gsYKDAODt7S3oKzAwkKsvhUIh0Lm7u3Pppk2bxv0jWUaPHj0EffGUa2nQoIFAw7uI5JNPPuH6gSyPt7c33NzckJSUhNTUVGRmZsLW1paWiBpKbW3NHxUVxQCw1atXG22DSo0QhOlQqRHTobr2BEEQJkKBlCAIwkQokBIEQZgIBVKCIAgToUBKEARhIrWTY1RHOXr0KNcuVYGBgejRo4douzVr1nD1O2LECFhbW+ttc/PmTZw4cULUloODA4YOHaq3zbFjx7gS/Vu0aMFV+ZV3nMOHD9dbALGwsBCbN2/msjV+/HjRNsePH8etW7dE2wUEBFTYM/dpfv31V6581B49eoimaRUVFXEl7gPi42SMoaioCAqFokL1XsKM1Fa6QF1Mfxo+fDgDIPoaN24clz0eWwBYamqqqK21a9dy2QoICBC1NWrUKC5bERERZh1nUlKSXjtJSUnctniIiIjgsjVq1ChRWwEBAVy21q5dK2orNTXVbONUKpVs7ty5bPjw4eyrr75iu3fvZvfv3xe0ofQn06ErUoJ4jikravfHH39AKpXqXi4uLggNDUVYWJhRK9EIIfUqkF69erXK2jV+fn6iq4Q2bdrEfcvFAzPjloGRkZGIjIw0i60NGzZgw4YNZrEFmG+c3t7eZv3M1q1bh3Xr1pnFFs8jAl48PDzMNk5bW1usWLECCxYsqLLNli1bzNJXfaZeBdKgoCCq2UTUKywsLES/82KFFQlx6OkzQRCEiVAgJQiCMBEKpARBECZCgZQgCMJEKJASBEGYSL2atechOTkZBQUFuuOGDRuK7tRfUFCA5ORk3bGDgwPXZsFPr5Li2Tg5KSlJsLmwv78/LC0tRXWPHz8WrLzx9vYWna0tKSlBQkKC7rhBgwaCzZerwphxpaWlCXaC9/Hx0bvKCXhS3jsxMVF3bGtry5WVodVqce/ePd2xpaUl/P39RXX3798XVCTgGVdmZqYgT9PDwwP29vZ6NRqNBvfv39cdW1lZoWHDhqJ93bt3T7CBOo9/KpWKqwoEIUJtrQR4Vlc2DRw4ULByJDY2VlSzZ88es6xs4qFPnz4CzfXr17l0EydOFOh2794tqomLixNowsPDufoyZlxjxowRaPbv3y+qOXfunEAzePBgrr6ysrIEutatW3PpXF1dDR7XrFmzTF7Z1L59e66+7OzsDPYvLi6OBQQEMCsrK/b1118ztVpdabtnYWVTcnIy27x5M1u5ciVbuXIlW7NmDTt+/LjA55SUFLZnzx62atUqtn37dlZQUFAjvtEVqRno2LEjdu3apTvmuboBgJUrV2Ly5MnV5RZBiGJvbw8rKytoNBpcvnwZZ8+eRW5uLu7cuQNra2s0btyYaz8FMR4/fowTJ05UKDnk4OCAzp07w8nJSdSGpaUlpFIpPvvsM+Tm5qJz585YtGiRoCyKlZUVGGNYtWoVPvroI0ilUpN956JGwnUlPKtXpCUlJayoqEj30mq1RvsnhlarFfTFg7H+qVQqgU6j0RjsX0lJCVdf5TW84zLGP41GY5R/T4+ruLiYS1dcXGzwuEpLSwWaqq749PlXnZ+7Vqtl4eHhTKFQsIkTJ7Lg4GAml8uZlZUVc3R0ZHK5nIWGhrLDhw+bdEWq0WjYunXrWIMGDZhMJtO95HI569OnD3v06BG3v9OnT2cA2AsvvMDi4+MrtLlx4wYbPXo0y83NNcpXY6Ar0qco/7yxoKAACQkJyMvLg7W1NZydneHk5GS2wmASiQQKhcJo/wxBLpdDLpcbpDHGPwBGaYzxz8LCwqi+jB2XMVVtZTKZwYUca/JzL/sul5SU4OeffxY8fy+rePrvv/9i9OjRBtsuj4WFBSIiItCkSRN8/vnnOHfunK5S7KFDh9CuXTvMnTsXr732Gjw8PKr8G5NIJIiIiMCqVatw8eJFXL58GY0aNRK0OXz4MPr16yf6LNqcUCCtgkuXLuGnn37CpUuX8OjRIzg5OaFZs2bo1asX3nvvPdja2ta2iwRhFhhjYIzprZCanJwMiUQCNzc3FBcX48SJE1wlsyvr6/XXX4dKpUJsbKxuoiszMxPTp0/HoUOHMGXKFPTu3btKG61bt0a/fv2wa9cubNq0Ca+++qruXHZ2Nv7++2+z7aHACwXSSrh+/TreeecdJCQkoFWrVmCM4eLFi7h48SL27t2La9euYcmSJUZfHRLEswRPCefy2Qo5OTl4//33BVkWxvT59PPS4uJi7Ny5E2fPnsXkyZPxv//9r8or08jISERHR2Pv3r24f/++rnz31q1bERoaCjc3N6N9Mwaz5JGWlpYiPz9f8GHXVbRaLcaNGwc7Ozvs3LkTp0+fxt27d7F79240adIESqUS27Ztw969e2vbVYIwC4ZeWUokEjg6OsLBwcGol52dHaysrCp95CGTydCqVSuMHTtW7yO0du3aoUuXLigqKsLSpUvBGINSqcTPP/+MCRMmVGivUqlw6NAhTJgwAe+//z727duH4uJig8atD5OuSDMzMxETE4ODBw9i586d2Lp1Kzp27Ggu32qFS5cuoaSkBPv27RPkgvbv3x/Lli3DxIkTkZKSgoMHD2LAgAFGPZciiGcJnmf+5dt4eHjg3LlzRvVVUFCA6OhofPHFFxW2tAwMDERkZCTGjh0LR0dHvXY8PT3Rt29fnD17Ftu2bcOMGTNw6tQpDBw4EA4ODhX6jIqKwq5du2Bra4vU1FRs2rQJI0aMwBdffCG6fSYPJl2RJiQk4J9//kFUVBTu3Llj1DOTZw2NRoM1a9ZUSKi3tLTEoEGDMHz4cABAYmIicnJyasNFgjArPI+oyp6jmkJOTg7mzJmDDz/8ENeuXdO9r1AoMGbMGGzYsAEffvihaBAFnkxO9unTB97e3sjLy8O6detw9uxZvPbaaxXa3r17F8XFxVi5ciW2bduGn376Cd26dcPq1auxatUqk8ZUhklXpEFBQZDJZNizZw9iY2PN4lBtExISUmXumUQiQb9+/fD1119DrVZXeMZTGUqlEqWlpXB0dKzwy3/v3j3RWkAAEBsbK/qruW3bNnz66aeitpo0aYLjx4/rbTNt2jT89ttvoraGDh2KJUuWiLbz8/MTbQMAFy5cgIeHR5Xn09LSuO94yq94qopPPvkEv/76q2i7N998E8uWLdPbJiwsTLAaqSoWL16Md955R2+bjIwMhISEiNoCxMdZXFyM/fv3QyaToUuXLpU+O+TJlpDJZCblZCYmJmLKlCm4ceMG5HK5bqWWi4sLPv74YwwePNjgCdyOHTsiODgYDx48wMqVKzFs2LAKM/gAoFarERkZqbs4atOmDb788kucO3cO+/fvx//93/8ZPa4yTAqkcrkclpaWBqd31BZFRUVVzkyWjUNsLBkZGZDJZGjbtm2lwa0ssfnHH3/EhQsXkJiYiOzsbHh5eeGtt95CREQEmjZtCplMBrVajUePHon6zfPsuaCggMuW2LJL4MnMJ4+t7Oxs0TYAuGwB4uPUaDTctngw5zhTU1O5bJVfflwV5hynSqXC9u3b8eeff0IqlaJJkybo3LkzOnfujA4dOsDLywulpaWQSqVwd3dHZmYmVCoVJBIJJBIJtFotFAoFQkJCkJ6ezuV/Zfj5+WH37t1mGVMZcrkcERER2LVrFwoLC9GxY0fY2dlVaNehQwfBsUQiQdu2baFQKMy20XvdiIBmIi0trcrbE1dX1wrPVirj0KFD8PT0xCuvvFLpLdHhw4exZMkSdO/eHcuWLYNGo8Hhw4exZcsWLF68GHv37sWKFSsQFhYGJycnTJ06VbRPnuAXFBTEZYtnNrNfv35cK006d+4s2gYAl1+A+E7tDRo04LbFQ58+fbhyDTt16iTaZtSoUUhPTxdtFxQUJNrGxsbGbONUKBQYNmwY2rdvL3g/Ly8PJ06cgJeXF/Ly8nRBqaSkBGfOnEFGRgZsbGxga2uLfv36ISwsDJMmTTI6kFYXffv2RZs2bSCXy9G1a1fuHO/bt29Dq9WanB+rw9SM/ps3b7JOnToxAOzUqVPcumd1ZZM+EhISmJ+fH5s0aVKlK0cyMzNZ69at2cSJEwVrfIuLi9mJEyeYp6cns7CwYK+88grLysoyyReCMBflq4gqlUp27949FhMTwy5fvszu37/P1Gr1M7HWviq2b9/Opk6dykpLS7k1q1evZqNHj+Ze1SaG2bfRKy4uxk8//YSWLVvCxcUFs2bNeuZ+xYxl48aNyMzMxP/+979KZ+u//fZb3Lt3D82bNxdcRVpZWaF79+7YtGkTGGPYu3cvrly5UpOuEwQXDRo0QJMmTRASEoI2bdqgcePGNbde3UjefPNNLF26lPsRY3JyMs6dO4c5c+YYtVqtMswaSO/fv4/JkydjzZo1um3a5s2bh4ULF5qzm1rhypUrOHHiBDZs2FDp5AljDCdPnoSlpWWVkyuhoaHo27cvGGPYs2dPdbtMEPUCiUQCCwu+UFZaWorjx49j6NCh8PX1NZsPZg2kO3fuRLdu3fD7778jOjoaixYtgo+PD1asWIGHDx+as6saJT8/Hz///DPCw8MxePDgStuUn+yp6hfc0tISr732GiwsLBATE1Nt/hIEUTl///03PDw80LNnT+7gy4NZA+mgQYMwatQoeHt7w9LSEi+99BKCg4ORm5tbp9OjoqKiYGVlhbFjx1aZc5efny+aR2thYQFfX19YWVnR8lKCqGEOHz4MAOjevbvu70+lUiEzM9Nk22YNpM2bNxcECEdHR13u1qVLl8zZVY1QNuN++/ZtzJ49W++sPiuXDcD0JC4rlUqUlJQgODjYrL4SBFE5arUaR48eRWFhIZo3b4779+/j1q1buHbtGubPn49Tp06Z3EeNpT/VlQmno0ePIikpCcCTdKm0tDQsX768QtKyRqNBQkICGjduXOH9qvIO1Wo1rl69CgcHB/Tr1w95eXmC3LqyVVP6OHz4MFJSUnTHgwYN4krbOnfuHG7fvq077tmzp+gzopycHMGzXG9vb7278pSxefNmwTHPuE6fPi0o//HSSy+J5vhlZmYiOjpad+zn58e1CXFZbmUZjo6OeOWVV0R1v/32m2B9Ns+44uLiBBOLXbt2RbNmzfRqiouLBQsinJ2dMXDgQNG+fv31V8FdEY9/vAtL6jKnTp3CnDlz8ODBgwrnWrVqhWnTppneianT/vrSn0pKSlhERAQDwD755BPBuWc1/enpUiOnT5+u0EalUrG//vqLffXVV7r3kpKSWOPGjZmlpSWbO3dupbbT09NZcHAwmzhxIlMqlezmzZtUauT/QaVG/n9qstTInTt3WNu2bZm1tTX78ccfq2z3LKc/iXHr1i12/PjxSl9Xr141Sx/1KiHfGCZMmFAhUby4uBgPHjxAVFRUhfalpaWIjo7G22+/jYCAAMH7EydOhK2tLaZPny6afE4QNUFeXh5yc3NRUlKC7du3o3v37oLv7fNAQEBAtY+JAmk5GGOYPHmybgcoALrb/Kdp27ZtpeuhpVIpHj16hDfffBNvvPEGQkJC8OjRI/z111+wtbXFli1bdOuMW7RoYfBGEAcPHjRwVE9YtWqVwRs0tG3b1qiNKozRrF+/HuvXrzdI06lTJ6P6cnJyMkrHs3LpaebMmYM5c+YYpPHw8DDKP2P2B23Tpg2aN2+OtLQ0hIeHw93dHYwxs1WBqC9QIC0HYwz29vZYvny5aFsfH59K80VtbGwwffp0WFtbIzExEYcPH4avry8+++wzdOvWrc7sS0DUD+RyOWQyGSQSCRwcHLh2XiIqUq1/1Vqttk49yLawsED37t1NtuPn54fXX38djDGo1WqDaxERBFG3MDn9KSMjQ5eH9XTJgrS0NEEivjG3K3WN8qssJBIJBVGCqAeYFEiPHj2KjRs3onnz5ujfvz82bNiA7du3o6CgAImJifj5559hb2+P/v37486dO/juu+8EqTvPE8XFxdBoNJDJZBU2hSYI4vnGpFv7nj17VsjbK9vH0MbGBjNnzqygeV4fYqelpUGlUkEqlVKFUYKoZ5gUSMuCpqHnnkeKiorQqlUrWFpamm2zWIIg6gY0hWwA2dnZKCoqqvRcYGAgNm3aBICvdAPwZDsvHjw9PUU3WCgsLOSqIcXz6CEnJ0dvjfMybGxsuGZ5ecfp4eGhd8s2jUaDtLQ0Llve3t6ibcw5zsePH+tqtOvD0dFRdKNurVZboTBcVYiNkzGG3NxcaDQaWFlZ6ap31qeLnJqAAqkBfPjhhxWWP1bGuHHjsGbNGtF2Pj4+XP2mpqbqrWUEPKnnPW7cOFFbAQEBuHXrlt42U6dOxcaNG0VtRUREYN26daLteMeZlJSkNzCkpaVx2+KZ2Pz444+5cldHjRqFDRs26G3TvXt3wRLcqli7di0iIyP1tklPTzfbOPPz8/HRRx8hNjYWLVu2RMuWLdGsWTN4e3vDy8sLXl5e9WISuLqpV4H0zp07VV61eXp6cpXXIIi6hFwuR4cOHXT1sO7evYvExES4urrC09MTHh4eyMjIqGUv6z71KpA2btwYnp6elZ7j2QV81apV+Pbbb0Xb8da65/0C8wT4ESNGVFqK9ml4xvn9999j6dKlou14dxc31zg9PT3N+kf/3XffYfHixaLteMZ59uxZriKFPBORbm5uZhuntbU1Jk6cqPduhefug9BPvQqkMpnMpLxOW1tbs87Iu7i4mM1W2fMvc/CsjtPCwsKsn5k5x2nOFUHmHqfY3rfm3OC4vkKfIEEQhIk894G0bA2xm5sbzVQSRCXY29vD1dWVVuGZwHMfSOVyOQoLC5Geno78/PzadocgnjkePXqEzMxMKn9jAs99ILWzs9Pl7VW1JR5B1FcKCgqQn58PqVQKNze32nanzvLcB9IGDRroJhR4E8MJor6QnZ2tW9pszgmu+sZzH0ilUimcnZ0hkUgENYGqYvz48QgMDNS9bty4Iao5fvy4QPN///d/XL6V1wQGBnJpxowZI9DwjAkAvvjiC4Hu6NGjoppbt24JNDwJ/4Bx4/rss88Emn///VdUc+XKFYFmypQpXH3l5eUJdDz1mgCgW7duBo9r+fLlAk35WkxVkZmZKdC8/vrrXH116NDBYP/u3buH/Px8WFhY0BWpCdSL9Cc3NzdYWFhUWZSuPElJSYKVP2U75etDqVQKNLzLGMVWGFXGo0ePBLqnty6sirS0NIFOqVSKakpKSgSapwv9VYUx40pNTRXoeIolFhcXCzS8wUOj0Qh0vJtt37171+D8zszMTEFfPMt41Wq1QMNblubOnTsGzwMkJSWhqKgIGo0GN2/ehLOzM3ceNPH/Uy8CqYeHByQSCR48eACNRqM3KT08PFxQXZPndqdhw4YYP3687jg0NJTLr/IaXgYOHIgmTZrojnnzF0NDQwWbbPv7+4tqnJ2dBT62bt2aqy9jxhUWFiaYNRarcAo8+YEs31e7du24+rKyshLoeDeZGTlyJNcPUHk6dOgg6Isn2FtbWws0ZaVpxBg9ejTXD395yrZ/dHBwwK1bt+Dn54dmzZpRhouhmKWEnhHUVBVRxhg7duwYUygULCgoiN25c8fo/gjieaKkpITNmDGDyWQy9v777+ttW5eriNYEdfoZqbOzM5o3bw57e3u97V544QW4uLggKSkJZ8+erSHvCOLZJjU1FefOnYNarcbIkSP1tpVKpfD19UXz5s1ryLu6RZ0OpHK5HNevXxedjZfL5XjvvfeQk5ODs2fPVrkVHkHUJ+Lj43Hp0iUEBASgU6dOetsWFhbizp07yM3NrSHv6hZ1OpC6urpCo9GgoKBAtMjeyJEjIZVKcerUqee23AlBGMKRI0eQnZ2Nt956S7RtaWkpioqK4OzsXAOe1T3qdCAt26NTqVSKzl63bNkSbdu2xdWrV3H9+vWacI8gnlm0Wi22b98Oa2trDBw4ULR9cXExCgoKKEWqCup0IC2bvU5PTxdNl7GwsMCwYcOgUqmwYsWKOlUmmiDMzcaNG3Hz5k107twZjRo1Em2fm5uLvLw8rmyP+kidTn9q3LgxZDIZHj9+DKVSKZqq9Nprr2Hr1q04dOgQDhw4gPDwcIP6u3DhAhITE0XbNWrUCCEhIaLt/vzzT65+Bw4cKLpF3oMHDxAbGytqy9bWFn379tXb5uLFi0hISBC15e/vj/bt24u24x3ngAED9OYwFhcXIzo6mssWz96sMTExgnLhVdGwYUN06NBBb5uDBw9ypUaFhISIBq6SkhLs27dP1BYgPk6tVou8vDwoFArdZ/v48WPMnj0btra2GDZsmGj1BcYY4uPjwRgTpN4R5aitdAFzpD8xxljjxo1Zw4YNWWxsrGjbkpIStmDBAmZtbc06dOjAcnNzDepr+PDhDIDoa9y4cVz2eGwBYKmpqaK21q5dy2UrICBA1NaoUaO4bEVERJh1nElJSXrtJCUlcdviISIigsvWqFGjRG0FBARw2Vq7dq2ordTUVLONU6lUsvnz57ORI0eyL774gm3bto1NnTqVWVhYsBdffJElJiaK2tBoNGzkyJHMwsKCHTlyRLR9faROX5ECQI8ePbBp0yZcu3YNwcHBettaWlpi2LBh2Lx5M65cuYI//vgDo0ePriFPCaLm0Wg0iImJwe+//w65XA5ra2uoVCpotVrk5OTg559/xgsvvIDOnTtXWZRPq9Xi4MGD8PX1pVv7qqitCG6uK9JNmzYxiUTChg0bxq1ZtmwZk0gk7MUXX2Tnz59nFy5cYGlpaSb5QRDPIlqtlhUUFLCcnByWmprKPv/8c6ZQKFhwcDDLyMhgOTk5LCcnh+Xl5VVpY//+/QwAGzx4MMvMzKxB7+sOdXqyCQDat28Pb29vREdHcz3XA55Uv+zVqxfOnj2LFStWoHHjxqIligmiLiKRSGBjYwMHBwccOHAAUVFRcHZ2xsqVK+Hi4gIHBwc4ODjAzs6uUr1KpcL8+fMhl8vRpUuXKtvVd+p8IPXx8UGfPn2Qm5vLVbANeLIj+KpVq9C6dWts374ds2fPpll84rlm7969mDFjBoqLizFz5kx07dqVS3fy5EmcOnUKvr6+CA0NpV30q6DOB1IHBwf07dsXjo6OWLt2LdLT07l0zZs3x7x582Bra4uVK1di3rx51ewpQdQOMTExGD9+PNLS0jB06FCMGDGCe1OSDRs2QKPRoG3btujcuXM1e1p3qfbJJo1Ggzt37lTYlSYpKQkymQzJycmIi4sTnLOyskLz5s25SgcDQK9evRAUFITTp09j165diIyMFNVIJBL06dMHU6ZMwcKFC7Fs2TK4ublh5MiR3NuWEcSzDGMMMTExmDZtGlJSUtClSxd89tln3Lfnt2/fxqVLlyCXyzF69GizVal9Lqnuh7DFxcXs448/Zr6+voKXq6srUygUzNXVtcK5Tz75hBUXFxvUT9nk1ZtvvsmUSiW37vHjx2zEiBFMIpEwNzc3NmvWLFZYWGjoMAnimWPfvn2sU6dOTCKRsMDAQHb27FlurVarZT///DNzdHRkffr0YUVFRdXoad2nRmbtExMTmZ+fH1denI+PD3v48KHBfeTn57NWrVoxT09Ptnv3bqbVarm16enpbNasWUyhUDAbGxv25ptvsqysLIN9IIhnAbVazaKiopiXlxeTSCSsb9++XHnW5UlNTWUDBgxgCoWCXb58uZo8fX6osfSnXbt2MblcrjeIyuVytmvXLqP7OHPmDLO0tGShoaHs0aNHBmlVKhVbu3Ytc3d3ZwBY79692d27d1lpaSmXNjs7W/cqKCjg6rO8Jjs7m0uTn58v0KjVai5dYWGhQKdSqUQ1arVaoOG90jdmXAUFBQINz+durH9arVag05f6U56cnByDx1VUVCTQlJSUVJt/Wq2W5ebmsiVLljA7Ozsml8vZ0KFDWUpKCpe+DI1Gw+bPn88kEgn78MMPDdLWV2oskObl5bGIiAgmk8kqDaJSqZRFRESw/Px8o/tQq9Vs8uTJTCqVsgkTJhi8ckmj0bDdu3ezjh07MgsLC9a0aVM2d+5cdvHiRb23Nnv27DHLyiYe+vTpI9Bcv36dSzdx4kSBbvfu3aKauLg4gSY8PJyrL2PGNWbMGIFm//79oppz584JNIMHD+bqKysrS6Br3bo1l87V1dXgcc2aNcvklU3t27fX216j0bCHDx+ybdu2sb59+zJLS0vm4+PDZs+ebfDfk1qtZtu3b2fW1tasTZs27OrVqwbp6ys1trLJ1tYWEydOxOnTpystKNeiRQtMnDjRpIkeqVSKSZMmTHehXwAABztJREFU4eLFi1i3bh0cHBwwZ84c7ho0FhYWGDRoEJo3b47169djy5YtmDVrFrZu3Yr+/ftj+PDhCAkJgYVFnU92IJ4TMjMz8csvv+DPP//EyZMnAQD9+/fH+PHjMXDgQIO/qwcOHMD06dNhaWmJyZMn00bOnEgYY6ymOtNoNPj222/x3//+F2q1Wve+XC7HggULMHXqVO6Z+qrQarU4dOgQhg8fjqKiIsyfPx9Tpkwx2G5ZYbWvvvoK27dvh0wmg4ODAzp16oSIiAgMGDBAV+a5uLhYkHZla2sLJycn0T6e3gDFz89PVJOeno7i4mLdsaenJ1duX3Z2tmBTDVdXV1hbW+vVlJaWIjU1VXesUCi4tlEzZlxZWVmCHbzc3NxEfwBVKpWg0KC1tTVcXV1F+9JqtUhKStIdy+VyeHp6iuqSkpIE+cY84yrbNakMZ2dn0YsFjUYj2Kzc0tJSsLGIRqPBlStX8NNPP2Hnzp2670STJk2wePFivPTSS7C3tze47tKVK1cwduxYXLhwAR9++CEWLVpEM/Wc1GggBYCioiL069dPUG43NDQUBw4cEP3DNoR169Zh6tSpsLe3xw8//IDBgwcbXdDryJEjmDt3Lq5cuYKcnBxoNBp4e3vjrbfewrvvvgs3NzfI5XLI5XJYWlpCLpdDJpNRATHCaLRaLVQqFUpLS3X/FhYW4siRI9i0aRMuXrwIjUaDBg0awMfHB2PGjMHUqVONDnypqakYP348oqOj8fLLL2PHjh2UfG8ANR5IAeDGjRsIDw9HQkIC/Pz8sH//frRq1crs/Sxbtgzz5s2Dq6srFi5ciFdffdXoK97s7Gz8888/OHnyJOLi4nD16lWkpKRAIpHAw8MDLi4uuperqyscHBzoEQBhFBKJBFKpFA8ePEBGRgYyMzORmZmp2y7S1tZWt1F5ly5dEBYWhmbNmhn9fbtx4wbmzJmDP/74A6+88gpWr15NS6YNpNoDaWpqKn755ZcKezUeOHAAp0+fRrdu3dCvXz/BOTs7O7z99tvcZXKrorCwEEuWLMHXX3+NBg0aYNq0afjggw+q3OWGB61Wi5SUFDx8+BAxMTE4fvw4kpOT8fjxY6SlpenqikskEtTCbxTxHCCTyeDt7Y2EhATI5XK4u7vD3d0dHh4eCA4ORo8ePdCkSRM0bNjQpLs4xhj++ecfzJw5E6dOnULPnj3x/fffIzAwkO6mDKTaA2lMTAxeeeUVwbO2Mhhjlf6H+fj44M8//0THjh1N7l+lUmHRokX48ssvIZVKMWHCBMydO1e08igP7EnWgy5gMsagVCrx8OFDpKWlobS01OQ+iPqHRCKBs7MzfH194eHhobvSlEgkupc5+PvvvzFu3DgkJiaic+fO2Llzp8kXL/WVap+1l0qlsLe3N6hyp52dncmTTmVYWlri888/h6+vL+bOnYsffvgB8fHxmDdvHlq2bGnSc6DKvtSOjo5wdHQ01W2CqBYYY0hJScHmzZsxZ84cyOVyREREYPny5bQ02gSq/Yo0KysLx44dMyiQ2tjYICwszOwVC48dO4ZFixbh8OHDaNSoEcaOHYt3332Xa/aVIOo6JSUliI6Oxvr167F37174+flh+vTpGD16tFnu0OoztTLZVFtotVokJydjxYoV+O677yCVStGmTRtERkbivffeM2vWAEE8KzDGcOrUKSxfvhxHjx5FZmYmevTogQULFiAkJIRSnMxAvQqk5UlMTMR///tf7N27F3l5efDy8sLHH3+Mt956Cy4uLlAoFDTrTtRZVCoVCgsLce7cOSxevBjHjh2DTCZDy5YtMWvWLAwZMoQmlMxIvQ2kwJMv2/Hjx7F69WocO3YMWVlZcHd3x0svvYTevXujWbNm8PPzg7e3N12tEs80arUaGRkZSExMREJCAs6ePYvo6Ghcv34dMpkM7dq1wzvvvIMRI0ZwLVogDKNeB9IysrOzcfToUezZswfHjh1DfHw8ZDIZPD090bBhQ/j6+sLT0xO+vr7w9vaGnZ0dbG1tYWtrSylORI1TWlqK/Px8KJVKXfBMTk5GcnIyEhMT8ejRIyiVSjRo0ADdu3dHv379MGDAAAQGBta2688tFEj/H4wxFBUVobCwEDExMfjtt99w4MABJCQkgDEGCwsL3YolCwsLWFhYwNvbGykpKbXtOlGPkEgkaNCgAfLy8qDVaqHRaFBaWgqNRgPGGBo0aICwsDC8+uqrePnll2Fvbw8bGxvIZHW+YPAzDQVSPajVaty8eRMXL17Ew4cP8fDhQzx69AhZWVkoKiqCi4sLHj9+XNtuEvUMOzs7qFQqODg46O6aGjVqhMDAQHTt2pXSmGoBCqRGwBhDSUkJioqKqGgeUeNYWVnB2trabLnWhOlQICUIgjARyu8hCIIwEQqkBEEQJkKBlCAIwkQokBIEQZgIBVKCIAgToUBKEARhIhRICYIgTIQCKUEQhIlQICUIgjCR/w+EpTIdRrUVYwAAAABJRU5ErkJggg==)
Equal volumes of two immiscible liquids of densities r and 2r are filled in a vessel as shown in figure. Two small holes are punched at depth h/2 and 3h/2 from the surface of lighter liquid. If v1 and v2 are the velocities of a flux at these two holes, then v1/v2 is :
![](data:image/png;base64,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)
physics-General
physics-
The diagram shows three concentric conducting spherical shells having radii T, 2R and 3R. The initial potential of each shell is as mentioned in the figure. If the inner most shell is earth then the charge present on its outer surface would be equal to
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)
The diagram shows three concentric conducting spherical shells having radii T, 2R and 3R. The initial potential of each shell is as mentioned in the figure. If the inner most shell is earth then the charge present on its outer surface would be equal to
![](data:image/png;base64,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)
physics-General
physics-
The variation of gravitational field E and potential f as a function of x from the center of a uniform spherical mass distribution of radius R is correctly represented, from the following plots, by
![](data:image/png;base64,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)
The variation of gravitational field E and potential f as a function of x from the center of a uniform spherical mass distribution of radius R is correctly represented, from the following plots, by
![](data:image/png;base64,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)
physics-General
physics-
A (nonrotating) star collapses onto itself from an initial radius Ri with its mass remaining unchanged. Which curve in figure best gives the gravitational acceleration ag on the surface of the star as a function of the radius of the star during the collapse?
![](data:image/png;base64,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)
A (nonrotating) star collapses onto itself from an initial radius Ri with its mass remaining unchanged. Which curve in figure best gives the gravitational acceleration ag on the surface of the star as a function of the radius of the star during the collapse?
![](data:image/png;base64,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)
physics-General
physics-
Inside a charged thin conducting spherical shell of radius R, a point charge +Q is placed as shown in figure. The potential of the shell would be
![](data:image/png;base64,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)
Inside a charged thin conducting spherical shell of radius R, a point charge +Q is placed as shown in figure. The potential of the shell would be
![](data:image/png;base64,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)
physics-General
Physics-
Two objects of masses m and 4m are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If G is the universal gravitational constant, then at a separation r
Two objects of masses m and 4m are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If G is the universal gravitational constant, then at a separation r
Physics-General
physics-
A spherical hole of radius R 2 is excavated from the asteroid of mass M as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
![](data:image/png;base64,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)
A spherical hole of radius R 2 is excavated from the asteroid of mass M as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
![](data:image/png;base64,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)
physics-General
physics-
A point negative charge – Q is placed at a distance r from a dipole with dipole moment P as shown in figure. The force acting on the charge – Q is
![](data:image/png;base64,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)
A point negative charge – Q is placed at a distance r from a dipole with dipole moment P as shown in figure. The force acting on the charge – Q is
![](data:image/png;base64,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)
physics-General
physics-
A conducting sphere of radius R and charge Q is placed near a uniformly charged . Then
non conducting infinitely large thin plate having surface charge density find the potential at point A (on the surface of sphere) due to charge on sphere (here
)
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)
A conducting sphere of radius R and charge Q is placed near a uniformly charged . Then
non conducting infinitely large thin plate having surface charge density find the potential at point A (on the surface of sphere) due to charge on sphere (here
)
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)
physics-General
physics-
We have two electric dipoles. Each dipole consists of two equal and opposite point charges at the end of an insulating rod of length d. The dipoles are placed along the x-axis at a large distance r apart oriented as shown below:
![](data:image/png;base64,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)
The dipole on the left
We have two electric dipoles. Each dipole consists of two equal and opposite point charges at the end of an insulating rod of length d. The dipoles are placed along the x-axis at a large distance r apart oriented as shown below:
![](data:image/png;base64,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)
The dipole on the left
physics-General