Physics-
General
Easy
Question
Resistors R1 and R2 have an equivalent resistance of 6 ohms when connected in the circuit shown below. The resistance of R1 could be
![](data:image/png;base64,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)
- 1
- 5
- 8
- 4
The correct answer is: 5
Related Questions to study
physics-
In the two circuits shown, all the light bulbs and batteries are identical. If A, B and C respectively denotes the brightness of light bulbs A, B & C then
![](data:image/png;base64,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)
In the two circuits shown, all the light bulbs and batteries are identical. If A, B and C respectively denotes the brightness of light bulbs A, B & C then
![](data:image/png;base64,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)
physics-General
physics-
Two strings support a uniform rod as shown. String at end B is cut. Which of the following is true just after cut
I] initial acceleration of A is vertical
II] initial acceleration of A is horizontal
III] initial acceleration of centre of mass of rod is vertical
IV] initial acceleration of centre of mass of rod is horizontal
![](data:image/png;base64,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)
Two strings support a uniform rod as shown. String at end B is cut. Which of the following is true just after cut
I] initial acceleration of A is vertical
II] initial acceleration of A is horizontal
III] initial acceleration of centre of mass of rod is vertical
IV] initial acceleration of centre of mass of rod is horizontal
![](data:image/png;base64,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)
physics-General
physics-
The potential of point O in the steady state circuit shown on the right is
![](data:image/png;base64,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)
The potential of point O in the steady state circuit shown on the right is
![](data:image/png;base64,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)
physics-General
physics-
A mass is at the center of a square, with four masses at the corners as shown.
![](data:image/png;base64,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)
Rank the choices according to the magnitude of the gravitational force on the center mass.
A mass is at the center of a square, with four masses at the corners as shown.
![](data:image/png;base64,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)
Rank the choices according to the magnitude of the gravitational force on the center mass.
physics-General
physics-
In the figure shown the electric potential energy of the system is (q is at the centre of the conducting neutral spherical shell of inner radius a and outer radius b)
![](data:image/png;base64,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)
In the figure shown the electric potential energy of the system is (q is at the centre of the conducting neutral spherical shell of inner radius a and outer radius b)
![](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
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
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,iVBORw0KGgoAAAANSUhEUgAAARkAAACNCAYAAACDkA72AAAgAElEQVR4nO3deVTN+f8H8GebUoSakZQtSUhGRkqkLGWYGUvWScRBZDRkzBzGLKjGOmUdnEkbDbJkb6IsFZEWRanUaGEm6kqb6nZ7//7w6341Wm51P/fe6vU4p3O6n8/7836/LvXq83nf9yLHGGMghBCOyEs7AEJI20ZJhhDCKUoyhBBOUZIhhHCKkgwhhFOUZAghnKIkQwjhFCUZ0i7cunULPB5P2mG0S5RkSLvw+PFjlJSU1Hs+LS0N33zzjQQjaj8oyZA2TyAQ4Pnz58jKyqrzfHV1NZYsWYK9e/fi+vXrEo6u7Wt2kikrK4O9vT0EAoE44yFErCorK2Fvb4+qqipcuXIFBw4c+KDM77//jqioKADA0qVL8fbtW0mH2aY1O8n88MMPCAwMhKenpzjjIUSsYmNjIS8vjz59+mDp0qXYvHnzB2Xu3buHHj16wMDAAFlZWcjLy5NCpG1Xs5LMvXv3sHfvXgDAjz/+iIyMDLEGRYi4VFdXC79XUlKCiorKB2WUlJTg4eGBgQMHYvLkyZIMr11odpJRUlKCuro6KisrER8fL+64CBGLTz/9FKWlpSgrK0NcXBzs7e0/KLN+/XoYGxtDTk4Ofn5+UFdXl0KkbVezH5d27tyJTp06Yf369eKMhxCxUlZWxtGjR/HkyRMUFxdjy5YtH5QxNDQUft+9e3doaGhIMsQ2r1lJZuLEiVi9ejUAwM3NDcbGxmINihBx0tTUhImJCcaNGwclJSVph9PuNCvJDB48WPi9oqIiDAwMxBYQIVwYO3YsunXrJu0w2iXF+k5ERERg9uzZmDVrFkaPHg3GGOLj46Guro6ffvpJkjES0mJDhw6VdgjtVr1JZuzYsejZsydGjhyJr776CgAwZ84cnDhxQmLBEUJavwYfl+Tk5Gq9Li8vh4ODA6cBEULalkb7ZAoKCpCTk4P09HT4+flJIiZCSBtS7+NSjZcvXyIjIwNFRUX4559/JBETIaQNaTTJDBo0CFZWVgCA0aNHcx4QIaRtadJH2B999BEePXqEoqIiruIhhLQxDSaZ0tJSlJaWAng3ByQzMxPe3t407JoQIrJ6H5fu3r2LDRs2AAACAgLAGANjDEuWLJFYcFxLTk7GgAEDaBQoIRyqN8mYm5vD3NxckrFIVHV1NT7//HNERERAR0dH2uEQ0ma125XxwsPDMWrUKEowhHCs3SaZAwcOYM2aNdIOg5BGMcZw5coV9O7dGwsXLoSfnx/mz58PHx8fMMakHV6jGv0Iuy0KCwtDdXU1Ro0aJe1QCGmUnJwcpkyZgg4dOmDmzJmYPn06rKys0L9/f6ioqGD+/PnSDrFB7S7JVFVVYd26dTQHi7Q68vL/e/DQ1dVFhw4dkJaWJsWIRNPuHpe2bt2KsWPHwtDQENeuXUN6erq0QyKkyU6cOIEuXbrI/F0M0M7uZKKjo3H69GnExMQAAIKDg2FjY4MBAwZIOTJCRHPz5k0EBgaisrISmZmZda5ZLGvaTZIpKirC4sWLERAQAFVVVQDAmjVraCEj0qpYWVnBwMAAZmZmuH//PsaNGyftkBrVLh6XGGNwcHDA0qVL8emnnwqPBwYGIiEhQYqREdJ0gwcPxs6dOzF37txWMWlZKncyz58/x4EDB5Cfny+cfFlQUIDHjx/j0KFDYm9vy5YtUFNTw7p162odLy4uRmVlpdjbI0TcGGN48+aNcN7g8uXLERISgrlz5+LSpUvNnurz9u1b/Pjjj0hNTYWGhgbc3NzQq1cvAMDDhw+FfZZqamqYMGECBAIBQkNDwefzoaurCzMzs0bbkEqS0dHRgZaWFiIiInDkyBHh8bo23mqpEydO4Pz584iMjPzg3Lp169CpUyext0lkU1ZWFrKzs+s8l5qairy8PEREREg4qsYxxpCYmIgFCxYgMzMTFy5cQLdu3bB06VKEh4fDy8sLo0aNEnYDNNWkSZOQlJQEf39/BAcHw9PTE4sXL8aQIUNw48YNrF27FmfOnEGHDh0AAK9evUJaWhqmT58uUv1S65OpCfh93333nVjbCA4OhpubG8LCwur8D3Bzc4ONjQ2mTZsm1naJbLp37x7OnTtX5zkej4fExETY2NhAXV0d3bp1Q7du3aCpqYnOnTtLONKGpaam1nr94sULpKSkIDk5udYi/01RVVUFFRUVFBUV4ciRI5gyZQp69OiBNWvWIDs7G9u3b8e0adNQUlKC+Ph47NixA4qKIqYP1gI9e/Zs9rUHDx5kY8aMEb6+f/8+y8/Pb0k4tVy5coUZGhqy3Nzcesv4+/uz2NhYsbVJWq8HDx4wfX19NmLECBYcHMx8fX2Zi4sLMzU1ZTo6Omz69Ols586d7P79+6y6ulra4dZJR0enyddUVVWxrVu3Mnl5edahQwe2bds2xufza5UpKytj+vr6bMeOHWzlypXs5cuXTWpDqklmwIABzN/fn/n4+LAxY8aILcn4+voyQ0ND9uzZswbLXb16laWmpoqlTdK6PXjwgH355ZcsNDSU6evrMy8vL2EyKS0tZTdu3GBubm7M2tqa6erqssWLF7MzZ86w4uJiKUf+PxEREU2+pry8nGVnZ7Ps7OwGf//Cw8OZnJwcO3r0aJPbkJk7maysLPbmzZtaZbKzs1lQUFCT6v3555+ZmZmZSNnW2dmZBQcHN6l+0jbVJBnGGOPxeGz+/PlswoQJLDs7+4OyBQUFzN/fn9nZ2TFNTU02Y8YMdvLkSVZaWirpsGuxsLDgrO5bt26x4cOHM0NDQ1ZWVtaka2XmI+zevXtDXV0dWVlZAN4txbBhwwbcuXNHpOtrdlJ4+PAhwsPD8fHHHzd6jZOTE0xNTVsUN2l7unXrhsDAQCxbtgxWVlY4duxYrfMaGhpwcHDA6dOnkZ2djXnz5uHkyZPo06cPFixYgNu3b0sl7venHYjTixcvEBYWhtu3b0MgEAjXmRI5Lk6iEkFVVdUHx65fv46cnBwAwKlTpzB58mSR6srOzsaYMWPQu3dvnDlzBh07dhTpupCQkFYx94NIx9y5cxEREYFjx45h9uzZKCgo+KCMqqoq5syZgzNnziAzMxPjx4/Ht99+iyFDhmDPnj0SXarWw8ND7HW+ffsWu3fvxsaNG9GpUyf8+eefOHToEMLDw0WuQypJJjc3F8XFxRgwYAB8fHwQEBCA/fv34+LFi7CwsEBaWho0NTXRs2fPRusKCwuDtbU1fvjhB7i7uzcpm2dlZaGwsLAlb4W0cT179kRISAisra0xatQoXL16td6ynTt3xpIlS3D//n0cO3ZM+GmPh4cHSkpKOI913rx5Yq3v1q1bGDduXK3fqe7du0NTUxP29va4du2aaBW15DmtJX0yDVm+fDnz9fVl3333HbOxsWGPHj36oEx5eTlzdXVlw4YNY8nJyc1q5/Xr101+viRt0/t9MvVJTU1lo0aNYk5OTqykpESkel++fMl+/PFHNnDgQLZz505Of962b98u1vqqq6trfdV3rDEy0yfzvkmTJkFZWRlKSkpQUFCAgoJCrfMJCQkwNTWFoqIi7t+/D3V1dWzbtg2bNm1CYGAgAgMDsXfvXvz8888NtvPDDz8gNDSUy7dC2hADAwNERUVBR0cHI0eOxN27dxu95uOPP8aWLVsQGxsLxhhGjhyJw4cP19ld0FKvX78Wa31ycnK1vuo71qiWZDqu7mRqhIWFsbVr1wpfV1RUCP8q3L59u1bZ3bt31/q0ijHG1q9f32D9hw8fZtHR0eILmLRaotzJvHnzhv3111/C8kZGRmzjxo2ssrJS5Hby8/OZi4sLGzRoELt8+XKLYv6v5oyTkQSZvJOpYWlpiV9//RUAEBMTg5EjR6KoqAhxcXEYO3ZsrbJ1dfZ+//33DdZvaGiI7t27iy9g0qaVl5fj0aNHAIARI0YgJiYGpaWlMDMzw+PHj0WqQ1NTE3v27MG5c+fg4eEBBwcH8Hg8ka51d3dv8HxD/UXSJNNJRlFREUVFRfj666/h6OiIgwcPwsvLS6Q5GikpKY12Ap88eRKJiYniCpe0cRkZGXj27Bn4fD4AQEVFBV5eXtixYwdmzJiB3377TeQ1dwcOHIjbt29j5MiRGDlyJC5dutToNcXFxQ2eX7BggUhtS5rMJpm3b9/Cw8MDlpaWGDJkCBISEmBhYdHgNXl5eQgICICvry+WLFmC6urqBss7ODhg+PDh4gybtFHu7u54+PAh5OXlMXv2bOHs/YqKClhZWSEmJgbx8fGYMGFCvZMw/0teXh4uLi4IDQ2Fm5sbvvnmG1RUVHxQjjGGixcvIiUlBTdv3qy3vuZOkOSazCWZ8vJy7Nu3D+bm5lBSUkJcXBxWrlwp0gZsWlpacHBwgKOjI3x8fGp1GF+5cgUHDhxAWVmZ8FhMTAxyc3M5eR+kbTl69CimTZuG3r17Q0VFBTdu3MCuXbswf/58DBo0CGlpaQgICICzszOsra3h5+cnct39+/dHREQEOnbsiNGjRyMzM7PW+T179uCff/7BoEGD4O/vjxs3bgjPvf+YtmfPnpa/UQ7ITJIpLS3F7t27YWRkhLy8PNy+fRvr168XeWDdfxkaGqJr1654+fIl4uLioKKiAh6PB1dXV2GZJ0+e4NWrV+J6C6QNe/8xqHPnzigvL4eVlRXOnj2L48ePC5cpmTVrFiIjI3Hq1CnY2dkhPz9fpPqVlJSwbds2eHh4wNbWFtHR0cJzkZGRGDFiBABg/PjxCA4OBgCcPn0aU6ZMEZabOXNmi98nF6SeZJ4+fQpXV1fo6enh6dOniIiIgJubW5MX4anr0Sg+Ph5JSUkYPnw4xo8fDxcXF+GCPACE/6GENGbevHmIjo5GSUkJCgsLMXXqVOEqi/r6+ujdu7ewrLa2Ni5fvgwbGxuYmZnh8uXLIrdja2uLc+fOYdGiRTh9+jSAdwPgagaNVlZWCn+GZ82aBU1NTeG1y5cvb/H75IJU1pPh8/m4dOkSDh8+jMePH2PZsmV4+PAhevTo0az6cnNzkZ2dDXV1dfj4+EBRURFv3rxBdHQ0/Pz8ICcnh8TERPzyyy+1FsbauHEjrSdDROLu7o4zZ84gNzcX+/fvr7WWysWLF+tcC8nJyQkTJkzAokWLcP78efz2228iLZJmZGSEmzdvYurUqSgtLcW6devg5eUFHo+HvLw87Nu3T1j2/bEqonY6S1xLPv9u6jiZBw8esNWrVzMtLS1ma2vLgoKCPli7gisCgYCdPXuWGRoaCo95enqyyMhIibRPZJso42Ty8vLY7t27ax178uQJS09Pb/C6qqoq5u7uzgwNDZv085afn89MTEyYj48Pq6ysZGvWrPmgjImJifB7WR0nw/mdTFJSEk6dOoWgoCAoKChg0aJFiIuLE2lekjjJy8tjxowZCAoKEh6zsLCAtra2ROMgrVfnzp0xadIk4eubN2+ioqICffv2xalTpzBp0qQ6d79QUFDAxo0b8dlnn8HR0RFTpkzB5s2b61wd8n2ampoIDQ2FjY0NFBUVoays3GD5CxcuNO+NcUzsSebvv//GnTt3cOfOHYSHh6NTp06YPn06zp492+ylAVvq2LFj6NGjB3g8HmbNmiU87uvrCxsbG+jq6japvrCwMLi5uUEgEGDOnDlwdnaGvLw8SktLcfnyZZSXlwMARo8eDX19fSQmJiIhIQEKCgr44osvmr3oM5Gujh07YujQoQDeLXzv6+sr/Mi5V69emDNnToPXDx8+HPfu3cPGjRthZmYGf39/GBkZNXiNpqYmQkJCYGlpiZ07d9Y6V11djYqKCjDGICcnBycnJ+GeYrJEjrH6H+SeP3+O+Pj4Os89e/YMrq6u0NfXR0lJCUpKSlBaWgolJSWoq6tDXV0dXbp0aTT7SkJFRQUqKiqgqqpa61m6qqoKixcvbtbdTFJSEnbt2gUejwcrKyscPXoU/fr1w/PnzzFjxgyUl5fj4cOHkJOTA2MM1tbW8Pb2Rv/+/cX51oiYxMbGYsuWLTh//rxE2rtx4wacnJywfPlyuLq6NjpwNC0tDVOnTsWFCxcwaNAgAO8+HU1LS0P//v0xZMgQjBgxArGxsZIIv0kavJPJzc2t9x/91atX4PP5SE1NhbKyMpSVlaGurg45OTlUVVWBx+OJPFxaWqqrq3H58mWRFrj6r4qKCqipqYHH4yE+Ph737t1Dv379oKOjg+DgYBgbGyM4OBgzZszAoUOHsGnTJkowRMja2hoxMTFwcXERjqvp27dvveUNDAzg4+MDOzs73L17F126dIGhoSEMDQ2FZf744w9JhN50LenQ0dbWZkFBQczMzIwZGxszX19fVlFRIY6+IomoWX6zpKSEPXv2TPiVl5fXYIf03bt3WZ8+fRgANnnyZJaTk/NBmYCAAKalpcWCgoLY3r17uXwbRAxE6fjlypkzZ5ienp5I6+d6eXkxOzu7Os/Jasev2D5dioqKYjNmzGC6urrMw8OD8Xi8FgfHtfz8fFZaWsoqKyvZwYMHGQB24sQJdvr0aWZkZMS8vb3rvK64uJi9efOGvXnzpt41Naqrq5mtrS3r06cPEwgEXL4NIgbSTDKMMfbvv/+yqVOnsmnTpjW6PvWMGTPq/MO1adMmrsJrEbF/hJ2ens5WrVrFunfvzr7++mv29OnTljTBqdWrV7Pz588zxhhLTk5m79/YnT17lgFgmZmZzaqbz+czZ2dnpqamxg4dOiSWeAl3pJ1kahw5coTp6ekJfy7r8vr1a2ZgYPDB75a7uzvX4TWL2Ef86uvrY//+/UhJSYG2tjbGjRsHOzs7kRcEb0zNNpmffPIJ3NzccPz4cfj7+8PZ2RknTpxoUl3a2tr1ftLD/r8/vGbGbVPt2rULrq6uOHjwIFxdXfH06dNm1UPal2XLluHatWvYsWMHlixZUufM665du8LT0xPffPNNreMHDx6UVJhN05IMJcpgvIqKCubj48OGDh3KzMzMWFBQEKuqqmpJs4wxxrS0tFhISIjwdXFxMTtw4ECT6khKSmL//vsvY+x/dzICgYClp6czKysr9t133zUrtqCgIHbp0iXG2LvHpq+++opZWFhIbOAhaTpZuZOpIRAI2LZt25iBgQG7detWnWXmzZvHLly4IHwdFRUlqfCaRKIjfv/66y9mY2PD9PT02J49e1q0MVbPnj1rJZnmdDi/v+9STZI5efIk09LSYr6+vk2ur6CggG3ZsoX16tVLOAq0oqKCubu7MxUVFbZq1Sr2zz//NLlewj1ZSzI1EhIS2LBhw9j69etZeXl5rXN5eXlsxIgRwj9e/10ZUlZIZfnNxMRE5ujoyLS0tNj333/f4FayDbVdk2TKy8vZiRMnmlzH5cuXWUpKCmOsdp9MSEgIU1dXp90l2xFZTTKMvfv5/vbbb9mwYcNYQkJCrXNbtmxhv//+O2OMMSMjI2mE1yipzMIeOnQofHx8EB8fDwUFBYwYMQILFy7Ew4cPm1TP9evXERAQgH379iEhIaHJcRQWFgpH577P1tYWS5cuhZ2dXa31ZwiRBmVlZezcuRN79+7F3LlzsW3bNuGqA2vXrsXhw4fx9u1bnDx5UsqR1k2qSz1oa2vD3d0dGRkZMDU1hZ2dHSZOnIirV6+KNKN04sSJcHBwwLfffosVK1YIj588eRKff/45fvrpJwgEgnqvj4qKEu5YmZqaCgDCDloPDw8oKSnB3t4eL1++bMnbJEQsLC0tERMTg7S0NFhaWiIzMxOdOnWCo6Mj9u3bBxsbG2mHWLeW3AaJe7cCgUDAzpw5w0aPHs0GDx7M/vjjjw+eQ99v+/0+GcbezYj9+++/mZ+fHystLWWOjo7My8ur3vZycnJYYWEhKywsZAkJCcKvt2/fMsbejaNJSEhgSUlJ4nuTRCbJ8uNSXYKDg5menh47cuQIKykpYQMHDqxzlrYskPqiVe+Tl5fHzJkzERUVBW9vb4SEhEBPTw9bt279YIWxmolhNYqKinD8+HHo6Ohg4cKFUFVVhaOjY4PbhO7btw937txBly5dMGzYMOGXiooKgHeT04YNG9boJDZCJG3atGm4e/cuLl26hHnz5sHa2hoZGRnSDqtOUlm0ShRmZmYICgrC33//DS8vLwwePBh2dnZwcXHBq1evsGLFCjx+/Bj5+fmoqqrCixcv8Pnnn9daC/j+/ftYtGhRvW0oKyvXmjBJ2jfGGMLCwqQdRpO4uLggJCQEx48fF3mpT0lrcBZ2Y3R0dPD8+XNxxlOvwsJCHD58GPv374eJiQnWrVsHS0vLestHRUVBTk4Oo0ePrrdMZmYmunbtCg0NDS5CJq1IbGwsfvnllzrXg2kNUlJSoKam1uBuBlLTkmctrneQrEtlZSXz9/dnw4YNY59++in7888/PxjklpmZyWJjYxlj74Zg1+f9cTKkfWttfTLvy87OZv369ZPZcTIy1ScjCiUlJTg4OCAhIQHbtm2Dv78/9PX1sXv3bhQVFSEjIwOLFi3Cxo0bMXnyZHh6etZbl7W1NfT09CQYPWmN7t27h/T0dGmHUa8VK1Zg69at+Pfff6UdSp1adYfEhAkTMGHCBCQnJ2P37t3Q19eHg4MDjh07Vmv1+PooKCg0ulgQIS9evBB9c3kJO3LkCBQUFGBvbw9TU1Nph1OnNvEbNnjwYHh7eyMpKQmqqqowNTXF/Pnz8eDBgwavu379Ok1cJA3i8/lITk5GfHx8ozuSSlpaWhq2b98Ob29vAO/uzGVRm0gyNbS0tLB161ZkZmbC0tISX331FcaNG4eLFy/WObhvzZo1jW59S9qvqqoqzJ07F506dcKbN2+wevVq4bm8vLwGB3pyjc/nY8GCBdi/f79wZcfZs2dLLZ6GtKkkU0NVVRUrV67EkydP4Orqip07d2LQoEHC4dc1AgMDmzUdgbQPWVlZKCoqQu/evWFlZYWrV6/i5cuXOHLkCDZs2IDJkydLLdGsWrUKFhYW+Oyzz4TH+vXrJ5VYGtMmk0wNeXl5TJs2Dbdv30ZAQABu3LgBPT09/Pzzz3j58iWKi4uFG6cT8l9KSkq11hNSVVVFhw4dMHPmTBw9ehSKioq1/mhJiqenJ3JycrBr165ax3fs2CHxWETR7I5fPp8PgUDQavaS7tu3L/bt24ecnBwcOXIEgwcPxrhx46ClpSXt0IiM6tWrF3r16oWcnBzk5+fD1tYWXbt2BfDuLsfW1lakHSHF6dKlS/Dx8UFkZCQUFBRqnTt69KhEYxFVs5NMbGwsCgoKMGHCBHHGIzFaWloIDw9H7969hZuZE/I+OTk5+Pj4wMPDA2pqati+fTuAd1NawsPD4eXlBVNT0wYHfIpTeHg4XF1dERoaWueKjp6enjI5SbLZScbMzAzdu3dHYmKiOOORqICAAAwZMkTaYRAZpqSkBGNjY+jo6AinoCgrK2Px4sXQ0NBAcHCwRJJMZGQkVqxYgStXrtS7dUpycjLncTSHzIyTYYwJd+P7L0VFRU7mGH388ccSv90lrc/IkSPRsWNHABDuKda9e3dUVFQ0OLVFXEJDQ+Hs7IyLFy9CX1+/3nKRkZGcx9IcMpNkACAuLg6TJk2Cs7MzzM3NUV1djfv376Nbt27YsGGD2Nu7ePEibGxsYGBgIPa6Sdvx/jbGhYWF+Omnn2Bubo6ePXvW2hubCwEBAfj111/x119/Nbo5oLm5OXJzczmNpzlkJsnUTGbU0dGBmZkZZs6cCQD48ssvcfHiRU7adHJyatbukaT9+uijj3Do0CHO26mursbmzZtx9epV3Lp1S6Sf0y+++ILzuJpDZpJMjf8O3y4rK4OdnR0nbRkbG3NSLyEtkZ+fD3t7e2hra+PmzZtQVVUV6brff/+d48iaRybHyTx79gyJiYmIjo6Gj4+PtMMhRGKuXbsGCwsLzJkzB76+viInGFkmc3cy76usrKxzoW9C2prXr1/D1dUVaWlpOHfuHAYPHiztkMRGJu9k+vbtC2NjY1haWmLlypXC469evcLatWsRGBgoxegIEZ/q6mp4e3vD1NQUJiYmiIiIaFMJBpDRJPO+rl274s6dO3j79i26desGbW1t2qaEtAk3b97E6NGjERcXh6ioKKxevbpNLj0iU49LjDEUFxcjLy8PhYWFEAgEePr0Kc6dOycc8NS5c2cpR0lI8/H5fJw6dQp79uyBnp4e/P392/wQCplJMowx3LlzB4cPHwYARERECM+tWrVKWmERIhbPnj3DH3/8AT8/P4wZMwZ+fn4YNGiQtMOSCJlJMnJycrS2C2lTXr9+jeDgYJw4cQLJyclwdHREZGQk+vTpI+3QJEpmkgwhrR2fz0dsbCyioqJw/fp1PHr0CJMnT8aaNWtgY2Pzwazp9qJVJZnS0lJhp29ZWVmbGENAWic+n4/U1FTExsYiLi4OcXFxyMjIwCeffAILCwts2rQJ5ubmwo7cV69eISAgAK6urlKOXPJaVZJRU1PDunXrpB0GaQdKS0tRUFCAnJwc5OTkIDs7G1lZWUhPT0dGRgb4fD4GDBiA4cOHw9TUFE5OTjA0NGzw06G6loBtD1pVkiGES0lJScLJkGpqatDQ0ICuri569eoFXV1dWFtbY9myZdDX12/S7H0ej4fjx48jKioK1tbWMDEx4eotyCRKMoT8vyFDhnAyGXfevHnYtm0b+Hw+vv76awQFBUFHRwcAkJubCx6P16bn0bW9kT+ENBNXA+GePn0KXV1dyMvLw8jICNHR0QDerU2zcuVK2dxaVowoyRDCsS5duggXrC8rKxMOvjt+/DjGjx8vzdAkgpIMIQB69OjB2ZIiu3fvxt69exEXF4f+/ftj6NChiI6OxrBhw4QLk7dllGQIAaCjo4OFCxdyUvf48eOxfv16mJiYYPPmzeDxeLh69SrKy8uRkZGBZ8+egcfjcdK2LGhRxy/NIyKk6V6/fo38/HwEBAQgJSUFfD4f2dnZ0NDQkHZonJBj7fXDe0IkiDEGgUDwwYL4Pj4+KC4uhouLi9s4aQ0AAADVSURBVJQi4x4lGUKkKDc3FwKBoE3PZ6IkQwjhFHX8EkI4RUmGEMIpSjKEEE5RkiGEcIqSDCGEU5RkCCGcoiRDCOEUJRlCCKcoyRBCOEVJhhDCKUoyhBBOUZIhhHCKkgwhhFOUZAghnKIkQwjhFCUZQginKMkQQjhFSYYQwilKMoQQTlGSIYRwipIMIYRTlGQIIZyiJEMI4RQlGUIIpyjJEEI4RUmGEMIpSjKEEE5RkiGEcIqSDCGEU5RkCCGcoiRDCOEUJRlCCKcoyRBCOEVJhhDCqf8DOpdgxM1lSDkAAAAASUVORK5CYII=)
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,iVBORw0KGgoAAAANSUhEUgAAAKwAAACCCAYAAADblyOeAAAPRUlEQVR4nO3da1BU5R8H8O+yLLusyGVBXW6KmSBiyqig0UpJacqEGXgpDUvCSwTolIQ6QL6gkTIwmVp0KhUD1PCWGTRJYqCpyJBX8IIMIkjiguiictnl/F847j+M617YPYff51XrnvOcnzPfHp/znOc5y2MYhgEhLGFm7AII6QsKLGEVCixhFQosYRUKLGEVCixhFQosYRWdA1tdXa2POgjpFZ0Cm5eXB5lMBqVSqa96COmW1oF9+PAhli1bhps3b+LTTz/VZ02EdEnrwKampqKyshIikQjbtm3DlStX9FkXIZ0y//eHGzduYPv27XB1dUVpaSk2bdoEoVDY6Yn37t3D1KlT8fDhQ1RWVqKxsbFfCiYDW4ceNiUlBX5+fli5ciXq6uqQk5PT5Yn29vZITU2FpaUlvv32W4MXSgjwTA/75ZdfAgB2796Nuro61NfXd3niqlWrNN+HhoaiubnZgGUS8kSHHvbChQtITk7GG2+8AXd3925PFIlE3X4mxBA6BHbNmjWYMWMGxGIxWlpaAAAMw0ClUqGkpIR6UWJ0HQI7ZcoULF++HOHh4aipqUF2djauX7+OFStWQCwWY8GCBdiyZQva29uNVS8Z4DqMYZOTk1FdXQ2pVAqVSgWGYdDW1oYbN25gzJgxeP311yEUCmFmRk90iXF0SB6Px4OrqysEAgEsLS0hFothY2MDNzc3HD58GFVVVXjzzTeNVSshPT84aG1txYMHD8Dn8zFjxgw8fvy4P+oipFO9+rd94sSJqK2txd9//43169fTQwJiNOY9HbBnzx60tbVBJpOhra0NFhYWNIVFjKbHHvadd96Bl5cXsrOzceXKFURERFBgidH02MMKBAIsWLCgP2ohpEc0P6VH9GDF8CiwelJZWQkfHx/cv3/f2KVwGgVWT9zc3BAeHo5FixbRk0ADosDq0apVqzBs2DCsX7/e2KVwFgVWz9LS0lBQUIA9e/YYuxRO6nGWgPSNUCjE/v374e/vD3d3d0ycONHYJXEK9bAG4OjoiMzMTLz99tuoq6szdjmcQoE1EF9fX8TFxWHevHloa2szdjmcQYHtRltbG3R53/OSJUswadIkREVF6bGqgY0C243PPvsMhw4d0qmNr776Cjdu3MDWrVu1bkOhUGDp0qVIS0vTqRYuoMB2IzY2Fs7OzmhoaNC6DT6fj71792LLli0oLCzUqg0HBwfY2NjQ0AIU2G7Z2Njgr7/+QmxsrE7tSCQS7Nu3D++//z6qqqr6dK5KpUJ9fT14PJ5ONXAFBbYHkZGRmD9/PpqamnRqx8vLC8nJyQgODu71IvgjR44gJSUFOTk5+Pnnn3W6PlfQPGwPzM3N4eXlBV9fXxQVFcHKykrrtubOnYvz588jLCwMu3fv7vbYpqYmxMfHo7i4GHw+H3l5eVpfl0uoh+0FZ2dnrF69Gnfv3u3ymPr6eixdurTHt+AkJCSgtbUVSUlJ3R537NgxDB48GHw+H8CTYQWhwPba8uXLkZ6ejl9++aXT7+3t7WFnZ9fjjRGPx0N6ejr27NnT7augmpqaaOVXJyiwfRAaGopdu3Z1OTf79MZIpVJ1O061srLCwYMHERUVhatXr3Z6zNSpU3Hp0iXk5eWBYRgoFAqd5oS5ggLbB6NGjcLWrVvxySefdBmeS5cuYfr06XBwcOh23nTkyJH47rvvEBIS0mlP+txzz2Hnzp2IiYnBBx98AFtbWzAMQ7uWGR1UV1czvr6+ujTBSqGhoUxmZuZ//vzjjz9mIiIimNbWVub8+fOMlZUVc/fu3W7b+vrrr5nAwEBGrVYbqlxOoR5WC9u3b8eIESOwY8eO/3w3evRoCAQCjB8/Hj4+PigrK+u2LVpD2zcUWC08neqSy+UoLy/v8jiBQIAhQ4b02B6toe09CqyWbG1tcebMGVy9ehVHjx7V/PnT7TENDQ0wNzeHh4dHj209XUMbHx+PkpISg9XMBfTgQAdmZmbw8PDA4sWLIZPJEBQUhC1btsDa2hpKpRI7duzo9SPVf6+hPXHiBIYOHWrg6llKlwHwQL3pelZ7ezsTHx/P5OXl6dxWeno6M23aNKa1tVUPlXEPDQn0gMfj4d1338WmTZugUql0aovW0HaPAqsn7u7uyM3NRXR0NORyuU6T/PpYQ8tVFFg94vF4SExMxPXr11FZWan1+wn0sYaWqyiweiaRSLB582bs2LEDwcHBWodWlzW0XMZjdPi3q6amBsHBwThz5ow+a+KM48eP459//sHQoUMREBCgVRuHDh1CYmIiCgsLYWlpqecK2Yd6WAN65ZVXMGHCBKxfvx7V1dWaX+bpi7lz5yIoKAhhYWEGqJB9KLAG5unpidOnT6OyshJTpkzpcnVWd3q7hnYgoMD2E5lMhtTUVIjFYiQkJHT7K5PP6u0a2oGAAtuP/P394ezsDA8PD6SmpuLatWu9vinrzRragYAzj2YZhkFGRgZaWlpQVVWFyMhIk3y8aWZmhsWLFwN4Mt964MABHD9+HBYWFj2e++81tCdPnoSNjY2hyzU5nOlhT506hV9//RXh4eEYPXo0K5brrVmzBrm5ucjLy8Ps2bNx+fLlHs8JCAjAsmXLBux7aDkT2AkTJuDzzz9HRUUFysrKWDN3aWNjg8DAQGzcuBFisRgymQw//PBDt+cM5DW0nAmsUCjEvn37cO3aNbz66qvGLqfPvL29MXLkSMjlclhaWiIjIwMRERG4fft2p8c/XUPb03ZxruFMYHfu3Im6ujrMmjXL2KXoZPz48Vi0aBECAwMxfPhwPHr0CPPmzUNubm6H44RCIQ4cOICEhIQBtYaWMzddEokEP/30EywtLVFVVYXy8nL89ttvrA2wRCLB2rVroVarsWTJEly8eBE1NTU4e/Ys1q5dCzc3N0ilUmRlZQ2oNbScCexbb72FIUOGYPDgwRg7diyKiorw4osvGrssnfH5fMyZMwdz5sxBbW0tVCoVxGIxJk2ahGnTpmHDhg2IiYlBSEgIjh07BoFAYOySDcrk1hIolUpER0frrT2uUqlUaGxsxOPHj3Hq1CnY2dlBrVbjhRdewLhx45CSkmLsEg3C5AJbV1eHYcOG6a29gcjJyQk1NTXGLsMgTG5IYG9v36v5SDYrKyvDrVu3MHPmTADAhQsXsHXrVsyePRtBQUEAgLCwMDQ3NyMrKwsAcPnyZRw9ehQzZ87E2LFjATxZDSYWi+Hr69uhfU4PC3TZX0N7uv6rsrKSOX78uGZPVlFRESOTyZjU1FTNMWvXrmWio6M1nxUKBVNSUsI0Njb2e71sY3I9rKljGAbt7e3g8/mor6+HXC7HkCFDsHLlSgBAVlYWzp07Bw8PD0ilUnh6euL777+Hs7Ozpo2NGzd2aNPe3h729vb9+vdgK87MwxqCWq1GbW2t5vM333wDR0dHnDhxAgBgaWkJGxsb+Pj4aI5Zt24d9u7dC6lUCuDJohUPDw+d3itL/s/kbrqMRa1Wo6KiAiKRCK6urgCePH3y9PTUPE1qaGjAoEGDIBQKjVnqgDZge1iFQoGDBw9qfjK+sLAQ7733HkpLSzXHnDt3rsOjT4lEQmE1sgET2Fu3buH06dOaz1988QUOHz6MR48eAXiyCCUmJgYHDx5EQUGBscokPdHljs2UZwnKy8uZO3fuMAzDMPfv32fGjx/PJCUldXpsWVkZExUVxTAMwxw5coRxdXXttzpJ33Cmh1UqlZr/3r9/PxYuXKhZmW9tbY3z5893+fNFGRkZmhunwMBAXLp0yfAFE61wIrAxMTEYN24cHjx4AAAICQlBcXExpk2b1qvz7927p9ljxePxIBKJdH7lEDEMVgZ26dKlCAkJ0XyOi4vDzZs3YW1trVV7EydOxLZt29DU1KTZakM/5GaaTD6wCoUCaWlp+P333zV/tnjxYuzatUvzWde9TaGhobCzs4Obmxt8fX3h6Oio+bkhYlpM8kmXWq3G48ePYWVlBYVCgYsXL+Kll17SfP/aa6/p9XoWFhYoKCjAtWvX4OLionVPTQzPJAPL5/Nx9+5dWFlZYcyYMZDL5Qa/prm5uWZRCTFdJjskGDlypLFLICbIZANLtFdbW8vZLeAmOSQgupk5cyby8/Ph4OBg1DqUSiUyMjKQn58Pb29vODg4oLa2FpGRkVqvTqMelhjM4MGDMWPGDGRnZyM6OhrLly+HSqWCt7e3Zs68ryiwxKCeXSwUFBSE6upqrbem05CA6KSxsRFJSUloamqCi4sLVq9eDZFI1OXx+fn5cHR0hLe3t1bX0zmwarWaNa8FGihaW1tRXV2tWYlmaLNmzcJHH32E0tJS/Pjjj0hPT8fkyZM7HLN//37k5ORAKpXi5MmTsLW11epaOgW2ra0NUqkUCxcu1KUZomdisRgrV67s98fLZmZmKC0txYoVK/Dnn3922GUREhKCc+fO4ezZs3BxcdH+IsZeLkbYrb29nUlJSWEEAgHD5/OZuLg4pqWlRfN9VVUVA4BRKpVMc3MzM2HCBGb16tVaX4/GsBzQ0NCg+V0wHo8HOzu7futd79+/Dx8fHxw7dgxSqRTPP/98h++f7uhobm6GlZUVdu/ejcmTJ8PPzw/z58/v8/X4GzZs2KCXyonRlJeXw8fHB5cvX4ZEIsG6detw9OhRBAQE9OpFyboQiUQYPnw4hg8fDolE0uE7pVKJP/74A2KxGIMGDcKIESPg5OSE0aNHIzc3FyKRCKNGjerT/1w6bUIkpsPPzw9hYWEIDw9HS0sLXFxcEBUVhYSEBGOXplc0D8tBT3tVbSfnTRmNYTmmubkZcrkcrq6u+PDDD41djt7RkIAj/Pz8MGbMGM0cbH5+foex4ZUrV+Dh4cH6nRQ0JOAQPz8/yOVyVFVVYfPmzR2+S0xMhEKhMFJl+kNDAo6xtrZGVlYWpk+fDl9fX8hkMgBPdgZzAfWwHNDa2orbt29rHpFPnToV8fHxWLBgAYqLi3Hnzh34+/tTD0tMQ2lpKTIzMwEAt2/fhpOTE2JjY/Hyyy+jpaUFQqEQAoEAXLhdocByQGcrn/h8foeNm4Z+gNBfaEhAWIUCOwA0NjbCy8sLFRUVxi5FZzQPS1iFeljCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwioUWMIqFFjCKhRYwir/A10CDm0CEaJCAAAAAElFTkSuQmCC)
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
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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-
A spherical hole of radius R2 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 R2 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-
Net charge on the outer surface of conducting sphere is
Net charge on the outer surface of conducting sphere is
physics-General
maths-
where
are the co-factors of the elements
for
are the direction cosines of of three mutually perpendicular lines then
and
are
where
are the co-factors of the elements
for
are the direction cosines of of three mutually perpendicular lines then
and
are
maths-General
maths-
The point collinear with A(0,1,-2),B(3,l,-1) and C(m-3,-4) is
The point collinear with A(0,1,-2),B(3,l,-1) and C(m-3,-4) is
maths-General
maths-
The shortest distance between any two opposite edges of the tetrahedron formed by planes x+y=0,y+z=0,z+x=0,x+y+z=a is constant, equal to ___
The shortest distance between any two opposite edges of the tetrahedron formed by planes x+y=0,y+z=0,z+x=0,x+y+z=a is constant, equal to ___
maths-General
maths-
In a three dimensional coordinate system P,Q and R are images of a point
in the x-y the y-z and z-x planes, respectly. If G is the centroid of triangle P Q R then area of triangle AOG is (O is origin)
In a three dimensional coordinate system P,Q and R are images of a point
in the x-y the y-z and z-x planes, respectly. If G is the centroid of triangle P Q R then area of triangle AOG is (O is origin)
maths-General