Physics-
General
Easy
Question
A mountain climber is sliding down a vertical rope. Her total mass including the equipments is 65 kg. By adjusting the friction on the rope, she controls the tension force on the rope as a function of time is shown in the fig. The speed of the mountaineer at the end of 2 sec if she starts from rest is ![open square brackets T a k e blank g equals 9.8 m s to the power of negative 2 end exponent close square brackets](data:image/png;base64,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)
![](data:image/png;base64,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)
The correct answer is: ![4.5 m s to the power of negative 1 end exponent](data:image/png;base64,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)
Related Questions to study
physics-
The minimum value of mass m required to lift the load M shown in figure is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFMAAABsCAYAAAAWno54AAAItElEQVR4nO2caUhUbRvH/45rao6ouWWkjPsQllaUEJakhB+CvmRBVkKK4r4wSkoqpknSuBSiRBT6qKAmFQhRmIlIDIIkWKZoWi6ZWmrm3ni9H543X3rVnHHu8eh4fh/Pdc65/vzmvs/MWeZoERGBhwkCrgNoErxMhvAyGcLLZAgvkyG8TIbwMhnCucyhoSHMz89zHYMJnMqUyWTw9/eHVCrlMgYzOJXZ398PfX195OXlYWhoiMsoTOB8mhsYGCAsLAzJyclcR1EZzmUCQHJyMhobGyGTybiOohJbQqahoSFycnIQHR2N7XzdZUvIBICLFy9CT08PpaWlXEfZMFtGJgAUFBQgJSUFU1NTXEfZEFtKpqenJ86cOYOsrCyuo2yILSUTALKzs/Hw4UP09PRwHUVptpxMS0tLSCQSxMfHcx1FabacTACIjo5GZ2cnXr58+df1ZmdnNymRYmxJmbq6upBKpYiNjcWvX79W1AcGBhAUFITQ0FAO0q3NlpQJAAEBAbC3t0dRUdHysrm5Ody8eRNubm4QCARoaGjAP//8w2HK/4MY0N3dTTKZjBYXF5Xarrq6mry9vdesf/jwgSwtLWl0dJRqa2vJwcGBjh8/Ti0tLUREVFVVRba2tjQ1NaVSflaoLDM3N5cyMzOpoqKCnJ2daXZ2VuFt15NJRBQREUFOTk5kbW1NpaWltLS09Efd19eXJBLJhrKzRmWZGRkZ1NHRQePj42RlZUWdnZ0Kb6uIzImJCTIwMKDIyMhV6+3t7WRoaKhUX3Wh8jEzKioKjY2NKCsrg7a2Nosjzx8IhULcuHEDJSUlGBkZWVEXi8UICQlBTEwM895Ko+qn4enpuTwqRCIR85FJRCSXy8nKyop8fX1XrU9MTJClpSU9ffpU4d7qQOWROTg4iBcvXqC6uhrT09Pr/jbcCAKBAKWlpWhsbMSbN29W1IVCIW7duoW4uDjMzc0x768oKst8/PgxJicnceTIEeTl5cHDw4NFrhX4+/vj8OHDuHDhwqr14OBgWFhYIDc3Vy39FYLLaaHoNP/N58+fSUdHh+7du7dqXSaTkZGREX369IlVRKXYsj/aV2Pfvn24evUqJBIJZmZmVtQ9PDzg7e2N9PR0DtJt4TOgtSgsLISWlhYiIiL+WF5bWwuxWAyhUIiUlBRuwnEyH/6LstP8N8XFxaStrU29vb309u1bOnXqFB08eJBev36thpSKsy1lEhHZ29uTk5MT2djY0P3790kulzNOpzw6io7gV69e4f379wCAXbt24dKlS9DX11fbjFmPqqoq+Pr6oqOjA3Z2dpzl+IP1bH/79o2CgoIIAAGgAwcOUHt7O5NPUpWRSUQUFhZGCQkJTLKwQIto7Xurz549Q2hoKL5+/QoAcHR0xKFDhxQ6bfTy8kJiYuJf16mpqUFeXh6am5uVGgC/GRsbg1gsRlNTE5ydnTe0D5b8dZq7u7vD1dV1Webi4iKcnJxgbm6+7o5FIhGbhH/BwsICKSkpiIuLQ11dndr7rct6Q1cul1NRUREZGxsTADIxMaHy8nIm00LVaU5EtLi4SO7u7lRXV8ckkyqs+wUkEAgQHh6Oc+fOob+/f3n5/Pw8p19Av9HR0UF+fj6ioqLg5+cHXV1d7rIouqK1tTWsra3VmWXD+Pn5wcXFBYWFhUhISOAsx7Y7A1oLqVSK27dvr3rNc7PQGJkikQjBwcG4fv06Zxk0RiYApKam4vnz52htbeWkv0bJNDY2RlZWFqKjoznpr1EyAeDy5ctYXFxEZWXlpvfWOJlaWlq4e/cukpOTV73mqU40TiYAHD16FCdPnkROTs6m9tVImQCQk5OD4uJi9PX1bVpPjZVpY2ODhISEdS+2sERjZQJAXFwc2tra0NDQsCn9NFqmnp4e7ty5g5iYGMjlcrX302iZAHD27FnY2NigpKRE7b00XiYA5OfnIzMzE+Pj42rtsyNkurm5ITAwEGlpaWrtsyNkAkB6ejqqq6vx7t07tfXYMTJNTU2RlpaG2NhYtfXYMTIBIDQ0FKOjo3jy5Ila9r+jZAoEAhQUFCAxMVEtb1/QCJl9fX3o6uoCACwsLEAmk2FpaQkAIJfLUV9fj58/fwIAfHx84Onpiby8POY5trXMubk5pKWloaurC46Ojpifn4dEIoFQKFy+4v7o0SO4uLigvLx8+e/Xubm5kEql+PLlC9M821pmfHw8xGIx/P39IRAIUFtbC1NTU7i6umJ4eBg9PT3Q19eHjY0NzM3Nl8+C9u/fj/DwcOZvX9i2MmdmZlBWVobZ2VmcOHECbW1t+PjxI4RCIYB/n+Vsa2tDQEAAampq4OXlBR2d/92MTUpKQn19Paqqqphl2rYyh4eHIRaLceXKFURFRSE7OxsCgQAGBgYA/pVNRDAzM0NgYCAcHByWt/3+/TskEgnGxsYQGxvL7O0L21amnZ3d8rR1dHTE7t27cfr06eW30IyNjcHHx2fFdk1NTXB3d8fk5CQGBwchEonYvX2By8dJVH08Jj8/n6RSKaWmplJ/fz8tLS2RVCqliooKqqysXLF+S0sLmZiY0IMHD5aXtba20t69e5n8ZXBby1SWY8eOUUZGxorl165do6SkJJX3v2Nkjo2NEQAaHBxcURsZGSFLS0vq7u5Wqce2PWYqy8DAAMzMzGBra7uitmfPHiQlJan8nNKOkamnp4eFhYU161FRUQq9feFvrPnk8Pnz59HZ2bnhHSvCzMwMpqamYGVlpdY+ALC0tITe3l7Y29uv+eTz9PQ0AMDIyEipfYeEhCAyMnJtmc3Nzfjx44eSkXcmjo6OcHJyWlsmj/LsmGPmZsDLZAgvkyG8TIbwMhnCy2QIL5MhvEyG8DIZwstkCC+TIbxMhvAyGcLLZAgvkyG8TIbwMhnCy2QIL5MhvEyG8DIZwstkCC+TIbxMhvAyGcLLZAgvkyG8TIbwMhnCy2QIL5MhvEyG8DIZwstkCC+TIf8BBvy/ta3DkLkAAAAASUVORK5CYII=)
The minimum value of mass m required to lift the load M shown in figure is
![](data:image/png;base64,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)
physics-General
physics-
One end of a light inextensible string is attached to a ceiling. The string passes under a smooth light pulley carrying a weight C and then over a fixed smooth light pulley. To the free end of the string is attached a light scale pan in which two weights A and B are placed with A on top of B as shown. The portions of the string not in contact with the pulleys are vertical. Each of the weights A and B has a mass M and the weight C has a mass 5M. If the system is released from rest
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)
One end of a light inextensible string is attached to a ceiling. The string passes under a smooth light pulley carrying a weight C and then over a fixed smooth light pulley. To the free end of the string is attached a light scale pan in which two weights A and B are placed with A on top of B as shown. The portions of the string not in contact with the pulleys are vertical. Each of the weights A and B has a mass M and the weight C has a mass 5M. If the system is released from rest
![](data:image/png;base64,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)
physics-General
physics-
A heavy spherical ball is constrained in a frame as in figure. The inclined surface is smooth. The maximum acceleration with which the frame can move without causing the ball to leave the frame:
![](data:image/png;base64,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)
A heavy spherical ball is constrained in a frame as in figure. The inclined surface is smooth. The maximum acceleration with which the frame can move without causing the ball to leave the frame:
![](data:image/png;base64,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)
physics-General
physics-
A string is wrapped round a log of wood and it is pulled with a force F as shown in the figure Choose the correct statement(s)
I Tension T in the string decreases with increase in q
![I I blank T e n s i o n blank T greater than F blank i f blank theta greater than pi divided by 3](data:image/png;base64,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)
![](data:image/png;base64,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)
A string is wrapped round a log of wood and it is pulled with a force F as shown in the figure Choose the correct statement(s)
I Tension T in the string decreases with increase in q
![I I blank T e n s i o n blank T greater than F blank i f blank theta greater than pi divided by 3](data:image/png;base64,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)
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physics-General
physics-
A child is swinging a ball of mass M around on a light spring which has spring constant k. The ball describes a horizontal circle a distance h above the floor. The stretched spring has a length l and makes an angle q with the vertical as shown below. The acceleration due to gravity is g. Neglect air resistance.
A child is swinging a ball of mass M around on a light spring which has spring constant k. The ball describes a horizontal circle a distance h above the floor. The stretched spring has a length l and makes an angle q with the vertical as shown below. The acceleration due to gravity is g. Neglect air resistance.
physics-General
physics-
Slider block A move to the left with a constant velocity of 6 m/s. Determine
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)
Slider block A move to the left with a constant velocity of 6 m/s. Determine
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)
physics-General
physics-
An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is :
![](data:image/png;base64,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)
An ideal monoatomic gas is carried around the cycle ABCDA as shown in the figure. The efficiency of the gas cycle is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIYAAACMCAYAAAC54tH3AAAaP0lEQVR4nO2d23MT5/nHP7s6y9bZknyWT9jYMmACTUIpdgiUNCRNJ+m00zadtBfNNHed3PSmf0LbXHV6nHZ60elM2qSZTsqQNCElARIKjjEYgg22sC3ZWJZsWZJ1PuzvgtEWJyLBxsYWv/3MMIOltffd3e++7/O+z+EVJEmSUFD4FOJmN0Bha6IIQ6EsijAUyqIIQ6EsijAUyqIIQ6EsijAUyqIIQ6EsijAUyqIIQ6EsijAUyqIIQ6Es6rX8kiRJfNr3JggCgiB87vH5fB6NRnPH4xS2DmsSRiQSIRgMEo1GEQQBnU5HbW0tNpsNnU73meMTiQRjY2O88cYbvPjii3g8nntuuMLGsiZhGI1GAoEAp0+fpr6+ns7OTt59911cLhcDAwMrHrwkSYyNjfHrX/+a999/n+7ubgwGAy6Xa90uQmH9WZONodfryeVyhMNh8vk8LpeLfD7PhQsXOHv27IpjA4EAH3zwAcePH8fn8/H6669z6dIlcrnculyAwsawZuNTp9NhsViw2+14PB62b99ONptlbGxsxXGffPIJp06dIhQKodVqee+997hw4QKxWOyeG6+wcdzTrESSJLLZLMlkklAohEajoba2dsUxfr+fmZkZampqqKmpIZfLMTs7SygUuqeGK2wsa7IxSsTjcQYHB1leXiabzfK1r32NRx55ZMUxgiDQ1tbGvn37uHDhAsvLy9jt9ntqtMLGc0/CMBqNNDc3c/DgQQwGAxaLBYvFsuKYbdu2USwWMRqNXL16lW9961ts374drVZ7Tw1X2FjWLAxJkhBFEZvNRnNzM9XV1WWP6+rqwmq1MjMzgyAI7N27l7a2trLTWoWtw5qEkclkyGQy5PN5+f9GoxFR/KzJ4na70Wg0zMzMAGAymZSpagWwJuNzeXkZAJvNhkqlIp1OUygU1rVhCpvLmnoMu93OE088weHDhxFFEbVarSxzP2CsSRiCIKBWq1Gr78l2VdjCKN5VhbJU3CtfKBRWeHZFUSxr9CrcGxUlDEmSiMfjzM3NkU6ncTqdqNVqUqkURqMRs9mMXq/f7GY+EFSUMAAmJiZ45ZVXGBsb48c//jEAH374Ib29vRw9epTu7u5NbuGDQUX1wYIg0NPTQ2trK62trTz33HM899xzfO973+PGjRu89tprm93EB4aK6zEMBgM6nQ6dTofD4QCgWCySTqcVV/46UnHCgFu2xtLSEsPDwySTSU6cOAFAR0fHJrfswaEihQG3wgV9Ph+Li4sEg0G5J1leXr6j30bh7qkoG6OEIAg0NDTw3HPP8aMf/YhXXnkFnU7H3//+d3w+32cClTcLSZIoFovkcjl5mr1V2vZFVGyPcTtmsxmr1crCwsKWuvHJZJLZ2VkmJydpamrC6XRiMBjQaDRoNJrNbt7nckdhSJLE8PAwk5OTVFVV4fV6qa+vJxQKcfHiRcLhMFqtFoPBgMPhoLOzE5vNtqGNlSSJiYkJQqEQ4XCYN998E51Oh9/vp1gsMjAwQEtLy5bw25w+fZqJiQmMRiPd3d1kMhn+/Oc/y/ErNTU1m93Ez6WsMAqFAtFolGQySSwWY2xsjMnJSV588UW0Wi3j4+PcvHmTjo4ObDYb77zzDsFgkD179tDQ0LBhjRUEAYPBwKFDh+jr68PhcKDRaCgUCrS0tODxeD4TKPRpcrkcPp+PK1eusLS0hFqtpre3l/b29i/83btBkiQCgQCnTp2iUChw8OBBmpubSSaTuFwuBEEgHo9XpjCKxSKZTIaGhgYMBgOhUIihoSEEQcBqtcpBOs3NzezcuZM33niDkydPUl1dXVYYpWSjYrFILBaTexu9Xk80GgWgurqaYrFIMplErVZjMBhIpVJIkoRGo0EURZLJJCaTif7+fhKJBOl0GoPBQHNzs9xLzM/Pf+4FZzIZxsbGOHHiBCMjI8Tjcfbv38+BAwfo6enB6XQiiuKqex2NRoPBYEClUjE4OIjf7+ehhx5iz5496PV6zGYzTz31FEtLS1t+GIE7CEOj0VBXV0ehUMBsNtPV1bXiRqlUKtk/odVq6e7u5vz58wSDwbInyefzpFIp8vk8Y2NjhMNhXC4XLS0tfPjhhwiCQG9vL7lcjrGxMSwWCx0dHUxMTJDL5XA6neh0Oq5du0Z9fT3xeJzR0VFmZmZobm7GYrGsytNbKBRob29nfHycjz/+mOHhYY4fP05/fz+PP/44RqNxVcKQJAmHw0FHRwdOp5Nz585hMplobW1dsURvt9ux2Wxbyg66E597N0OhEH/9618JBAJ85StfWfFdNpslEokQCAQ4ceIE3d3dbNu2rezfyefzcsDw0NAQ+Xwer9eLwWDg2LFjCIKA0WgkkUhw7NgxmpubMRgMnD59mkQiQU9PD2azmX/961/s3buXmZkZTp48yezsLB0dHVit1lUJoxTdnk6n0Wq1ZDIZ+Tpu3ryJ3W5flWMulUrh8Xg4cuQIBw8eZHl5GbPZXDZ88fNSObcSn3s3bTYbBw4c4NixY7z11lv09/fLBmYikcDv92M0GvnhD39Ie3s7TU1NRCIRrl27Ri6Xw+v1YrPZ0Gq12O129Ho9Tz31FE1NTVRXV2Oz2Xj55ZcBqK2tJZ/P09nZiV6vx+FwyIlM1dXVqNVqOjo6MJvNnDx5knA4zNGjRzl48CB6vf6ub7YkSYyOjnL8+HGuXLlCIpFg586dPPnkk/T391NTU7Pqrv79999nfn6eVCqFIAjU19cTDoflYbJcG7a6OD5XGDqdju7ubnw+H/Pz84RCIUwmE3ArG83lctHW1obD4cBkMrG4uMiNGzcIh8NoNBquXbtGS0sLGo0GnU6HWq2msbGRnp4e+Rxer3fFOd1ut/x/q9W64rtSrKjVasVut9PV1cVDDz20qgeZy+XQ6XSk02lcLheiKOL1etm7dy/t7e1ril6/fv060WiUYrGISqVi3759vPrqq4yPj7O0tCRfRyQSIZfLYTAY5Pu4VSkrjHw+TyQSQavVolarcblceDwetFotgiDIWetut3vF8OH3+xkbG6O+vh6Xy8XQ0BCiKNLe3n7fLuhucLvdHDp0iEOHDqHRaLBaresWtS6KIn19fXJvdO7cOWpra9HpdOTzeXmFdqtTVhjZbJbx8XG0Wi1VVVXkcjnq6+tpaWlZEShTKBQoFAqoVCoAwuEw8/Pz9Pb2UldXx8zMDC6Xa0sJQ6PRYLPZNmzNpTRze/755zl37hzDw8MYDAbsdjsdHR243e51mRZvNGWFUVovuHjxIkajke3bt/PYY48hiiKBQICWlhZ5DSEej2M2mxFFURZNyar//+zxtFqtHD58mEOHDsmfVYrhCXcQhk6no7Ozk4aGBkRRxGg0ygVPamtrsVgsFAoFNBrNinySuro6YrEYCwsLFItF2traqKuru68XtJWo5JDDssIoicFoNH7mu1IsRDk8Hg+SJOH3+4lEIvT29tLa2rq+LVa4L6yrE81utyMIAsVikUKhIK8xLC0tredpFO4D6yoMQRCw2+1KNvsDQOUOggobiiIMhbIowlAoS0UKI5fLyWUYKsFTWYlUnDAkSSIajRIIBLh58+amCUOSJAqFAuFwmFQqBdxaMZ6dnSWfz29Km9aTihNGKpVicnKSjz76iFOnTpFMJjdFHCXX/alTp5ienkaSJMLhMP/617/k+iGVTMUFA584cYJz587JpZsGBwd5+OGHN83/8Pvf/x6tVkt7ezt+v59z585x5MiRz3iGK42KEYYkSaRSKY4dO8aFCxcoFouEw2H+8Ic/0NjYuGnCCIVCLC4uMjMzQzqdJhqNPhDVhSpOGJOTkxSLRdlje+nSJeLx+H1vT6l4TH19PX6/n1AohNFoxOv1PhAVCSvKxigUCnJs5e7du3n44YfvWBRuoykJ4/Dhw9TV1ZFKpTCbzTz77LMPRCZcxfQYcOthHDhwAKfTSVVVFQ0NDVRVVW1aNJQgCHznO99haGgIv99PV1cXL7zwwpaPzrobKqbHKAUMf/vb32bfvn0IgoDT6eSnP/3ppm5z4XQ66enpYf/+/ezbt0+OTal0KqbHKAUP6fV6OSRfrVbLYXOb2a76+np6enrweDwVE4jzRVSMMOB/gS+3v5GlONTNRK/XU11djcFg2NR2rCeV3+dtATZbmBvBlu4xSmmNpSKzCvePLX23I5EIyWQSvV6/It9EYePZ0kPJmTNn+Mtf/sK777672U35f8eWFUYulyMSiXDx4kXOnj0rZ74r3B/ueiiRJIlcLkcgECAej1MsFuXCKQ0NDes6OygWi0xMTGC322lsbCQWi3H58mV27dpVEcvNkiSxsLBALBaT82oEQcBsNmOxWCpi9rJqYYyPjzM8PIxWq6WpqYlsNovH46G7u3vdsrsKhQLnz5/H4/Gwf/9+BgcHOXbsGJ2dnRUhDIDFxUUGBwcJBoN0dnYiiiIGgwGj0YjD4aC5uXlL18m466GkdGEul4upqSlEUeThhx8mGAzys5/9TPZ43iulOIfJyUmCwSAmkwmj0cjx48eJxWLrco6NplQ8zufz8dZbb7F792527tzJ/Pw8f/rTn/jNb35DMBjc0teyahtDp9Oh0WhQqVTU1tbyzDPPMDs7y8TExLrkjyQSCUZHR2lsbMTpdFJXV0dnZye1tbUMDg6yuLh4z+e4HxgMBvmfy+XC7XZz9OhRnnnmGURR5Fe/+hXpdHqzm3lHVjVdFQRBXnWUJIlEIsH169cxGAxYrdZ1KfAei8X473//y4EDB6irq0On0yGKIo8++ijvvPPOuhV5LbnxP/jgA2ZnZ8lkMrjdbh599FFqa2vv2d9R2hWh5IWFW+Wkuru7uXz5Mq+99hovv/wyer1+S/pW1rwn2szMDJ988gmhUIjvf//79Pb2IggCoVCIaDSK2+3GaDTKmfClmpelfVpLi1bZbBZJktBqtaRSKaanp5mbm0Ov16PValGpVFRXV1NXV8fo6CiBQICFhQU5KCYajWIwGFZl+CaTSW7cuMHp06d5//33iUajtLW1MTAwQC6XI5FIrLqiTi6Xu6uhwWKxYDabmZ+f39LBzGsSRrFYJJFIkEqlaG5u5qmnnsJkMuH3+5menkaj0RAMBvF6vVitVgqFAplMhmw2y+joKMFgEIvFQlNTE1euXCGVSrFz504ikQjvvfcei4uLLC4uMj09TS6Xk4cuuFWkZG5uDp/PRzweRxAETCaT/P0XUYrNHBoa4p///CfBYJDq6mqqqqpYXFzk448/XvX9GB4eZmlp6a68vCUBWa1WOVF8K7IqYZQq2xoMBrZt27YixT+fzzM8PIzf7+f555/nF7/4BQ6HQ86MTyaTJBIJ/vOf/7CwsEBHRwdHjhzhj3/8I8FgkJ/85Cckk0nefvtt3G43kiTx5ptv4vf72bNnD729vczNzREIBJidnWVkZIREIsFHH320omf6IorFIvF4nHA4LBuzkiRx5coVAoHAmqaS0WgUh8PxmRpkn+4N8vm8nPC9Z8+eTQsyuhtW3WPcvrXm7cRiMSKRiGxQLS0tEY/H5TfearVis9l48cUX2bZtGyqVCp1Ox549e+QNewGOHj2KKIpy0dlSuQW1Ws2BAwdQq9WcPn2anTt3sm3bNr785S+vetqXTqe5fPkyv/3tb/n3v/9NIpHgoYce4oUXXuDpp5++a5GVOHnyJIFAYIUwSkVlbhfH1NQUb7/9Nn6/n5deemlLb7pz18Iobf0QDAZpaWmhpqaGubk5eS/3kiBKhdJEUSSRSJDJZOSfS+UVbo+g/vS6xO0369MPvBR3sW3bNqqrq3G73dTU1Kz6QRaLRaqqqnA6nRw6dIjZ2Vl5h6RsNkttbe2q/mapglApmVuSJG7cuIFWq6WhoYHXX39d/nzHjh0cOXKEnp6eVbf7fnLXwihZ121tbTidToxG44put6qqCqPRSDKZBG7VAi3VzV7vqjqRSES2Zdra2lb9+6IoYrFY2LVrF263m2g0Si6XQ6/Xr7rGJ8DCwgKBQGDFZyaTiQMHDrBr1y6qqqqAWy9BTU0NNTU1W74O16qEodVq7zhdNJlMuN1ukskkoVCIpqYm+QaUxLJexONxQqEQLpfrnqx6URSpr6+nvr7+ntpTqnZcSmEQBAG3213RHuF1c7uLokhrayuSJDEzM0N/fz9Op3NDrG63201XV9e6rDesB3V1dYiiWNFC+DTrGo/h8Xhobm6Wf96oqZhWq8VoNG6Z7rjUnkrx49wN6/q63W5krqVQ+90yNTXF+fPnuXHjxpbwN/h8PoaGhrhx48ZmN2Xd2NIRXHfCZrPR2NiIzWbbEgtEdruddDr9QJWY2vwBeg2Uppomk2lLCMNkMsllsx8UKrLHiEaj8trDVvA1LC0tMTc390AFLFfklYRCIcbHxzGbzVtCGMFgEJ/P90AZnxUpjB07dqx51XMj2L17Ny0tLRu+J9z9pCJtjNJQsrS0tCV6jEgkwtzcHJFIZLObsm5UZI8xPz/P+Pg4er1e3iNkMykNJVvBEF4vKlIYpc3nVhugs1GUNqbZiOjvQqHA8vKy7KktReZvtKFbkcLYsWMHbW1tq4rD2Ej6+vrYvn37hqzEplIprl69SjgcJpPJUFNTQ1tbG263e0MDfSpSGBcuXGBkZISenh76+/s3PQy/tArb2trKV7/61XX922q1GqvVyu9+9zs++ugjMpkMO3fu5KWXXqK/v1/23K43gnQfrLdwOMyZM2f45S9/Ke+IeC/4/X7C4TAOh4PGxsZNd6RNTU0RjUaxWCzrXsSlUCjIvYbP52NhYQGtVktXVxdPPPEE3/3ud+ns7Fz3nuO+9Bg6nY6GhgaefPJJ4N6dayaTiXw+j1qt3vTeAv63mbBKpdqQ9pRybebn55mfnyedThOLxTCZTBu2dnJfhGEwGOTNareCsVhJZLNZbt68STqdxuFwUCwWaW5u5rHHHuMb3/gG9fX1G3JP74swSuPkWouiltIOstksgiDISU/wv7riKpVK3vVxI8lms2QyGQqFgrzbU+mNzuVyckkolUolp3VmMhk0Go2cDrEaIpEIIyMjpFIpent7aWpqYt++fQwMDGzoS3ZfbIx7JRqNcuXKFUZGRtDr9fT19eH1eikWi1y/fp2hoSFcLhe9vb1l95ZfT0ZGRjh//jwLCwt86UtfYteuXWQyGT755BPGxsYwGAwcPnwYt9tNKpXi+vXrDA4O0tHRQV9fHw6HY1XnkySJfD4v56CU8nE2+gWoiJXPqqoqPB4P169fZ3p6mnQ6jUqlQq1W4/F4WFpaQhTFVd/01TI+Ps7ExIS8U+TPf/5zzpw5I/8cCoW4ePGi/PCMRiN6vZ5gMEhra+uq6n8mEgkuXrzIq6++ymuvvUYwGESlUsk7Wf7tb3/jxIkThEKhDbnWihCGWq3GbrfT19fH7OwsgUBA3nttaWmJuro6amtrNzwcv1Qz/NFHH2Xv3r14PB6mp6dZXl6mubkZj8fDxx9/TCKRkAOIVCoVFosFu92+KkNRo9EgiiLBYJBjx46RzWZlYeRyOXw+H9XV1RsWxVYRwoBbD6WUQjg9Pc3S0hLZbJaRkRHa2to2fAgBcDgcdHV14fV6aW9vx+v1Ul1djSiKuFwutm/fTrFYZHx8nFgsxuLiItFolB07dqxq/3m4db21tbU0NDQwOjoqi63UUwqCgMfj2bB1jIoRhkqloqmpiebmZpaWlhgdHSWTyTA+Pk5NTQ02m00ej2OxGKlUat2LvVdVVaHVauUcm3g8jtfrxeVyyTVHDx48yNmzZ5mZmWFmZoa5uTn27Nkj9xaZTIbl5eW7qhBUU1NDd3c3er2e69evE4lEyGQy5HK5z+QGrzcVI4wSAwMDSJLEBx98QDqdRqfToVKp5KElEolw6tQpRkdHicViG9KGRCLB4uIibreblpYWOXLL6XTy7LPPcubMGfx+P+l0mnQ6jcViQRRFeU/a8+fPMzo6+oXCFQQBh8PBN7/5Tc6ePcvU1BSzs7NMT0/zyCOPbOjQWXHC6Ovrw2g08uGHH/Lee++xb98+OQ7i6tWr/OMf/2D37t0MDw8zPj5ONptd1/NnMhlmZ2eZm5vj61//+ortMPR6PW1tbbhcLs6ePcv09PSKldDTp0/j8/mQJImxsTF8Pp+8O9KdsNlsPP3001y9epWpqSlCoRCRSITW1tYNXdyrOGGYzWba29uxWq1cuXKFhoYG+c2Zn5/n0qVL8sbAwWBwXa32TCbD5cuXuXr1KpIkyecLh8MAcs7twMAAU1NTzM/Pr8hnvXTpEqFQCKfTiV6vZ3h4+Au31NBqtTQ2NtLa2srExARjY2PodLpV2yyrpeKEIQgCXq+Xxx57jPr6eqqqqmRfSSaTIRqNylPFeDy+rhV45ubmuHbtGpOTk8zPzzM4OMjs7OyKyjgqlYqBgQE5Ier2yPFgMEgmk8Fut1NdXY3P5/vCLL3Sgt7jjz/O9PQ0U1NTa0rLXC0V6V1tbW3FarWyvLy8YqFHo9HIWfOl6eJ6vlXLy8sYDAbMZrOcj+tyuVbMDERRpLOzk2efffYz8SJqtRqtVosoihQKhbt2/gmCwP79+zl37pxcgmKjqUhhlGpbfZqqqipqa2spFArE43FaWlruOS/1drxeL16v9wuPE0WR7du3f+bz1tZWTCYT4XCYeDzOjh077srTLAgCdXV1/OAHP0Cj0dyXDLyKWBK/W2ZnZ7l8+TKFQoFYLEZfXx8dHR1bIpgHYHp6Gp/Px82bNwF44oknsFgsd92+kiF9P6LRHyhhZDIZ4vG4PObbbLYNWwBaC9lsllgsxvLyMqIo0tDQsGVE+2keKGEorB8VNytRuD8owlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoiyIMhbIowlAoy/8BKa25g5Fy/NoAAAAASUVORK5CYII=)
physics-General
physics-
A body of mass m starts sliding down a movable inclined plane of mass 2m at t = 0, assuming friction is absent everywhere the kinetic energy of 2m as a function of time is (m remains on 2m) best represented by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJEAAACHCAYAAAAWV7ulAAAUSElEQVR4nO2deVhU1f/H3wyYjrKIoZnmklbgErLL5ggCgmulpA6gIlKGuaYVZT6WC1m5PS4okkumho8Bpj4gCBKCiAKyiKmYEVKikqMwIDDMzPn90S++TeciM3MHBvC8nmf+4H3P/ZzPvbzP55y5M3OvASGEgMHggUDfCTA6PsxEDN4wEzF4w0zE4A0zEYM3zEQM3jATMXjDTMTgDTMRgzed30REru8MOj2d20TKh4CBkb6z6PR0XhMpylGUlKHvLJ4JDNgHsAy+dN5KpGeuX78OmUym7zTaBGaiViA+Ph4zZszAlClTUFdXp+90Wh1mIh1CCMHatWsREhKCtWvXghCCSZMmoba2Vi/5/PXXX23SD1sT6YgnT54gODgYBQUFOHnyJKysrNDQ0AB/f39IJBIkJibC1NS0TXKRyWRYsWIF6uvrER0d3er9sUqkA+7cuQM3Nzc8fvwYly5dgpWVFQCga9euiIuLQ79+/eDl5QWJRNLquZSUlMDFxQWxsbEwMmqbyxvMRDzJzMyEo6Mjxo4di8TERJibm6ts79KlC2JiYmBpaQlPT09UVla2Wi779++Hg4MD/Pz8EBQUhK5du7ZaXyoQhtZER0cTY2Njsm/fvhbbKhQKMn/+fDJs2DBy9+5dnebx6NEjMmPGDNK/f39y7tw5QgghH3/8MVm6dKlO+2kOVom0QC6XY/Hixfjss8+QlJSEkJCQFvcRCASIjo6Gp6cnRCIR7ty5o5NcLly4ABsbG8hkMhQVFcHT01MncTWBmUhDJBIJ/Pz8cOHCBeTk5MDV1VXtfQ0MDLBr1y688cYbEIlE+O2337TOQ6FQ4IsvvoCfnx/Cw8MRHx+PXr16aR2PD+yDJQ345ZdfMHXqVNjb2+PkyZPo3r27VnE2bdoEoVAIkUiE1NRUWFpaarT/nTt3EBgYiKqqKmRnZ2PEiBFa5aErWCVSk9OnT8PV1RXBwcE4duxYswaSyWT49ddfW4y3bt06LFy4EGPHjkVxcbHaeRw/fhw2NjawtbXF5cuX9W4gAGxhrQ4RERHE1NSUxMfHt9j28OHDJDAwUO3YW7ZsIRYWFiQvL++p7WpqakhISAjp3bs3OXXqVItx23JhzUz0FJ48eULEYjF5+eWXydWrV1tsr1Qqib29PXnuuefIgwcP1O5n9+7dxNzcnFy8eJFz+5UrV4ilpSXx8fFR+50de3fWDvjzzz8hEolQUVGBnJwcjBw5ssV9MjMzMWTIEMjlchw4cEDtvt577z1s3rwZfn5+OH/+fJNOCMGWLVsgEokwf/58JCUl4cUXX9TqeFqVNrFqB+PixYukb9++JCwsjDQ2Nqq938yZM0l5eTl58803yZAhQ4hCodCo36NHjxJTU1OSnJxM7t27R3x9fcmrr75KcnJyND0ENp3pk0OHDpEePXqQyMhIjfa7ffs2CQkJIYQQcu7cOQKAJCYmatx/bGwsEQqFxMzMjAQHBxOpVKpxDELYdKY3ampqsGfPHri5uWHBggUa7btz504sX74cAODh4QFra2vs3r1boxgymQwZGRkQCAQIDw/HgQMHYGxsrFEMfcCuE/0LY2NjREZGwsvLC/Pnz8e+ffsgELQ8zqqrq5GXl4dBgwYhNTUVADBq1CgcOXIEd+7cwcCBA1uMcePGDYjFYgiFQhQXF2Pw4MG8j6fNaJN618HIz88nvXr1IiEhIUSpVLbYfsuWLeTMmTMq2uPHj0mXLl3IqlWrWtx/7969xMTEhKxevVqjNdjTYGuidsCVK1eIubk5CQ0NfaqRlEolEYlERC6XU9smTZpEevfuTerq6jj3lUgkZPr06WTAgAEkPT1dZ7kTwtZE7QJbW1ukpKQgNjYWCxYsAOH47p5EIsEXX3yB6upq5ObmqmwrLS1FY2MjKisrsWTJElRUVKhsP3/+PEaNGgUAKCwshEgkar2DaW3axKodmJycHNKzZ0+yYMECqiIpFAoik8maXv9GLperbPunUsnlcrJ69WpiYmJC9u7d22p5t2UlYgvrFnBwcEBycjJ8fHwgEAgQGRnZtE0gEDS78DY0NIShoaGK9vvvvyMwMBC1tbW4dOkShg0b1qq5txVsOlMDR0dHJCcn48iRI1i0aJFWMWJiYmBrawsnJ6dOZSCAvcVXGycnJyQlJcHX1xcCgQDbt29Xa7+amhosWrQIiYmJOHr0KCZMmMDZTiqVorCwUGXtZWRkhAEDBqB///4wMDDQyXG0BqwSaYCzszPOnDmDgwcPYtmyZS22z8vLg52dHe7du4eioqJmDQQAJiYm6Nu3LyZPnoxVq1ZBqVSioqICixYtgqOjIy5cuKDLQ9EtbbLy6mRcuHCBGBsbk2XLlnFuVyqV5OuvvybGxsZk8+bNal1r+gdbW1syZ84clVjTpk0jQqGQlJaWqh2HLazbOa6urkhMTMSECRMgEAiwefPmpm337t3DnDlzUFZWhvT0dNjZ2WkU+7/TloGBATw9PREXF4dLly61yyvZbDrTEnd3dyQkJCAqKgoffvghgL+//WhtbY2BAwfiypUrGhuoOa5duwYjIyM4OzvrJJ6uYZWIB2PGjEFCQgImTJiAmzdvIjMzE1FRUXj77bd5xS0oKEBUVBTq6upw7do1xMfHIz4+HoMGDdJR5rqFmYgnFhYWGDBgACQSCQoKCtT6sLUlRowYgTlz5qC2thbnz59Hamoq1q1bBysrK7zyyis6yFq3sOmMB3v27IGzszNmzZqF9PR0nRgI+PtXs0KhEBYWFpg2bRrS0tKQm5uLlStX6iS+rmGVSAskEglCQ0ORl5eHhIQEuLu7t2p/AwcOhIWFBX755ZdW7UdbWCXSkJ9//hnW1tbo0qULCgsLdW6gxsZGSjt37hwePHiAefPm6bQvXcEqkZrI5XKsWbMGO3bswLZt29T66bQmSKVSpKWlobS0tKkvc3NzlJeXIycnBxEREfj444912qeuYCZSg9LSUgQEBKChoQG5ubl47bXXdN6HiYkJpk6dCqlUqvPYrQ2bzlrgyJEjsLW1haurK7Kzs1vFQB0dVomaQSqV4v3330dycjKOHTsGX19ffafUbmGViIPLly/D1tYWDx8+RFFRETNQCzAT/QulUomNGzfCy8sLixcvxunTp9GnTx99p9XuYdPZ/3P37l3Mnj0bd+/eRUZGBmxsbPSdUoeBVSIAJ0+exKhRozB06FDk5eUxA2nIM12J6uvrsWLFCsTExGDv3r2YPn26vlPqkDyzJiouLoZYLEavXr1QUFCAAQMG6DulDsszOZ3t2rULLi4umDFjBtLS0piBePJMVaKHDx8iJCQERUVFSE5OhouLi75T6hQ8M5UoNTUV1tbW6NGjBwoKCpiBdEinN1FjYyPCw8Mxbdo0RERE4OjRozAzM9N3Wp2KTj2d3b59G2KxGIQQ5Obm4tVXX9V3Sp2STluJDh06BDs7O3h4eCArK4sZqBXpdJWouroaYWFhSEtLQ2xsLLy9vfWdUqenU1WiS5cuwcbGBtXV1SgqKmIGaiM6hYmUSiU2bNgAb29vfPDBBzh16hQsLCz0ndYzQ4efzv744w/Mnj0bDx48QFZWFl5//XV9p/TM0aErUXx8PEaNGgUrKyvk5uYyA+mJDlmJ6urqsHz5cvz444/Yt28f3nzzTX2n9EzT4UxUVFQEsViMF154AYWFhejfv7++U3rm6VDT2fbt2+Hm5oagoCCkpKQwA7UTOkQlqqysxLx583D9+nWkpKRg9OjR+k6J8S/afSU6e/YsrK2t0bNnT+Tn5zMDtUPabSVqbGzEp59+iujoaOzcuRNBQUH6TonRDO3SRLdu3YJYLIahoSHy8vIwdOhQfafEeArtbjo7cOAAHBwc4OPjg8zMTE4DlZeX48iRIygtLdVDhoz/0m4qUVVVFcRiMQoLCxEfH49x48Zxtjt06BByc3MREBCAiIgIjBs3DmKxuI2zZfybdmGirKwsiMXiptuneHh4cLaTSCRYtWoVSkpKIBQKYWNjg+HDh8PDw6N9PtbyGUGv05lCocDatWvh6+uL8PBw3LhxA5mZmQgKCoJSqaTax8XF4bXXXoNQKAQAdOvWDQ4ODho/nI6hW/RmovLycnh6euL48ePIzs5GWFgYBg0ahIyMDFy7dg1Lliyh9rly5QqsrKxUNBcXF6Snp7dV2gwO9DKdxcbG4p133kFAQAA2bdqEbt26NW0zMzNDUlISrKysMHfuXDg6OjZtu3HjBoyNjRETE9OkXb9+HTdv3mzT/BmqtKmJnjx5gqVLl+LEiRP47rvvMGXKFM52ffv2xdy5c7Fx40bExsY26XV1dXjppZdU3rFdvXoVCoWi1XNnNE+bmaigoABisRj9+/dHYWEh+vXr99T2QUFB8Pb2hlKpbHocVJ8+fSAQCFSqU0pKSru8Le+zRKuviQgh2Lp1K8aMGYN58+bh7NmzLRoI+Ps5Y/X19SgvL2/SXn/9dep2dMXFxewGDHqmVSvRgwcPEBwcjFu3buHcuXMqFaQlJBIJZDKZyv2BAgMD4e7uDqlUChMTE8hkMly8eBE//PBDa6TPUJNWq0RJSUmwtrZG7969kZ+fr5GBACA7OxuWlpZNb+cBYNiwYViyZAnCwsKQlZWF0NBQfPTRR+xDWT2j80okk8kQHh6O/fv3Y/fu3VpfTY6JicG7775L6WvWrEFeXh5u376Nr776il1kbAfo1EQ3b96EWCxG165dkZ+fj5dfflmrOBkZGUhNTcXOnTs5t9vb28Pe3p5PqgwdorPp7Ntvv4WjoyMmTpyIjIwMrQ30119/ITg4GBs3bmS/me8gtFiJCCG4d+/eU9ssW7YMGRkZOHjwIFxcXFBZWalVMjU1NfD394elpSV8fHyoZ8kz1KempgYNDQ1qn8O+fftq/ZxZA0L+9eRaDh4/fgxzc3OtgjM6DlKpFMbGxlrt2+J01rNnTygUiqbXtGnTVP7+5zV9+nRKq62txaxZsyj99OnTWL9+PaWHh4fj4sWLnLEbGhrU6vP+/fsIDg6m9MOHDyMyMpLS169fj4SEBEqfNWsWamtr1T5OsVhM6adOncKGDRsofcWKFcjJyaH0OXPmoLKyktJnzJhBaY2NjfD396f0zMxMfPLJJ5S+du1anD17ljN2bW2t1gZSy0QAIBAIml5mZmY4deqUiiYQCHD37l3U19eraN27d8etW7eotr6+vvjpp58oferUqdiyZQulDxo0CIcOHaL0yspKSCQSFa1Pnz64du0a1faNN97A4cOHKd3f3x87duyg9BEjRmDnzp2UXl1djbKyMuo4S0pKqLZ+fn44ceIEpU+ePBmbNm2i9NGjR+Obb76hdLlcjoKCAhXNyMgIZWVl1P/Hzc0NZ8+e5TzObdu2Ufrw4cOxZ88erQ0EQPOnUZeUlJDx48dT+pdffkkiIiIoPTQ0lMTFxVG6s7MzkUqllO7k5ERpFRUVRCQSUXp0dDRZuXIlpfv7+5Ps7GzO2AqFgtLt7e0prba2lri4uFB6XFwcCQ0NpfR58+aREydOULqzszOpra2ldDs7O0prbGwkjo6OlJ6VlUVmzpxJ6R988AH59ttvKV0kEpHKykpK54pdVVVF3N3dKV0TtHqkOdcJqKurI87OzpT+22+/ER8fH0r/6quvyLp16yh94sSJ5MaNG5Tu4OBAGUChUHCemMuXL5Pp06dT+ocffkiioqIo3d/fn2RmZlK6o6MjaWxs5Mzlv5SUlBBfX19Kj4iIIOvXr6f08ePHk5KSEkpvznRcx3n//n0yduxYSo+KitJocDk7O3MOLnXRykQzZ84kaWlplO7k5MR50psb6aNHj6b0M2fOkLlz51L6u+++S44fP07prq6unBWN6x9dWVnJedIvX75M3nrrLUoPDw8nkZGRlO7h4UEqKioovbnj5BpcP/30EwkODqb05gbXhAkTmh1c/0XTwbVy5Ury/fffU7q6aGWivLw8MmXKFEr/7LPPyPbt2yk9ICCApKSkULqTkxOpq6ujdK4T8/vvvxNvb29K37x5M1mzZg2lT5o0iRQXF3P2yQWXAR4+fEjGjBlD6d999x1ZsmQJpc+cOZOkp6dz9qluRWuuoickJHAOrvfee48cO3aM0jUZXPfv3+dcoqiLViYihPukV1VVETc3N0q/evUqmTRpEqWvXr2abN26ldK9vb1JWVkZpXONroaGBk5jJCcnk9mzZ1P6woULSUxMDKVPnjyZFBYWUjrXSW9Oz8/P5xxcn376KefgGjduHCkvL6d0TUxXVlZGvLy8KL25wTVx4kTOwcU1WNRFaxNNmTKF5OfnUzrX2oUQbtM9evSIuLq6UnpMTAwJCwuj9NmzZ5MzZ85QuiYVrby8nLOipaSkkICAAEpfvHgxZ6l3d3cnjx49ovTmjpNr8Xr48GGyaNEiSl+9ejXZtm0bpXt5eXEOLq4+GxoaOJcLycnJJDAwkNLDwsJIcnIypauD4eeff/65Nu/qbGxsUF9fT91U4aWXXkKvXr3QvXt3Fd3MzAzDhw9XuSrarVs3dO3aFdbW1iptR44cierqaup+Q3Z2dpBKpRg8eLCKPnToUAiFQpiamqroPXr0oGKbmpqiS5cuVOwhQ4agvr6eam9vb4/q6mrqi2+WlpYwMDDA888/r6KbmJhgxIgRah2ntbU1qqqqqFzs7e3x+PFj6vvkI0eOhFwupx6f9fzzz2PIkCEwMvrfBxCGhoYQCoVUn0OHDkVdXR2l29rawsjISKtHc7V4xZrBaIl29wtYRseDmYjBG2YiBm+YiRi8YSZi8IaZiMEbZiIGb5iJGLxhJmLwhpmIwRtmIgZvmIkYvGEmYvCGmYjBG2YiBm+YiRi8YSZi8IaZiMEbZiIGb5iJGLxhJmLwhpmIwRtmIgZvmIkYvGEmYvCGmYjBG2YiBm+YiRi8YSZi8IaZiMEbZiIGb5iJGLxhJmLw5v8AOzWyKAPNA1QAAAAASUVORK5CYII=)
A body of mass m starts sliding down a movable inclined plane of mass 2m at t = 0, assuming friction is absent everywhere the kinetic energy of 2m as a function of time is (m remains on 2m) best represented by
![](data:image/png;base64,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)
physics-General
physics-
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,iVBORw0KGgoAAAANSUhEUgAAAI8AAACMCAYAAABF9/o9AAAUWElEQVR4nO2de1RUVRvGHwZIR7kIoVmmlpbgDbnLzREEAi+oKakDqIikUWiWVpS5zEtkpeYyQ5G8pobLAFMXCIKEIKKAXMRUzAgpUclRGBAYZmZ/f1T00T7IzHGGAdy/tfiD5+zz7vecefa795yZOUePEELAYPBAoOsEGF0XZh4Gb5h5GLxh5mHwhpmHwRtmHgZvmHkYvOne5iFyXWfQrem+5lHeA/QMdJ1Ft6Z7mkdRiZKULF1n0e3RYx9PMPjSPSuPjrly5QpkMpmu09A6zDwaJjExEbNmzYK/vz8aGhp0nY5WYebREIQQrF27FqGhoVi7di0IIZg8eTLq6+t1ks+ff/6p9T7YmkcDPHz4ECEhISgqKsKxY8dgZWWFpqYmBAQEQCKRIDk5GSYmJh2Si0wmw/Lly9HY2IjY2Fit9sUqz2Ny8+ZNuLm54cGDBzh//jysrKwAAD169EBCQgKee+45eHl5QSKRaD2XsrIyuLi4ID4+HgYG2r9MwczzGGRnZ8PR0RHjx49HcnIyzMzMWm03NDREXFwcLC0t4enpierqaq3lsnv3bjg4OMDPzw/BwcHo0aOH1vpqgTB4ERsbS4yMjMiuXbvabatQKMjChQvJ8OHDya1btzSax/3798msWbPIgAEDyOnTpwkhhHzwwQfk7bff1mg/XLDKoyZyuRxLlizBxx9/jJSUFISGhra7j0AgQGxsLDw9PSESiXDz5k2N5HL27FnY2NhAJpOhpKQEnp6eGomrKsw8aiCRSODn54ezZ88iLy8Prq6uKu+rp6eHb775BtOmTYNIJMKvv/7KOw+FQoE1a9bAz88PkZGRSExMhLm5Oe94fGEf/qjIzz//jKlTp8Le3h7Hjh1Dr169eMXZuHEjhEIhRCIR0tPTYWlpqdb+N2/eRFBQEGpqapCbm4uRI0fyykMTsMqjAidOnICrqytCQkJw+PDhNo0jk8nwyy+/tBtv3bp1ePPNNzF+/HiUlpaqnMeRI0dgY2MDW1tbXLhwQafGAcAWzO0RFRVFTExMSGJiYrttDxw4QIKCglSOvXnzZmJhYUEKCgoe2a6uro6EhoaSvn37kuPHj7cbt6MWzMw8bfDw4UMiFovJiy++SC5dutRue6VSSezt7clTTz1F7t69q3I/27dvJ2ZmZuTcuXOc2y9evEgsLS2Jj4+Pyu/U2LstHfLHH39AJBKhqqoKeXl5GDVqVLv7ZGdnY8iQIZDL5dizZ4/Kfb3xxhvYtGkT/Pz8cObMmRadEILNmzdDJBJh4cKFSElJwbPPPsvreLSG1u3ZxTh37hzp378/CQ8PJ83NzSrvN3v2bFJZWUmmT59OhgwZQhQKhVr9Hjp0iJiYmJDU1FRy+/Zt4uvrS15++WWSl5en7iGwaUsX7N+/n/Tu3ZtER0ertd+NGzdIaGgoIYSQ06dPEwAkOTlZ7f7j4+OJUCgkpqamJCQkhEilUrVjEMKmrQ6nrq4OO3bsgJubGxYvXqzWvtu2bcM777wDAPDw8IC1tTW2b9+uVgyZTIasrCwIBAJERkZiz549MDIyUitGR8Ou8/yNkZERoqOj4eXlhYULF2LXrl0QCNofW7W1tSgoKMDgwYORnp4OABgzZgwOHjyImzdvYtCgQe3GuHr1KsRiMYRCIUpLS/HCCy889vF0CFqvbV2MwsJCYm5uTkJDQ4lSqWy3/ebNm8nJkydbaQ8ePCCGhoZk5cqV7e6/c+dOYmxsTFatWqXWGutRsDWPDrl48SIxMzMjYWFhjzSQUqkkIpGIyOVyatvkyZNJ3759SUNDA+e+EomEzJw5kwwcOJBkZmZqLHdC2JpHp9ja2iItLQ3x8fFYvHgxCMf35SQSCdasWYPa2lrk5+e32lZeXo7m5mZUV1dj6dKlqKqqarX9zJkzGDNmDACguLgYIpFIewejTbRuzy5MXl4e6dOnD1m8eDFVgRQKBZHJZC1//49cLm+17Z/KJJfLyapVq4ixsTHZuXOn1vLuqMrDFsyPwMHBAampqfDx8YFAIEB0dHTLNoFA0OaCWl9fH/r6+q203377DUFBQaivr8f58+cxfPhwrebeEbBpqx0cHR2RmpqKgwcPIiIigleMuLg42NrawsnJqdsYB2Bv1VXCyckJKSkp8PX1hUAgwNatW1Xar66uDhEREUhOTsahQ4cwceJEznZSqRTFxcWt1lYGBgYYOHAgBgwYAD09PY0ch6ZhlUdFnJ2dcfLkSezduxfLli1rt31BQQHs7Oxw+/ZtlJSUtGkcADA2Nkb//v0xZcoUrFy5EkqlElVVVYiIiICjoyPOnj2ryUPRHFpfVXUzzp49S4yMjMiyZcs4tyuVSvLFF18QIyMjsmnTJpWuFf2Dra0tmTdvXqtYM2bMIEKhkJSXl6schy2YOymurq5ITk7GxIkTIRAIsGnTppZtt2/fxrx581BRUYHMzEzY2dmpFfu/05Oenh48PT2RkJCA8+fPd7orz2za4oG7uzuSkpIQExOD9957D8Bf3za0trbGoEGDcPHiRbWN0xaXL1+GgYEBnJ2dNRJPk7DKw5Nx48YhKSkJEydOxLVr15CdnY2YmBi89tprjxW3qKgIMTExaGhowOXLl5GYmIjExEQMHjxYQ5lrDmaex8DCwgIDBw6ERCJBUVGRSh+CtsfIkSMxb9481NfX48yZM0hPT8e6detgZWWFl156SQNZaw42bfFkx44dcHZ2xpw5c5CZmakR4wB//cpUKBTCwsICM2bMQEZGBvLz87FixQqNxNckrPKoiUQiQVhYGAoKCpCUlAR3d3et9jdo0CBYWFjg559/1mo/fGCVRw1++uknWFtbw9DQEMXFxRo3TnNzM6WdPn0ad+/exYIFCzTalyZglUcF5HI5Vq9eja+//hpbtmxR6SfG6iCVSpGRkYHy8vKWvszMzFBZWYm8vDxERUXhgw8+0GifmoCZpx3Ky8sRGBiIpqYm5OfnY9iwYRrvw9jYGFOnToVUKtV4bG3Cpq1HcPDgQdja2sLV1RW5ublaMU5XhlUeDqRSKd566y2kpqbi8OHD8PX11XVKnRJWef7DhQsXYGtri3v37qGkpIQZ5xEw8/yNUqnEhg0b4OXlhSVLluDEiRPo16+frtPq1LBpC8CtW7cwd+5c3Lp1C1lZWbCxsdF1Sl2CJ77yHDt2DGPGjMHQoUNRUFDAjKMGT2zlaWxsxPLlyxEXF4edO3di5syZuk6py/FEmqe0tBRisRjm5uYoKirCwIEDdZ1Sl+SJm7a++eYbuLi4YNasWcjIyGDGeQyemMpz7949hIaGoqSkBKmpqXBxcdF1Sl2eJ6LypKenw9raGr1790ZRUREzjobo1uZpbm5GZGQkZsyYgaioKBw6dAimpqa6Tqvb0G2nrRs3bkAsFoMQgvz8fLz88su6Tqnb0S0rz/79+2FnZwcPDw/k5OQw42iJblV5amtrER4ejoyMDMTHx8Pb21vXKXVruk3lOX/+PGxsbFBbW4uSkhJmnA6gy5tHqVTi008/hbe3N959910cP34cFhYWuk7riaBLT1u///475s6di7t37yInJwejR4/WdUpPFF228iQmJmLMmDGwsrJCfn4+M44O6HKVp6GhAe+88w5++OEH7Nq1C9OnT9d1Sk8sXco8JSUlEIvFeOaZZ1BcXIwBAwboOqUnmi4zbW3duhVubm4IDg5GWloaM04noNNXnurqaixYsABXrlxBWloaxo4dq+uUGH/TqSvPqVOnYG1tjT59+qCwsJAZp5PRKStPc3MzPvroI8TGxmLbtm0IDg7WdUoMDjqdea5fvw6xWAx9fX0UFBRg6NChuk6J0Qadatras2cPHBwc4OPjg+zsbE7jVFZW4uDBgygvL9dBhoz/p1NUnpqaGojFYhQXFyMxMRETJkzgbLd//37k5+cjMDAQUVFRmDBhAsRicQdny/gHnZsnJycHYrG45TYiHh4enO0kEglWrlyJsrIyCIVC2NjYYMSIEfDw8Oh8j098QtDZtKVQKLB27Vr4+voiMjISV69eRXZ2NoKDg6FUKqn2CQkJGDZsGIRCIQCgZ8+ecHBwUPuhaAzNoRPzVFZWwtPTE0eOHEFubi7Cw8MxePBgZGVl4fLly1i6dCm1z8WLF2FlZdVKc3FxQWZmZkelzfgPHT5txcfH4/XXX0dgYCA2btyInj17tmwzNTVFSkoKrKysMH/+fDg6OrZsu3r1KoyMjBAXF9eiXblyBdeuXevQ/Bn/0mHmefjwId5++20cPXoU+/btg7+/P2e7/v37Y/78+diwYQPi4+Nb9IaGBjz//POt3oFdunQJCoVC67kzuOkQ8xQVFUEsFmPAgAEoLi7Gc88998j2wcHB8Pb2hlKpbHksUb9+/SAQCFpVo7S0tE53e9knCa2ueQgh+OqrrzBu3DgsWLAAp06datc4wF/PuWpsbERlZWWLNnr0aOq2a6WlpezGBDpEa5Xn7t27CAkJwfXr13H69OlWFaM9JBIJZDJZq/vjBAUFwd3dHVKpFMbGxpDJZDh37hy+//57baTPUAGtVJ6UlBRYW1ujb9++KCwsVMs4AJCbmwtLS8uWt+UAMHz4cCxduhTh4eHIyclBWFgY3n//ffZhqQ7RaOWRyWSIjIzE7t27sX37dt5Xf+Pi4rBo0SJKX716NQoKCnDjxg18/vnn7OKgjtGYea5duwaxWIwePXqgsLAQL774Iq84WVlZSE9Px7Zt2zi329vbw97e/nFSZWgIjUxb3377LRwdHTFp0iRkZWXxNs6ff/6JkJAQbNiwgf2mvAvwyMpDCMHt27cfGWDZsmXIysrC3r174eLigurqal6J1NXVISAgAJaWlvDx8aGeRc5Qnbq6OjQ1Nal8Dvv378/rOaZ6hHA8cf5vHjx4ADMzM7WDMroWUqkURkZGau/3yGmrT58+UCgULX8zZsxo9f8/fzNnzqS0+vp6zJkzh9JPnDiB9evXU3pkZCTOnTvHGbupqUmlPu/cuYOQkBBKP3DgAKKjoyl9/fr1SEpKovQ5c+agvr5e5eMUi8WUfvz4cXz66aeUvnz5cuTl5VH6vHnzUF1dTemzZs2itObmZgQEBFB6dnY2PvzwQ0pfu3YtTp06xRm7vr6el3HaNQ/w78PnBQIBTE1Ncfz48VaaQCDArVu30NjY2Err1asXrl+/TrX19fXFjz/+SOlTp07F5s2bKX3w4MHYv38/pVdXV0MikbTS+vXrh8uXL1Ntp02bhgMHDlB6QEAAvv76a0ofOXIktm3bRum1tbWoqKigjrOsrIxq6+fnh6NHj1L6lClTsHHjRkofO3YsvvzyS0qXy+UoKipqpRkYGKCiooJ6fdzc3HDq1CnO49yyZQuljxgxAjt27OBlHADqPd24rKyMvPLKK5T+2WefkaioKEoPCwsjCQkJlO7s7EykUimlOzk5UVpVVRURiUSUHhsbS1asWEHpAQEBJDc3lzO2QqGgdHt7e0qrr68nLi4ulJ6QkEDCwsIofcGCBeTo0aOU7uzsTOrr6yndzs6O0pqbm4mjoyOl5+TkkNmzZ1P6u+++S7799ltKF4lEpLq6mtK5YtfU1BB3d3dKVxW1H43NdeANDQ3E2dmZ0n/99Vfi4+ND6Z9//jlZt24dpU+aNIlcvXqV0h0cHKgXXqFQcJ6QCxcukJkzZ1L6e++9R2JiYig9ICCAZGdnU7qjoyNpbm7mzOW/lJWVEV9fX0qPiooi69evp/RXXnmFlJWVUXpbZuM6zjt37pDx48dTekxMjFqDytnZmXNQqYLa5pk9ezbJyMigdCcnJ86T3dbIHjt2LKWfPHmSzJ8/n9IXLVpEjhw5Qumurq6cFYzrBa6uruY82RcuXCCvvvoqpUdGRpLo6GhK9/DwIFVVVZTe1nFyDaoff/yRhISEUHpbg2rixIltDqr/ou6gWrFiBfnuu+8oXRXUNk9BQQHx9/en9I8//phs3bqV0gMDA0laWhqlOzk5kYaGBkrnOiG//fYb8fb2pvRNmzaR1atXU/rkyZNJaWkpZ59ccL3w9+7dI+PGjaP0ffv2kaVLl1L67NmzSWZmJmefqlawtip4UlIS56B64403yOHDhyldnUF1584dzqWIKqhtHkK4T3ZNTQ1xc3Oj9EuXLpHJkydT+qpVq8hXX31F6d7e3qSiooLSuUZTU1MTpyFSU1PJ3LlzKf3NN98kcXFxlD5lyhRSXFxM6Vwnuy29sLCQc1B99NFHnINqwoQJpLKyktLVMVtFRQXx8vKi9LYG1aRJkzgHFdcgUQVe5vH39yeFhYWUzrU2IYTbbPfv3yeurq6UHhcXR8LDwyl97ty55OTJk5SuTgWrrKzkrGBpaWkkMDCQ0pcsWcJZ0t3d3cn9+/cpva3j5FqUHjhwgERERFD6qlWryJYtWyjdy8uLc1Bx9dnU1MS5LEhNTSVBQUGUHh4eTlJTUym9PfQ/+eSTT9R9h2ZjY4PGxkbqZgPPP/88zM3N0atXr1a6qakpRowY0eoqZs+ePdGjRw9YW1u3ajtq1CjU1tZS99uxs7ODVCrFCy+80EofOnQohEIhTExMWum9e/emYpuYmMDQ0JCKPWTIEDQ2NlLt7e3tUVtbS33hzNLSEnp6enj66adb6cbGxhg5cqRKx2ltbY2amhoqF3t7ezx48ID6vvaoUaMgl8upxzg9/fTTGDJkCAwM/v2wQF9fH0KhkOpz6NChaGhooHRbW1sYGBio/YioR15hZjAeRaf6xSija8HMw+ANMw+DN8w8DN4w8zB4w8zD4A0zD4M3zDwM3jDzMHjDzMPgDTMPgzfMPAzeMPMweMPMw+ANMw+DN8w8DN4w8zB4w8zD4A0zD4M3zDwM3jDzMHjDzMPgDTMPgzfMPAzeMPMweMPMw+ANMw+DN8w8DN4w8zB4w8zD4A0zD4M3zDwM3jDzMHjDzMPgDTMPgzfMPAzeMPMweMPMw+ANMw+DN8w8DN78Dy39OqqI3FsoAAAAAElFTkSuQmCC)
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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)
physics-General
physics-
The ends of two rods of different materials with their thermal conductivities, radii of cross sections and lengths all are in the ratio 1 : 2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 cal/sec, that in the shorter rod in cal/sec. will be
The ends of two rods of different materials with their thermal conductivities, radii of cross sections and lengths all are in the ratio 1 : 2 are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is 4 cal/sec, that in the shorter rod in cal/sec. will be
physics-General
physics-
The diagram shows an equiconvex lens. What should be the condition on the refractive indices so that the lens become diverging?
![](data:image/png;base64,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)
The diagram shows an equiconvex lens. What should be the condition on the refractive indices so that the lens become diverging?
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown man is balanced by counter weight of same mass. He starts to climb the rope with an accelerator of 2 m/s2 w.r.t. rope. The time after which he reaches the pulley will be
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)
In the figure shown man is balanced by counter weight of same mass. He starts to climb the rope with an accelerator of 2 m/s2 w.r.t. rope. The time after which he reaches the pulley will be
![](data:image/png;base64,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)
physics-General
physics-
An unknown mass, m1 , hangs from a massless string and descends with an acceleration g/2. The other end is attached to a mass m2 which slides on a frictionless horizontal table. The string goes over a uniform cylinder of mass
and radius R (see figure). The cylinder rotates about a horizontal axis without friction and the string does not slip on the cylinder. Express your answers in parts b, c and d in terms of g, ![m subscript 2 end subscript blank a n d blank R](data:image/png;base64,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)
![](data:image/png;base64,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)
An unknown mass, m1 , hangs from a massless string and descends with an acceleration g/2. The other end is attached to a mass m2 which slides on a frictionless horizontal table. The string goes over a uniform cylinder of mass
and radius R (see figure). The cylinder rotates about a horizontal axis without friction and the string does not slip on the cylinder. Express your answers in parts b, c and d in terms of g, ![m subscript 2 end subscript blank a n d blank R](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A block of weight 9.8N is placed on a table. The table surface exerts an upward force of 10N on the block. Assume ![g equals 9.8 m divided by s to the power of 2 end exponent](data:image/png;base64,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)
A block of weight 9.8N is placed on a table. The table surface exerts an upward force of 10N on the block. Assume ![g equals 9.8 m divided by s to the power of 2 end exponent](data:image/png;base64,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)
physics-General
physics-
The values of
for final rays to be parallel to the principle axis are: (focal lengths of the lenses are written on the lenses)
![](data:image/png;base64,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)
The values of
for final rays to be parallel to the principle axis are: (focal lengths of the lenses are written on the lenses)
![](data:image/png;base64,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)
physics-General