Maths-
General
Easy
Question
Measure of
in the following figure is
![](data:image/png;base64,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)
- 1300
- 1200
- 1500
- 1150
The correct answer is: 1500
Related Questions to study
physics-
A particle executing SHM while moving from one extremity is found to be at distances x1, x2 and x3 from the mean position at the end of three successive seconds. The time period of oscillation is ('
' used in the following choices is given by
)
A particle executing SHM while moving from one extremity is found to be at distances x1, x2 and x3 from the mean position at the end of three successive seconds. The time period of oscillation is ('
' used in the following choices is given by
)
physics-General
physics-
A block of mass m is suspended by different springs of force constant shown in figure. Let time period of oscillation in these four positions be
and
. Then
i) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/570064/1/1063688/Picture4.png)
ii) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/570064/1/1063688/Picture3.png)
iii) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/570064/1/1063688/Picture2.png)
iv) 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)
A block of mass m is suspended by different springs of force constant shown in figure. Let time period of oscillation in these four positions be
and
. Then
i) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/570064/1/1063688/Picture4.png)
ii) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/570064/1/1063688/Picture3.png)
iii) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/570064/1/1063688/Picture2.png)
iv) 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)
physics-General
physics-
A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance
. The pendulum is releases from rest. Throughout the motion the moving string makes small angle with vertical. Time after which the pendulum returns back to its initial position is
![](data:image/png;base64,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)
A pendulum has time period T for small oscillations. An obstacle P is situated below the point of suspension O at a distance
. The pendulum is releases from rest. Throughout the motion the moving string makes small angle with vertical. Time after which the pendulum returns back to its initial position is
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)
physics-General
physics-
A mass m=8 kg is attached to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is 200 N/m. The mass m is then released and begins to undergo small oscillations. The maximum velocity the mass will be ![open parentheses g equals 10 blank m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
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)
A mass m=8 kg is attached to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is 200 N/m. The mass m is then released and begins to undergo small oscillations. The maximum velocity the mass will be ![open parentheses g equals 10 blank m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
The two blocks of mass
and
are kept on a smooth horizontal table as shown in figure. Block of mass
but not
is fastened to the spring. If now both the blocks are pushed to the left so that the spring is compressed a distance
. The amplitude of oscillation of block of mass
after the system is released is
![](data:image/png;base64,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)
The two blocks of mass
and
are kept on a smooth horizontal table as shown in figure. Block of mass
but not
is fastened to the spring. If now both the blocks are pushed to the left so that the spring is compressed a distance
. The amplitude of oscillation of block of mass
after the system is released is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANoAAABSCAYAAAAy/spuAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABqwSURBVHhe7Z0JvE3VF8c1zyOVRho1EA1UKA0aaVCKBqGRSqUkmiQ0h2aKJpVGiahQXsZKEknDy5AhikQh4ln/9933rHeX7bzyvPvOu/9P+/f57M97d+9zz9ln7/1be6211963jAQEBJQ4AtECAhJAIFpAQAIIRAsISACBaAEBCSAQLSAgAQSiBQQkgEC0gIAEEIgWEJAAAtECAhJAIFpAQAIIRAsISACBaAEBCaBEifb777/L3LlzZdWqVVFOQMB/EyVGtKVLl8oFF1wgW265pcyaNSvKDQj4b6JEiPbiiy/KYYcdJuXKlZMyZcrITz/9FJUEBPw3kXGivfzyy7LRRhvJDjvsILvttptsvPHGMnPmzKg0IOC/iYwSjZlsww03lG233VbGjh0rjRs3djNaIFrpYOXKlU6FL6m0ZMmS2HxNlP/9999RbYoGvvvwww/LTTfdVGi65ZZbXCqsrG3btrFlbdq0ceU333xzoeX8vfvuu2XhwoVRjYqHjBHtueeec6TabrvtZOjQoS7vrLPOCkQrRQwcOFAqVqwou+yyi1Pj/VShQgXZZ599nObhl+2xxx6ubPfdd1+rrHz58gXfK1u27Frl3Jfn7rXXXtKjR4+oNkXDr7/+KrvuuqsbP6WZpk2bFtWoeMgI0Xr16uUqBcmGDRsW5Yo0aNDA5QeilQ5Q42l/BnzNmjXXSCeddJJsv/32rnznnXdeo+z44493ZKEM7cSWHXvssXL44Ye7MtIRRxxRUFarVi05+eST3TjQ8k6dOkW1KRoWLFjg6s39v/rqK5k0aZJMnDjRpdzcXOnSpYu7/8EHHyyffPJJQfmUKVPk9ddfly222EJ23HFHef/99wvKJk+eLF9++aUceeSR7rsdO3YsuDdJ74u5s9lmmzmhMWPGjKhGxUOxifb000+7SlOpjz/+OMpNNVS1atVkgw02CEQrJbz66quub/r27RvlpDF+/HjZaaed3Mzz7bffRrkp/Pnnn24w4jEePnx4lJtGy5Yt3X3btWsX5aQxatQod18GOn1/3333RSVFA+OH2bRu3bpRThqQhlmaGRWiWOTl5bnv8Ox33nknyk0DlZG6X3/99VFOGqNHj3azNYKiUqVKzs+QNUR78skn5ZBDDlmDZHPmzHESjhdCMgSilQ6UaNjOFt98840bpMxo2NIW2FT169d33+vZs2eUm0aHDh1c2aWXXuoGtQWk5J6Q7JprrnH2OjPE+gCiob6ecMIJsnr16ihXnFBApUQI5OTkRLlpXHLJJa5+DzzwQJSTRufOnV1Zw4YN17IdGb8QjNlswIABcuWVV8rmm2+ePUQDLEwrfvnlF6ldu7Z7ISq96aabJk60ZcuWORWCev3444/y7rvvyjPPPOPSm2++6QYawFnw3nvvyYcffugkfJ8+feTGG2+Uyy67zA2Uxx57TD7//HN33f8jlGgvvPBClCNuTRN1C8/woEGDotw0cATwndatW0c5adB+lKEe4qywGDFihFPVKH/77bfliy++cP8zuNcHcUSbPXu2E+r6DB+oqZQ1bdo0ykmDvqWMsblo0aIoNwXqzuzFLEibgYsvvthNEllFNMX8+fOlTp067oVuvfVWOf30093/SRENHRtPE2t4dDoDKs6g3mSTTVwHqkAgbb311gX/08BIY/181FFHOQmHw+e7775zEu+GG25w73rMMcc4uwViko+N+tZbb8m4cePczF6aUKI9//zz7jOCRzUNSz7Fs88+68rOOOOMtYQL70ZZlSpV5Oeff45yU2BWxHSgnHsAZhs+Z4JoAC8m/3PPOAcLxKOM9+NaC/qEPj/ggAPWWtMdM2aMc+jwXW0ncOGFF2Yn0SAZBjYVvvzyy13e+eef7z6XNNHwDLVq1cqpEzzPJhoYO4GO6Nevn1OHaEQkul6j/zOTQRDIhO7/xhtvSKNGjQquI9H4+j/kRKdXp4KfUEVQU1Dd/BkgCSjRcA4wK6gXOE6tghhoINgm8+bNi3JTgEhbbbWVE1poChbMXCrMMCMUH330kcsrLtFOO+00p+bRZ9zvnnvuia5IY8KECa6tcZ5MnTo1yk2BflTPKI4QC/qa/uO+PnmbNGmSfUSjY1AnqHCzZs0KpOE555zj8kqSaEz7e++9t3sOXi9sDxro8ccfl+bNm7t8BpoF6i2GNp41SDhkyBCn4tKZPlBDuEeLFi2cpOd//qJSooJAIKTiNttsI/vvv7+b/biGepxyyinufxKeug8++CC6azJQoqE2sS7E/6wd+fj+++/dgOMdGLQWEAsiYXfR1haQjPfkvl27do1yU6BNyC8O0egfxtXVV1/t7oXW4APTYM8993QC1XfcYM/Rz5TZtkfo4PjAacN9MREsGL/0cVbZaFRaZy4MUWtkHnfccS6/pIiGNw2C0JDMGnQ8sxqzEEBVQpqhQlp14rXXXnP16t69e5QjcvbZZ7uZjdlMoXbGueee6z5DUCTnmWee6T4r1K7B5sE+RCVFdcUWZBDfddddrp5cA2Hx6iUB2odnqjseB4Z1LADaCBUfGwWV1wIBiqufd8G2tcBVfuihhzr3/0MPPRTlpoCTRIl97733RrlFw2+//SYHHXSQG+zchzEWZyvjvkeNx862oA68D7amXXICf/31l1NxKfM9k7TPdddd58YU751VM9pLL70kV1xxhRtkijvvvNPZOVS4JIhG43F/JDFqCujWrZvrFNt4qJTkffbZZ1GOODuOPKSuAqlGHo4TxaOPPuryUCEVCA8GJRIXMCBQHRl0KmT69+/vvmelOes0OiPWq1dP/vjjj6ik5MBMzvNIkMm3XQD1Zx3qhx9+iHLSQLCgUjJr+EBd53v+0gDAoaTPvf/++6PcogE7EA2Be2CbJdFeQN3/pKxaR4sDC4FaWSRSpomGPbjvvvs6dcYSCLWVZ9qB0bt3b5dnvVQMdNRLBpIizkOHzYk6hbdLcdVVV7nr1HMJMflsScX1kA83uZ1B2C6kxGcxf/ny5VFJyYDZhGdVr17dRVokgdtuu809k0Xw4qyjYWuhjbBeVtI2voKQK+peo0aNgr7PWqJp5+L5w0PFrJPJhmLgMnvyDKv6AbyAqDKoQwqNjkBdBAz2Aw88UPbbb7819smhenKdrjmtWLHCzZa8hwW2H9fhWAF4qvisbmGA7YbdiArprzUBnC58Z32jJtYVOCd4jvWmlSQQNjyPxW4EHH2/vjYaMy2214knnhjlpEH8YaaXXLSt1DOJlxl1PyuJhjeLyjLIqOBFF13kPvterOKAqAAkJY4GO4h1cCONrJ2o6p86RJgNkZIY2RZ33HGHu+6pp55yn1FVkKh+R7/yyivuOu4L9P64vxVaF1z/cZtesdGImqEj+R5reCWRUNuoG84QC9SyTNuJmA88ixjI6dOnZ2wdjfa3WgFexGuvvdbk5cn82bny5eSp8tfShTJ26CAZOnpSfm6+UF00Sz4c8K7kjP/Rff4n4G1lFsb2BFnp3kcFUpLhKYIMQN3JfKbhMpFYn+OevuHOrInthKfTAkOd65VoqIt4m3AbW0AwrmOtDDAQ0dFxBlhojB1qBlCj34YCoTrijeP7/uKoAhuT7yWRLNGoG2qrCr/VeSvlu9H9pf1Nt8vAMePk7R73yEUXNpaegyfIorlTpGv7FtKo0aXSd0Suu74w4KzgfdVrmSn3vl2wpk+qVq3qhJRi0eyJcmO9ylKucj3p8UwPad2sgZTfYTdp2ekJ6dmtk1zc4GTZody+0nVQ2snlg/GLw8tGN2Ul0ZACNCozBZJUQeVth2cyYY9ZIKWRSBj9FrqrQB0aqISojXi07IyoqoM6Q5jRGDi6YKrAg8h16slSm0ttNoDag8DBQcLz4sBMhz3D9/FylUQ69dRTXd1UHeaZ2KfYzbqul7fiTxne5xbZuszG0ui27jJwYH/pctnxssVOlaTdg72kb98+cn39KlK+2vnyQ9rXtRZoF+v5yyTRFKhz3NOuA65csUz6dzhbtti7roz9KeUw6d6kmmxX+WyZ8AvOn8XSqs5+UrNZt0JnNfrIJ1RWEg19mc4cOXJklCOu0Zk50NNRoZgZMpEIGGUA+YuuNFblypWdCoD7VqGOGTxkCshII1oHAQ3Lgq160SAa7l2eaYE6jOqqHcACKve3a0xEhKgzpDTBNhnqpjOaOiogt1XHVi/Mkepld5N7h0SLvZNfll3L7iW9x853H2cNflB2r1BZhk13Hx0W/TpH5i5YHH1KtZdFpoiGU4K6qkeZ0ChbdzCie1PZtUZz+S363LdNXTmwXhtJ+Vjz5L5GR8kxF3URlPgFuSOlfYsL5aS69eWhvqNkzYjHNLI6BEvB2gaRBDQM0jNTm+f+DUhryGK9ieedd56rg40YUPc+keYA5wmkOvroowvsO6Q/sxIuZgUzIB48BsDixalBps4WtgopWAAnD7uvNKGeVBxB+j82j12GAcvnDpWjdtlbuo1IMWnZhBel4l5V5PUvU0SbNvBBqbBfNVEezpvykZx7XE3p8HJ6ecQH0SQ8r7hEY82SCA7uhZMlzs0/vGsTKX/kpTIv8o/0aX2iVDq9taSU9r+l8/k1pFaTh/Mpt0z69XxMXhs0RAY+0y6/fw+VV8bNdVdZIIA574Zxk7VEI0iX0CSIhirJInBSh/PoGogSiM6CQOxpsq50jYvTcB5dAoCAFkg16k9HA5YNWBC3bnsiRPgua0cKJbLV+UsDSi60DWZiHBV+nCJYMW+YI1rXTyzRKstr49NEq7j/YQUz2qoVf0ibBnXk5l5rb6EBrL0hZGi74hINpxVCjRlNbX8fY55oJrtUbx4RS+SNtidLpfptRXv8gcZHS+181dE5Tn7TULilcm29Y6Xzm5OizymgBSBgMRuybsFagX3D2haL1IMHD04s1lGBusrzsN8glhLviSeeiK5IgU5k0OE8QbVkSQDnhb+bVh0WGg2ujhhmMQWDgO+zlKGfiblDbdZZr7SgRKO+OBL8OEDF0hn9Zf9NtpWOg793AmTx2Kdl+232kN5j5rjP377RQbYtW1EGfJtWtO6/vL607b020XS7Cc8tzjqaEs23kRUq6JYsmC6dL6gqZXasKv2+mCq/zpwirepWkC0rnigfTflJZud+Lg2rlJOdqjaUcdNSQQZg9cLx0urK6+TTOWkBTH/Tl4xfxkdWEg0vIDotqpuuWSUR62iBuqcOANbK+EtkfZy6gVDQYGAIh7rrg/thE3KN7tFiXc3agEBDsAgF0l3lfuxfaUCJFreOVmDnrFwiw17sKMcfU0tadnlJps2ZIf0faye1a9WRto/3k5kzcuW5Ti2kVu060uX5ofJH9LV7m9dbi2jEDzI4sctxXDAWMr0fDaBF0Dfgr0Vz5bOROTIiZ7hMyp0jv/8yQ0aPyJGcjz+RKTPmyfxZuTIqv2x4ziiZ+rPOeatk2PMPS893v4g+pzasUnfai7HMWm3WqY4EnqImkGxMHPo1Fbc2U0kDUhMxj4rH4UD/tFUFxwe2VVwYkQKPKi5l3gO3sr+jFzAoNK6TRCdlekF1faBE87fEIFSocwqrZVVeNJBX50leflql7rn8/1fn26Xpj6vyr07BJxrtolH8rDVmah3NJxraCQ6S4mDm+CHyyoDR0ad85N8egUx9dZsPcbtZ5wzBuGbnLR1rQaAuldcZLkkUtn61PsBZ8umnn8bOjApUM2whjRjJBsQRjWUObJA00dYPD115ltz2UsoWBhrtQuQMyOR+NCWaqvJ+sME6I2+lTHy/l7RoebO8PWykfPDOqzIgZ6Isz5ckNaofuUYAdFa69+OAO50QJtQI65ELSA4+0XDq4KjinBAbPVNULJk/VZrWPFAatHtWFi1PkYAtSdbLmul1NLQm1kmx/2x8a1GwevFMeaD1JdKw0cXSrGkTueDcxvLc0Mluxh7iRf//XxANfRevDQ2NnpvJEKyAdYcSjVmW30CAYBj6LD8UB0vmT5fh7w+Sj8d8JYsjvuIRtAEAmSIaSzao/6q+42RLAllPNFQsZjIMYYxL/iblDAlYE0o0gq9197sf94hTQR0LcSgsskWx6u/48kwQjXjRmjVTx99xL7WfAGo64W82xlRBnQmpw+uMg8YHSxzEgbKV68fc+NCyrCYa3iB2tNIodDJOCf4PRCsd6MZP3Ulso2nYus+iLKcB+wHGDHIGKR5UHCe+14/ZkU2TBAMUtlaYCaKxYZd7kFiGUdx+++0ujxnPP54AJ5TaiwSY+0Sh7roLniM3/HdXZC3R8DKhQ/MCahCre59GC0geujCPVkH4lULDxtgSotHqCgaeblBlkdvfM2cPYGJvXmHeVcLxuGZ9N34Si8meQ+JSrY2ve8Y4tiIu4ojzGinHEecLCGJQ1TsMWf8JrMVCtEyZPRkjGsHESCC7QKnR+0TO40InctwmTq1CIvn5GL7o/H5+SEVLGijN8QlsXUFlon/IY4EeLx7E0euJfNFAcEK1+MxA03KOedCzYehbpD0zhJbbpLu7iZKJK/+39PXXXzubEg2JbTEsmegaJQmy8144YTSpgCARz4ogsOVECFHG0g+H73BPW24Tz2bjJ6aQX7f1cSRlVHX0JQyqhb44a2w4RvSzJqIH4vKRwkgUP59r8WT6+Rj5cfchFfYdnsH31jX/3xL1jatDYfnk6Vkifr6fR/q3d6Qt48qI1vHzeG5h9yos0Ydx+YW9HymuToVdS53i+ry0k9+2GpJXFGTcGaLAvY9tQCfjotVKEmnBQjbeJJWOfr6et8jA4jNRGfxFJycfIxnJSx6JvWV6H1QDvQ+JXbrkI6Hsd5B+xGMSHYItqfkkXOAkJKjNJzFr4wFDLbb59oxIpKnWWdUsEs/UfIKTyaN97L2IDyWfctQfzSfiRTub99P7kFQdYueCrbNGx6DS6zsyE+kz2Cpkr6feSgLub9tRI2RI1EXrbN/bvp/OHoQ02WfoOSD+s/X+kJk6ch/en9A28pmBCUDguSSbjz2l+drevAf9rfkkPaSIZ2Of2jLajjJCrzjciTyej2OPfOqt9Y07Q+XfUCJEw72vh1LqXig9Spp4QQvdumGNXaBxkuzcVaBOMkjQ3f3gWIx6rvfPVEcF0e8w7VtAdAaCH6xKB9FRcYY+HrDCIhNQOagDAbAWqCjk25hL1A8GF1Lcuqw5WAhCUQcfen+CoC1Q31BzGEj2/EjyEQx4f21EC+/FzIFTwD9vkjAynhFnW6ltZwOoAadrkW+PbSNMDQHLc+yJyJgKvDPP9h0R6jyzC+xEFfEOjCd7piTvBtl4N98hopqUjUkFEATBymnHvvZFHCgL+Qhze8gqDj6+w7Ow8dYXGScaOq1KTHt2O0azHkYKKRQMOLXl7ACiIdg4iYTTTZZAT8xlUGFfWOhA9Peq0dEMXu5nv4MKwAIodoD1jGKLMBNSZs85xLjGi8YzeBffLc6g1dnFdjIRJWzBId+e0MWuBgKQmT1xJinU4GcAW+BU0pnCd2vrBleOeLCnXWE7M1CQ/DaoWHcsoA3Y2E0Gv84u/ICJBetkera9jaIgeBrnBPl4mxW8H9oHs7Y941/rih1oyQapCHOjzB6mxGCnjfzdB/QN78aMbU/xghAQA43IF5ZqOzIT+0HfrC8yTviuHSdE0/AdlhrWN1A8Y0RjEHJ8m6p39tRaBeTRn8zhSDYF0ompGUmnW1wAsxGD3Y+s102ASH1rmBJ2hUuXMrbrWOjZHqgDdm1IG56Zyu7TIoSI+lAvf/ZUzxbBxD4gLGoqg8uu4TDIiQVkId96+vDOIfVRZ+xGVD3Ry9/TxoBiYCHhOcLOQrUDnAQW6n1EHbUDhV+DIZ9fh7HQmZBB55/Pb0mlx0MAHCMIJ9Rxe4wfURzk0SY4ZBT2xzKsd5BzMGknNA1LTj2TBEFiPaF6tB8CyB7KRNswdhiPvotej6NgV4bvmdRx4gtSFbAIGrswv67IGNGQ2swYVMY/+dWCgQJxUHXsjmxmFwYnHWJVBB0k7NK2rlY8UeT7e8iYjbANGYz2PqAwgujxBNzTQk+48juX2Rn7hTI9pMeCAQJJUUXsLKKxeuwAsGqI/ngEdokKAUiPxCefcgt+6JF8dpRbcjJosD0oe+SRR6LcFPTsFAaQChQGjKpZvrrLQEUoMGP4pxcj9Hg3vHfMNgoIhtBg5rGDW4UZs72dwQoTJtj3zEaMBStgdZsSC9V2WYF3JR9zw5JAxw7P9Te7qrobt7tAjxT0zRk9tdrPXxdkVHWkQf29X3FgMRNS2bUdQNQCDawH5CiQfngCrRqAuqNHbvsDEZuHfHRxK+UYxOoCZmBpZ/EXQ5d8PQVLoYujHEttwewMYSiLCyTWqAwkrQ1wJkqDfAa4HRQqBKzg0JmFd/dVRf1dOghv78//ql76p/DqmRuWhFyvjhmCv62EZ38fsxrrbf4BqxzdgDBBoFm1W08J4542CFtnERwX+gz7wxW0u51BdOc6tpxqFGgv2n/+uzGLk89CetxRFpgVlmxWnafO9r0xAVATKbO7UaivOn/4TlFQIs6QdQEGbJy+i61iVTtAwyFV/SmbGDgGmn8iFsBOQ2r5z8AOwMPEYLQNj07OoKYRrU0ICfW3uP3jrTGusbGQ7HE/2EcnE6XgR/1Dqvbt26/xPrwjC8S+oMJRw345Fm79++iJwOpwUlAvtAYcOnbG4fuoi/YAJaBn76NW+22sthwk9UEZ3/FVawQj7+07OyCD/94IE4jMTOhvvNUzQrmfAlLzDlYNBfQlHkfeg3sqIC9CFFXb/yUZ7kE7kfygCjQjxpb+TLQCgYPnMe4nr/4JpUa00gQdGueiZVDiCMChY4GaR6PH/VwQag5k8x0HmQTEJxTKqksA4kCyuP1+XI/q6dtxhYFTvHyvrALp7XtmMwk8omhDfhQKswzvR2DDuoD6x+0tRIgW1g74BNAW/LbNNP6TRPsn+BJ9XWAlaDbBqkMBpYtAtICABBCIFhCQAALRAgISQCBaQEACCEQLCEgAgWgBAQkgEC0gIAEEogUEJIBAtICABBCIFhCQAALRAgISQCBaQEACCEQLCEgAgWgBAQkgEC0gIAEEogUEJIBAtICABBCIFhCQAALRAgISQCBaQEACCEQLCEgAgWgBAQkgEC0gIAEEogUEJIBAtICABBCIFhBQ4hD5HyPHckfXOvZZAAAAAElFTkSuQmCC)
physics-General
physics-
Five identical springs are used in the following three configurations. The time period of vertical oscillations in configuration (i) (ii) and (iii) are in the ratio
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)
Five identical springs are used in the following three configurations. The time period of vertical oscillations in configuration (i) (ii) and (iii) are in the ratio
![](data:image/png;base64,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)
physics-General
chemistry-
For the process Cu(g) →Cu+ (g) + e– , the electron is to be removed from
For the process Cu(g) →Cu+ (g) + e– , the electron is to be removed from
chemistry-General
chemistry-
In the reaction, 2CuCl2 + 2H2O + SO2 → A + H2SO4 + 2HCl ; A is
In the reaction, 2CuCl2 + 2H2O + SO2 → A + H2SO4 + 2HCl ; A is
chemistry-General
physics-
The variation of PE of a simple harmonic oscillator is as shown. Then force constant of the system is (PE 'U' is in joules, displacement ' x ' is in mm )
![](data:image/png;base64,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)
The variation of PE of a simple harmonic oscillator is as shown. Then force constant of the system is (PE 'U' is in joules, displacement ' x ' is in mm )
![](data:image/png;base64,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)
physics-General
physics-
A particle at the end of the spring executes S.H.M with a period
, while the corresponding period for another spring is
. If the period of oscillation with two springs in series is ' T ', then (same particle connected in all the cases)
A particle at the end of the spring executes S.H.M with a period
, while the corresponding period for another spring is
. If the period of oscillation with two springs in series is ' T ', then (same particle connected in all the cases)
physics-General
General
The flagpole and ground are ________ to each other.
For such questions, we should know about perpendicular lines and parallel lines.
The flagpole and ground are ________ to each other.
GeneralGeneral
For such questions, we should know about perpendicular lines and parallel lines.
General
Identify the perpendicular lines in the given figure.
![](data:image/png;base64,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)
For such questions, we should know about perpendicular lines and parallel lines. We should start with horizontal lines or verical lines. We should follow the order or there are chances to miss the lines.
Identify the perpendicular lines in the given figure.
![](data:image/png;base64,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)
GeneralGeneral
For such questions, we should know about perpendicular lines and parallel lines. We should start with horizontal lines or verical lines. We should follow the order or there are chances to miss the lines.
physics-
Acceleration displacement graph of a particle executing S.H.M is as shown in given figure. The time period of its oscillation is (in sec)
![](data:image/png;base64,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)
Acceleration displacement graph of a particle executing S.H.M is as shown in given figure. The time period of its oscillation is (in sec)
![](data:image/png;base64,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)
physics-General
physics-
The time period of a particle performing linear SHM is 12 s. What is the time taken by it to cover a distance equal to half its amplitude starting its motion from the mean position ?
The time period of a particle performing linear SHM is 12 s. What is the time taken by it to cover a distance equal to half its amplitude starting its motion from the mean position ?
physics-General
physics-
A small mass particle is given an initial velocity
tangent to the horizontal rim of a smooth hemispherical bowl at radius
from the vertical centreline as shown at point A. As the particle slides past point B, on a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle
with the horizontal tangentto the bowl through B.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAP0AAACvCAYAAAA2c9gAAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACC0SURBVHhe7Z0HfJXV+cfVVq3VVttq0VqrrXWif6lWW3FiRYqKFWS5EFFUVEREZO8lypQtICIjElZkyEgYAmEIiAwhgIAMmSFAwpKR58/38J7kJiQxuXnfe9977/P9fM5H896b3MH7O+c5zzpniaIoMYWKXlFiDBW9osQYKnpFiTFU9IoSY6joFSXGUNErSoyholeUGENFrygxhopeUWIMFb0P2Lp6qcyZO09mz54rm/b+5FxVFG9Q0YeVTJk7sou82/ojmT1njsz8YqjUr9dYZq074DyuKO6jog8jR7+fJA+XflDiVxx0rojENasq5V7qIhnOz4riNir6MLIurrHcdE8VWRGg8JS45nLr3ZVkWfY8oCiuoqIPI1sntpWb7qwgi9OcC6dYNayJ3P5QDVl71LmgKC6jog8jmWkrpGa5B6TT+DXOlQzpUfcpeaPrZDnpXFEUt1HRh5mdKxOlY9sOMmxEnIwa0ke6DRwnO484DyqKB6jofcDJIwdkx44dkrJug2Q61xTFK1T0PmH69OlSqlQpmTd3rnNFUbxBRe8TunfvLmeddZZ8+umnzhVF8QYVvU/o3bu3Ef3w4cOdK4riDSp6n/DRRx8Z0X/22WfOFUXxBhW9T+jbt68R/ahRo5wriuINKnqfsGvXLklISJB9+/Y5VxTFG1T0PmH37t0yduxYFb3iOSp6n/Dxxx+rea+EBBW9T1BHnhIqVPQ+QUN2SqhQ0fuEHj16GNEPHTrUuaIo3qCi9wnDhg2TX/3qVzJp0iTniqJ4g4reJ/z000+SkpIiJ06ccK4oijeo6H3Cd999J40bN5YNGzY4VxTFG1T0PqFnz57qvVdCgoreJ/Tq1cuInr29oniJit5DTmbskBkT4mXq/NViutkf2yfzp0+Wxet3m8cD0ZCdEipU9B5y8nCq9HmzvDz0Ug8xfS5/2iBdWrSSmSl7zOOBaD29EipU9B5zeO0EqVKplnyTIXJ043wZM21Rnk0vp0yZInfccYfMmzfPuaIo3qCi95wj0qtuZWk5ZJYs+WqiJKfsda6f5oQzA2SePCk//vjj6R8UxUNU9CFgR/JAKVumvHQYNE3SbefLzHRZ+tUUGTNusmxOPSrJC5KlXLly8vXXXztPUBRvUNGHgpM7pFnNitL1y++dCyK7l02QDt2HysIZCTIwfoZ07DVQ9/RKSFDRh4gDe/bIwWPZ2XYrJvaWpt0myb7Ns6VDlyHSpusg9d4rIUFF7yEnT+3T82P7ojHStufnsmrBJOn96QTp1GeIxumVkKCi94hx48bJTTfdJHfffbdUq1ZN3nnnHenWrZvEx8fLvOQFcnj/FklMiJNBn4yU7348JL37ne6Rp1V2iteo6D2CajlEnN+YlphknnfwsEnbkSWLF8vLL78sq1evNj8rileo6D2EmPuVV155huAvv7yErF+/3nnWaY4fP26uFbQlUBQ3UNF7BKG3unXrykUXXXSG6Mm+yw1NMa+++mpJTEx0riiKN6joXYRVevLkyfLkk09mCfyBBx6QF154Ievnm2++Wfbv3+/8Rja2c46G7BSvUdG7wN69e40DrnTp0lnifuSRR2T8+PFy9OhRSU9PzzLzBw8e7PxWTrTgRgkVKvpiQNpsly5d5IYbbjCCPeecc+S5556TmTNnOs/IZuDAgfLmm2/KwYMHnSs5saW1Wk+veI2KPghWrVol7733nvzhD38wQv3jH/9oQnJcDxYr+pEjRzpXFMUbVPSFhP363LlzpWbNmnLeeecZgf7tb3+T999/XzZt2uQ8K3g2b95sDrzYuXOnc0VRvCHqRH88fb/s3JMmtq6luBw7dkwmTJggjz76qBE649///rcx1w8cOOA8q/gcOXJEZs+ebV5PUbwk6kS/cnQbqfhKZynuiXA45wYNGiT//Oc/s8ReoUIF+fLLL4ssTGLwhw8fNpNEamqqbN++XbZu3SpbtmwxK/wPP/wgH374oXmN/v37G8uBazzGcxj4DzjvjrPu8AvQPTcz062pTYklokr0mSfSZUq/xlK2fGUZu/zMsFhhQGwdO3bMcs79/ve/N/H2pUuXOs84zaFDh2Tjxo2ycOFC+eKLL4xp/sEHH0irVq3Mfv/111+X559/3kwUZcqUkXvuuUf+8Y9/yPXXXy9/+ctfjB/g4osvlvPPPz9ru2DHL3/5SzPOPfdc8zj98H/zm9/I5ZdfLn//+9+lVKlSct9998l///tfqVKlirz44ovmPTZp0kTat29v/AOciYflQIZfWlqa864VJcpEv+Pr8TIgfqoMbvqcVG86PM8ONfmxcuVKeffdd+VPf/qTEd7vfvc7eeyxx7IERLfat956SypWrCh33nmnEV+JEiVyiDX3wJuPsHneJZdcIhdeeKH5GUEj4ltuuUXKly8v//vf/8yEwO/cf//9xm9AFABBI+yHH37YxPvprEM+/1//+le54oorzN9kUsj9uoGDxy+77DK57rrrzOTDRMTk0KdPHzNZLV682FgSuq2IHaJI9Idk6md9ZMjYJEmK6yLlK7wgi3M2qTkDYuizZs0yQkCMViiIElGzGgcKKPc4++yzpUaNGlK7du08H+dv0gYLa4DJhOy8wNfhNTDzMzIysrYRjz/+uHTu3Nlk7U2bNs15pznhQAy2H5j/rORLliwxTkaeT24AYT9CifXr15eqVasaK+Oaa64xFoN97cBBFAI/Bd8DVg5/g4M3sGZ0CxF9RInoMyUlaZg0bd9Pdpnlfbc0qXCHVGk9+nQX2gD27NljxMHNXbJkyTMEgDAQPf/PCom53rBhwzOex0DI7L8RIKsxwn3ooYeMSU9WHmY32XeImv/nuh2I+5lnnjH7dPbrmP15vQYrMft4rIyWLVuaQp6iHojBKk6CEK+1Zs0aSUpKMiW8RB5q1apltgrWwrEDK4XtBJ+H7QpVg7nrBZTIJGpEv3XNEkleslaOOz/vWv+NxCXMlOVrN8o333xjjoJm1QsU+q9//WuzAlL+Snps7pUQIQOe9Q4dOpgJgDRZnHkIhy2BXQmtoy7YlZGJ46uvvpL58+dLQkKCDBgwQOLi4sxqu27duhyFO2wTbr/9drM14GQcKK55zsRDvcCYMWOkXbt25rtiK/Hb3/4263WxUth+sD3g8+/YsUMtgQgkqvb0lv370+WLSVPkgfvukfPPO1d+8YtfZN24DPvzU089ZTzrmML8zP4XM7dOnTrGm85kEaqbmn01/oO88vIBUbLatmjRwvTSw8mHQ5CEIB4j7bdSpUrmb1Ddl1/mX1EgNwFhU0/QvHlz+c9//pPDh4BfAouFrQgTkxIZRI3o2Z+zSrKPpVrN3ph5DUxXBg40YJVFUN9++62rsfeiYDPyCpN7z0SEqY25DkQc7r333hyTG/4CtiWECN0CXwJbC/IW3n77bWNtWOsIiwAnJ5aCJhj5m4gXPebvJ598Yval9oa/6qqrpEXL5tK0xoNy1tlnZ10/zwl/2Z/Zg2PKLlu2zPlr4cOKPth2WQgShx6hQ/wJfE4cjTNmzDCTBL4HLyY0LA0iG2yR7PfKpItloIdx+pOIFT3JKVSs2T06sW5CXKzYOL5gbs+aWTdimZpNZeXqNfL9+nVGYDjTCMvZx9nTN23a1IjE/n4ocbvKbtu2bUaQ7PXxxPNZyT3gdbxwyGFpLVq0yNQgEFLks2D+N2jQwEQZFP8QkaJPTk42+0tuLJxxmJorVqxwHs3mSGqK9GxaT95u1ls2pjsXA2AfOmLECKlevXpW8QyDmDatq3CoWRPaa7ysp8dPwHd0wQUXmNcgvv/aa6+Z79GL8/D5zsgDuPHGG83r4YQkbVnxBxEnerza1kQnrswq5gbs69mPvvLKK3Lttdeav89gheR1iH2TgecVxMYp4MHS8Api+oTfSAqyn4+IgVcQqqQZKFmN9t+L71kJLxEjepJY2Cdy85CNhhnvFTi/SGFFIIEhPlZIPOd9+/Y1AsLz7xasuDjkQgHbF9pz8X3i+WfiZMvjlQMOiwovP98hcX9yJZTwERGiZzWyHvlbb701KzYdChAjZjDJPIHOQsaDDz5oHIFk3BXXTGY/TLJOXtsUr6HrD5+HnH6vLA1CiGwpeB22U/gAlPAQEaK3nm3SYovTqKK4cKOS0cb7ITEmMKUWi6BRo0ZGNMGYsOHskUdiUePGjc3r4/Fv06aNyeBzG6IItn+gNgsJHxEherzq3ChkxLnNhoUJ0qN7V/mw51BZu6doWW14wdnrs0IHRgJIqSUfH0dgYePkxQ3ZuQEZgNbzzmdiT+42WGnkE2DmK+EhIkSPJ90rQWyc1lueeqaOJC5bKxmnNH/4YIYEY6gjbvwMOAJJjLETAE6sZ5991kwOBYXKbMgunKIH9t9U4/Fe+vXr51x1D7L8SpcubcJ5JFNpGm/oiQjRIySvBLFr/jCp36a/+f8fliXJiJGjZOL0hXKoGPciEwDNMTH3Az3lbAcolUXgbBPINbDYld4Px1rh6GO7QdKS2yE9nJ9U/fFZKeghzVcJLREh+tatW5ubpF69es4V91g1rpNUeO49+WHvLunfprnMWLlRBnZoJkkbctfnBQeiWbBggWluQU28nQAYFK9QyEOhy8xZs0wtAJOBn2DCpULQjVx+4LuwVYykQpNFyCSDR9+NgT8F3wtJSeQn5PUcLwaNSiLFaokI0RNewsFEPbrbceX0PVslZd0myUhbJi3qNpPVafvl41b1JH6h+91mWNkJ9bHSE/q7+OJLzM2PBXDHnXcayyCcjsq8IMuR94jHvbg3NT4CagQQO4U7/HuydWMyp/NPcQcJSNQbsH2gQpAJi4zAvJ7r5iAqQSGUWxOj10SE6FkdyLzj5iNG70lY6cRuGdChtUxetEL6tm8lydvci8Hnx/r130n1u68yn8sOzH834//Fha2Kzavnxg4W+gKS+szfQZxse3B45ldVGAzUFgT2PiCk6jfLyQ9EhOjXrl1rHD+UklJSymDPSZ27m2xbnSwjh4+UxPnfBeXMC4bBde7KukkZXbt29Z2ZSNIQDUVYoYNp9411ZtuB0bSDNF2cnf/6179cjdfTpYjKSVK077rrLnniiSdMOrCSk4gQPWYhMXpWnIkTJ5rGF9xA7JFxmLkqkhALbt+mhdK9XUu5v2xF85k+//xz55FjsmfrZtm1/7Dzc3ihyw7vj849hYUJgo4//B6D0Cs+Dpx3bGnoQejmv5098Zcmpl5EHqKFiBA9NwYeX2q2cdCw8rBi2JuJhI+pU6f6boUsCv36DzCfJStCkZkhAxu9LO3ivjn9c5jBdGZCKsxKTyyeJqNYZ3wmVl3+fSz0LSBWTy6+F9D3EItJyZuIED28+uqr5gYiXdXCsc6Bh1BQH0+BB9uBSIN2XjlEf4opfVpIi+5xsmz5Gjngg2a1eKjZi+d11DarNwVLTMDW/2JLeXMn+dBujMdxXHqBir5gIkb0HALBjZKX2YZjj5bRtvqOVYQuLqS00obKmn1+homKsF5g7fmUPk2kXvOu0qlJXflg9BLnavggHEbREdmHFEDhU6HJKCY8jUv47hl46Glskl8qLw0+eR6ThBeo6AsmYkTPCo8jqSCTEMGwYhL/tjcgNeQ4jKgoYz8ajCMqFCAgevIFJuxM7tVEuo5bLeuT+srbneOdq+GDeDrOMb5XevAHNutkVSc8RvfegpxzNjmHrRoVfl6goi+YiBE9oR3qzfH6FqbtEymeVMYRtqF7rL05aZZBl1vy+HEC0mHGixzzooJZj6VC/7nTnJCRrV+R5oOTZdGodlKjySA5HkKXBZMQXnYmIkqJidMHphcz6DbEKs+hGYU9RYeJmegLTlivOFP0J+Xg/r2SduCQa2ccRjIRI3rgxuNm40YsLDj32G9S/EIMFysgsIEk1gPxYrYDWAOkwdJNlrhyKKHPHO8nOw33kMwY2U8+m7BQvk6Mkz7Dp8pBj3YpTKKk3GJu46XnhB1O8SF5xn5PjNtuu83kEVBPwHYrmLbbOAP5W2QiegWTOd2Ms0mTTjUflDK1ep5xDkIsElGip+USNwzOoWDBvKRpBDc4HmZaR1NZZltJ2UFcmtjy008/bUJNvCYTB9sMfh/TlD2rWxEDVlNe1+2SU8pmd+3aZZpU4jWfPn266S1IHwAy1pgE6VUQOBGS/cjhF7QDJ2OObkWEwbCIGPx+sA03bB0FE6tXkBdAHkc2e6TRYzfI/1XtYn5K27VDUtPdzfGIJCJK9IiNG4bMLjexzSPZ83OzcPgk5ifCt0LIPS699FLT0KNs2bLmaCs80RxHhXhZrZlUCFNx3BSWCY46JgpWVV6PeDUDJyMjsLSWicRet89jsiLNE7EhYJptkKlIBIPJiF5/iJPoBZlzRDvYf7Ni//nPfzYmde7PwGBLQfMMKgHbtm1rymttPnxe0AMfCwDLqKhpp0wY7P15P+SrewVbjZy+m73Suuodck2px6RB/VfkiXJl5d77H5a6nUbK7hhc+iNK9DiIMDHxHnvlBLIgTPa0TAbsEelSi6jZwxKWIlGIbYHt/1bQYOWkWy9i4flUl2Fd0ICTv8He2E4wrLBMJuSOIxCeQ88+hMJEgwMMoQauzPkNfBlkMdKfnlz/l156yRQv0SabsNny5cvN90gb8cJCuI6/TXFQUbPpmKD4XayH0JIm7aveKuddeK20HTZN1pyagKd/3FAuPucCaTUx9tp0R5TogeOguXE4lSbcYN6zomD6YjazurNSE1bkfbLikmeO2Dgmim47hLOYuKyYET//Jf6NOHFWInDEymPWecnEQBQCJySrLNbFG2+8YY6YYn+MpTBkyBCzZ8ZiwZGJdeHmioq1wSk6fP+0ui4qtl1WYKJOaNgrzZ8oKTeUbyFZRn16ijx+3flS7cO5zoXYIeJEz8rEaolQCuPF9xuY6oTl8I6z32ZgUcyZM8dsLei4y8rLsI/zXFZVRBfOrEPeB5MTVgYe+6LA5EPkhImMv+MlNDXN2bAkVZo9eauUqvK+ZNkmu1dIhZsukqe7zHEuxA4RJ3pglWHFoBtNNEBrLbtNKEpuezjAhxGMTwVvOp+PBCSvIVTL9iWbVGnyxM1yS8UO2Sv97m/l0esukOoq+siAmnRSPd2u0goXhL9sk022AN9//73zSP6cxLl37Kjs35cm6Ue8z9HFx0FXYNppYZkUBTL52LJQNEVehNcQo2e7lc3plf62pzoGiH65PH7jhfJMVzXvIwa8zYiEcspowFaxMegZwP68IFM+bX2SNKhVU95o1ELi5/z8JFEcMMfxS9DxhrTbomLrCsiDCAVniv6E7N66UTZuS81OzjlxVLZuWCs/7i28EzNaiFjRE+flRqI8Mxqg7tt+HpveStea/JpAZB5YIm8++6JMWXdQTp70dp+PSc77IfW2qPF5Qn84Itm+hOpMuzNFrwQSsaIHEmu4Gb1M9AgVeN0JyeHQIyJAMwg+G9eIBuAADCTzwDJp+PKbMs/jo/Zw2BFyxDQPpguNLZTyqqIuL1T0BRPRoucflhuKEFakg0cfUVmTHpEjGBu/x3kWePpN+sZEqV3tORm91LskF/bw5ASQqjxq1CjnauFhlSc0SWVeKI+tVtEXTESLnhCWPb2WxI9IhkQZGkTm7gVAchAxfj4jzj7CejbnnYni2HHvGnvRkJQkoWBTg0n15X2TSxBKqGMgbKfkTUSLHvjHxcHEzenVAYyh4MyCm5zg2CNbj+dQ9LK0UEVHmZKetke2bv5Btu4sfHdfLA5O0bUtpIOByYp9PMdVh+qkWnIcsIbIOiSdmDRlog1KTiJe9EBGGmLgKKZIaJiRF4U51oqbmmYhPI8CIbL+Ck50yZSlYz+SjgPGy/ykcTJ0fLIUFNzDcsI0xo/AayDcYLEVkaz2TMb4KbwchALtSUhMNiQC8f807OCxvH7H7VHUUGa4iArRs/+1RyEXpwIvnPC+ef/k+P8cOP1sc1Cq5Dg1Nz/WJHSTpj0+l5mjesi7HUdKfm02aX5hD5ektx35+XYbUVTYFvB3WOXZspCKTM2Cl4PXoMgIByg99XE8Ev3geihenyItqg/DmTFZWKJC9ICjiJZNrICcGBNp2EKWwp5ay+ply1SpoKNCLq+qt7UTP5JWveJl1pheUq95X9mRywWA+Y4ocNbxt1ihi3NcNr0LcN5R7EONfjjg31/N+vyJGtED4SVuXKrU8isN9St4mzn/vqBVOy/otMOKyucmQ5GQXyDzP2kuddsPlUUzRkiDRl0k9w4dnwi/SxFQca0kSmetxYVZr/iTqBI94CnmpuP8tUgCXwTNJoOB1drWIzA4a95Oevu2b5Q1Ketl+7YfJf2Utb791GuQ/UfhDM46CnpYkYs7SeIPoH8hr4/fIditgeI9USd6TFzOPufmo9NOpJCUlGT253icg4WOMfZEWNqBB6Yo0/GnUcN35TLHSUf8383jwerXr2/+Lo078uuCq/iDqBM94HXGA41DqjgiCiVF3dPnBwdgln/k9KRH445uXbtKlcqVzc8M8vqp83fziGg69vC3aa/lZv2+4g1RKXqwHmRi2ytXrnSu+hfrvc8vZIf5j4ONeD297rAMBg0aZEJSNNSguQYmO3nuJS49XbHHuPzKK6T8qX12jVOmN1l1hJbchAIcJhe+5+KE+JTQEbWiBxv7putMKNNAg8G+V7Lf6PFGLzrbwJL4M3UGJUqUyBJz7sFjFMTQiivweuU670rGUW8awY0ePTqrfVfou+EowRLVogebuEO/ORo++hVr3iN6zjwPFC4FLzbZhEF/Okx0JgX697HC4v0nOYktDeG3++4pLW26DZHdB71J07WWCX3/xo0b51xVIoGoFz106tTJ3KCsgsHUg4cCTHYSWci6wwFH220663JKL5MV2V7WOx6Yh4Djkq40JKPwWOnSpSUhoWitrIqK/T5pnU1RjhJZxITogbPVSGIhT599sd8g5EVft9wltIHQSgux0V2HMBs1+PYMOXoGEq04fNjbTkK2tp7cgOIk8SjhI2ZED6ygdl9MO2s/gZONiENgmI19MkdyB7b7xmnH+7d97PkdesJl530fkQVJEyRuxCiZs2KLc6340JaMw0F4TZKfNOMtcokp0QOmMWmi3Ly0gPJLkQQls7wnG7IjuYXe+lwjmQbYv3M2H9cYJMFwVn8g6xKHSKseY2T7pkXS6J3WsmLvceeR4OE17JHghOUi8ShwJZuYEz3QtokQFzcxq5abSSrBkjtkh+/Bipv3yPFa/D9OPbIN88s/GNehjrzeZaLs3btW6ld7Uj5JLl5ZK046W9zD64aqTFbxjpgUPdBXnkaN3Mx4uznFNpz5+rZ5pK2yqxyQUGMHExWZdfmTKcObPC9PN/1YFn09TWpVKCu9E4OzZOjIy0GWvC5xeEpuleggZkVvoT86DTi4uTmwMme/9NBhD7DEW08yES2+rdjtIL244Mq1TEns2VAa9Kdn4H5pfmr78sXqop03h0ORNl023s9EEylZjUrhiHnRA6e6WicVA2cZvfVDCc46YvSc2kO4zr6XvAa17/mRvnmBdOvSS8aN+kx6Dp4g6UUI0+PvIDLAa+AgJGGIllxKdKGiD4Ay0zJlypibniQX2i6F6px6svDo80exCqfcErNv3KSpNGnaTOq9VVderPWSVK9WzTSJ+LkJ6eCezbJy1XopbF4OqbkNGjTIigiQ5KPOuuhFRZ8LVjYy3Tg4EgHgxOKwTK8dWHSq4fXi4+OdK6c5fDDD+T+REy43ZUlNTTWJPRTh8No4DEmtVaIbFX0+YPLTjcZmupF9RjzcK7PfOvJynM93aLt0eLWytIv/VlLXfiWDR04RN85joWcdExkn4/KaFMsQMtSS2NhARf8zbNmyxXj2bVIPbaDwrCckJLhq+ufXI29jUn95670ukjhnjqzaGrzkKaUlo4+wm+2qy4TWpk2bkJwvp/gHFX0hwdGGh53z5REMAw83GXNk07EnLw75tsA+ulWavVBB6nf9UorqUuM9Ya6ThGSFzqD8Fism2E49SmSjoi8ipKMSwqKZJPXrVkismjSqJOQXzJltmPU09aTnXW5WJSVI0vKfFyjtsJcuXWrqDEjmsVsTBuXFdG3FWUk/eyV2UdEXA/rLkc1HXz5WTyswWlGRtsp1invmz59vtgIkBOUHrZOLUvpLUw3CeyTRjBgxwrR/Js/AvgfG9ddfb94DDTfy6pSrxCYqepdgAqCmnV5xlLfaltJ2kNVWsmRJUwv/2muvSbNmzaRbt25mVcY/MGbMGOMoxIrAUqDtFWWrFODQ556WVOTgk0/AvrxcuXJZp9vawRnwlSpVMtlzrPjRcHa/4j4qeg+gWIajoYi7c+IsZjXxf0SKCR8o1NyD0l8OfGSSyOtxBhMK59qxknN4JyfdzJ0719W+d0r0oqIPIZj3JL2QP09BDQ5AUl7p7mOP3cZE56QZDq3k1BSy8wivYRFQ/DJz5kyTvENUIRJOU1H8h4reJ7D3R/TszxXFS1T0PsH2yMuRnKMoHqCi9wlU15EGy4EViuIlKnqfQAgudxccRfECFb1PmDdvnvHEh+ukVyV2UNH7hNw98hTFK1T0PsGecJO74EZR3EZF7xOs6PM7y05R3EJF7xNsyO6MKjtFcRkVvU+gKKdatWp6aoziOSp6n0BKLam1iuI1KnqfQKUdffn8cPCGEt2o6H2ChuyUUKGi9wn59chTFLdR0fsEDdkpoUJF7xNyn2WnKF6hovcJKSkpph11ME01FaUoqOgVJcZQ0fsIYvUFdcxVFDdQ0fuAjIwM0wOvZcuW5jSddu3amc66iuIFKvoww7lydevWlc6dO5v21+vWrTNNM7lGJ11tfqm4jYo+jCBoetQPGjTIuZINp9VwXDXNNRTFTVT0YQRhN2zYMN8DJDH5OeRCUdxERR9GTpw4YU61yX0mvYUJgT73iuImKvoww1l0tWvXloEDB5rGmJxPt3jxYmncuLF06tRJ9/SK66jofQDHYHNUdaNGjcxZdZxzN3bsWBW84gkqeh/BybKcKX/8+HHniqK4j4peUWIMFb2ixBgqekWJMVT0ihJjqOgVJcZQ0StKjKGiV5QYQ0WvKDGGil5RYgwVvaLEGCp6RYkxVPSKEmOo6BUlxlDRK0qMoaJXlBhDRa8oMYaKXlFiDBW9osQYKnpFiTFU9IoSY6joFSXGUNErSoyholeUGENFrygxhopeUWIMFb2ixBQi/w/kg+yb7gXbzwAAAABJRU5ErkJggg==)
A small mass particle is given an initial velocity
tangent to the horizontal rim of a smooth hemispherical bowl at radius
from the vertical centreline as shown at point A. As the particle slides past point B, on a vertical distance h below A and a distance r from the vertical centreline, its velocity v makes an angle
with the horizontal tangentto the bowl through B.
![](data:image/png;base64,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)
physics-General