Question
A spherical hollow is made in a lead sphere of radius
such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of lead sphere as a result of this hollowing?
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)
The correct answer is: ![fraction numerator R over denominator 14 end fraction](data:image/png;base64,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)
Let centre of mass of lead sphere after hollowing be at point
where ![O O subscript 2 end subscript equals x](data:image/png;base64,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)
Mass of spherical hollow
and
![x equals O O subscript 1 end subscript equals fraction numerator R over denominator 2 end fraction](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/904766/1/919328/Picture120.png)
![therefore blank x equals fraction numerator M cross times 0 minus open parentheses fraction numerator M over denominator 8 end fraction close parentheses cross times fraction numerator R over denominator 2 end fraction over denominator M minus fraction numerator M over denominator 8 end fraction end fraction equals fraction numerator fraction numerator M R over denominator 16 end fraction over denominator fraction numerator 7 M over denominator 8 end fraction end fraction equals negative fraction numerator R over denominator 14 end fraction](data:image/png;base64,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)
shift ![equals fraction numerator R over denominator 14 end fraction](data:image/png;base64,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)
Related Questions to study
On heating a mixture of
ans
, we get –
On heating a mixture of
ans
, we get –
Three identical blocks
and
are placed on horizontal frictionless surface. The blocks
and
are at rest. But
is approaching towards
with a speed 10
. The coefficient of restitution for all collisions is 0.5. The speed of the block
just after collision is
![](data:image/png;base64,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)
Three identical blocks
and
are placed on horizontal frictionless surface. The blocks
and
are at rest. But
is approaching towards
with a speed 10
. The coefficient of restitution for all collisions is 0.5. The speed of the block
just after collision is
![](data:image/png;base64,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)
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then
![](data:image/png;base64,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)
Two identical masses
and
are hanging stationary by a light pulley (shown in the figure). A shell
moving upwards with velocity
collides with the block
and gets stick to it. Then
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGAAAADECAYAAABgFSTAAAAgAElEQVR4nO29aZBc13Xn+btvy5d7rSigsBMgxBUAKXFfgrTsFiU1NZQoWWN7JsiW2z1uO/zJ4Q/2dDiiZ9od4S89ER0zbss9tsNqa2RJtoKaEU0RTYqLRHGnQHADSIAECkvtlXvm2998eHlvvSwUgAJYWShSPIwMsKoyX753z71n/Z9zRBzHMZ/QZSPtct/ALzt9woDLTJ8w4DLTJwy4zPQJAy4zGat3qbj7Eqnfie7vzveZ9HuX0tLfxcTyM91/hNBS11nuGhc28uIYhEhfY7nr9IdWiQExEAAxYRgQhiGapuMHPhkrg+u6eL5HLpsjiiK1iKZpkDaC4zgmiiKiKCIMQ+IoSlgqBHEcY5omhm4QhAFBEBDHMRnLJiYijmKEphEEfrJ8QiAQCF1DQ6i9EEYhURRhGAa6poFI/hArhgo0kUHXV3FvnodW9QREUchCZYHp6WmiKKLT6TAwMECr1cJxHAaHBnE6Do7TIYwiTMNMPhnHaJpGqVQiiiKCICAMAxzHJYoixYBMJoNlWQRB0H1Pspjpa5hmcs0oitRndF1XdxmGYfLghoFhGAgBnucj3aE4FsSRzu7deygWC4RhmDBF64+0XlU2CyHwfI+pqSnCMMTzPDzPo9Vq0Wq16HQ6+L6vdu/SzzqOQxzHaoFt20bXdfXeTqdDs9lUf9c0jWw2ixCJyIiiENPMJX8PAwI/oF6vKyZJ0jQtxQChmAIQhhGdTsCWLVspFgtEUdS3xYdVZ4BGIVcgk8lgmiZRFFEul7FtWz3IwMAA+XweIQTNZrPn85qmqYXVdV3t4jiOEUKg67razfJ38u9pCsMQ3/NxHEcttny/ECIRP7quGOB7ntIUmqZjmXn1PbquKwb3g1bEALkQkpY7klEcAxFRHFEoFNRCNptNPM9jaGiIIAiYm5vD8zwGBgYIgkA9nNyJrVaLIAjI5/OKifLU6LqObdu0222CIFC7eHJykjiOGRgYYGJigkKhoERgoVBQ15EMkyfI9331LJIpQmhoIoNUxCtZfKm70pQWe+ej1TsBcWIFBUGApmtEXnJDvu8ThqHahXEc4/s+ruue9XCmaSo5n8lkeh5GbgLXdZXIkHpgcHBQ6QO54KZp9ux8wzDUZxZFVqT+X8p6Xde6m21tQmSrxoBkd3V3TLxoucgHlHLftm00TcP3/Z7PR1HE9PS0Oln1ep1yuYxpmur0yVMAqPc5jsPg4CBRFNFoNJR4i6KIfD6vGJMWQendmhZxi8+wWqtyYVo1BsRxrEzG9BNIySV3mNzZiYjSuw+evKdUKlEoFJTokvJXCIHQkp3peR6apmHbNp7nqV1uGAalUgmAVquF7/sUi8Ue8SPvQzIgEXsRnud1f9bQNIEm1s4/XRED5CKcj4IwMeFcJ6TT9jF0C93QMY1kh4VhSAxomuja4SbFQoF2p0Oz0cD1PDJWhmbTpZDPIzBpNNrJYmcyaATEIqJQsIiiZNGkBVStVtF1nVwuT6ft0Wi0GR4exjRsOh0HAE0IojhG13U0zSTwfTzPQ2gaAwMjeK6L67gEYUgUdbgqkyEIAvU9F1qfS7WUVsyAC7wD08gghGBhocb3vvuPeJ5HuVzuOmUajuPiOB2kctN1Hcsy8TwPx3HwPI9Op0O73SafLxCGAUJo2HaGQqFAu91G02LKA3k8zyUMI6W0HcdB1zUsy8b3BYEXMDwyjGEYtFotQBDHEdIbS4vGbDZLuTyA57k4jkOj0cAwDEaGR7jmmmvIZDIrUsSXaimJ1UjISPlbKpWoVqu8+OKLAGrnSCcpvUvkqZDm4NIdJITA8zx832dgYICFhQUOHnyFeqNCGIYEQUC5XObuu+9OmagGYaAhxKJVI8WLpCAIiKKITCZDJpNB0zQ6nY66H8dxMAyDvXv3qr9L564ftCo6QNM08vk8AIODg9x3332XdB3pK6RldhAEmKZJrVZjZuYM2nSsTMyxsTGuuuoqisXSopUVGQkjwpAwDMlkMj0m6FJGp0/D0ntptVpYlnVJz7JSWjUlLM08QClKTdPO+eBpkna0fK80W9MKs9Fo8NbbbzM1dYpcLqd2sjx5AgjCiCj00TRd3dO5Dng67pT2ReRL0zQKhUJfnTBYZU9Y0tJdc6GHkCJEOl3S+kkUpkYYhmSzWXLZLGNjY8rsLBaLiVUVgx/4RGGMrtuK2ekFXXofSz3rc91Xv2ltQn4rpHSMR54iQJmvA4ODVOvzNJtNGo0GURSRy+aUZRPpIUGQ7HjpZ6QduvVIq6KEV4vkotdqNV566SWmp6dxOg62beO4Du8dPYyuxxQKBfXerVu2gqCrJ+rs3LGHf/EvPodlWSrsvJ5pXd2dbgh0TafRqHHg8R9z0803sWPnHuUYDQ4Vcd02Q0NDKmBXKpao1+vk8jmmp2d44YUXuPXW29iwYUNfo5irReuIATGaiIliB9MS2DmdwaEi27ePU683GBwY4JZbP42uaxi6TRT7OE4H13WZmpqiXC4BGjt2JCEMz/MwTXNN5PiHoXW1RWISkzCbtRkbG6Ner9HpdBAiyWT5vkcQBECSsPE8D9d1ieMYx3Gp12tYlqWU+DqSruekdXQCgK5Nns/n2bp1K2EYUi6XldNkGqZKZwqEMiOlyVqv18lkEitouTzBeqR1dQKi7qJlrAwjIyNUq1WazSbtdptWq0UYhYsipftP2nlrt9tnmcDrnQnrigGLcfgk8dJoNFRk1Pf9rqebOFBxlERAZU7ANA1c1yWfz9NqtXpC0OuZ1o0IiruICl03ESSe8wcffECtVmN8fFzFY0zLRNMM5a3msjnK5bKKDY2Pb6JQKKjM13qndcMAAVimhSYSXM6ePZ9ibGwMXdeVg6ZEUTeIJ/MDtm3jui6u62IY69/ySdO6YQAINM0AYhrNKqdPnyKfz3PkyBF+9rOf0el0GBkZodPpqCBZsVjEtm0sy2JoaJAwhPn5eVzXxTTPjrCuR7psnrCU3YvRSliozHDixAc88cQTNBoNFaeZn58HYOPGjYyOjqoslzRDO50OnU6nm/YUbBjdwP4b9nPLzbeRyxWJY099p9AMDN1S+CM4O3a1lnTZGCCT85Zl4boer732Cq++9iJvvPE6IyMj7Nmzh7GxsZ5YjkTMySSPYRiKgTKG5DgOzz77LJVKhX379rJ7125uuulmisUSnu+g6xlMI/sJAyBZ0LfeeovHHnuMd955m81bNrB37/XcfPPNdDodFhYWVPLF931s2yaOYyqVCrquk8lkaLfb5HI5hoaGME2TbDaLbdtMTEzw8ssv89Zbb7Fv3z6+8pUH2bJ5e9d3ED2R0supMy4bA1qtFgcOHOCxxx7Dtm2+/vVfZ2R0gKHBMvVGg/n5eZVudByHTqeDZVlks1k8z1MIOZnIt22bUqnUA6gyDIOZmRmee+45Wq0W119/PbfecgebN29XifzLTZeFAe12m3/6p3/i5z//Ofv37+eee+5h06aNzMyeRtMEvu/T6XQwdJ0YEnBvd9El4sF1XQA2bNhAPp/Htm0FWykUCuTzeSWi4ijm2Z8+y4EDB9ixfRe//dv/C6Ojo32HHa6E1owBEhDlui7f+ta3eOqpp/jqV7/KnXfeied5jIwM0WrX6HTaKknvuq4yQdMyXipoy7LQNE2JH9/3MQwD0zSxbVsl1IeHhjEti+eff45/+M4/EgTwB3/wB1x//fX4vt/XnO+FaE3ZHwQB3//+9zl06BBf+9rX+OIXv8imTZsolUrEMeTzeYrFonoJIZS1JNFwadSbTLpL+KNlWQquKBnheR6O62AaJrfccitfefBBFhYW+Iu/+AuOHz++Yghhv2jNGBCGIY8++s+8/PLL3HbbbTzwwJfJ5XIA5HK57mKHytKRVopUwEEQ4DiOQlqn0db1el0packg0zTRdV0pZT/wMA2LX/3s5/izP/szSqUSP/jBD5ibm1urJViW+soAmWAH+PnPn+OZZ3/Cli2buOeeu2i1arRadYLQo9GoYpoGQeDjeW6P+Im7YCpITpD0eB3HwXVdlfz3PE8p1jT8fGR4RN1HUgvQYvfunXz9619jauo0P/x/f0AUJ8UlcRwCEWuFC4U+M0Bicqanp3nxpee55to9PPjVByiWspiWBiIgCB0Gh0uYJui6hq4vipAkN5ClWCxiWRamaZLL5chms+TzeTKZDNlsltHRUaWYpW5Q8HMtuYbUB37gMj1zmh07N7Nv/7W89NLP+cUvXgI8hAgII3dNI6h9Y4Dcjbqu88Ybb+A6DnfecQejoyNMTk4SRYl9HwYBge8ThIFaNKOLVsjlcuRyObWg8rppq10iJ6TIkS/53TIo5zgOrXYLz/MIw5BqtcKdd97B+Pg4jzzyCEePHQV0wiBYrENbA+obAyTs49133+UnP/kJm7dsYWxsjPn5uSTLhehxsiQWyDAM9O6/hUJBxXt60HMp5LVUvHLRJSMM3VAlUEEQ0Ol0aDQaOI5Du92m03GwrAzXXnstMzMzvPLKK0CIEBrio1ekdzZ5nocQgpdffpl2u82uK65gbm4uSaSXSkzPTJPP59VCpgsuZKwHULs4XakiPyMzX5qmKUaoYgsjYYjv+/hdIG6S3hSJj2EYTExMsHPnTrZt28aRI0doNpsUCkXWskpy1U6ANBXlyzAMjh49yuuvv851113HwOCgqhmTylRie8IwpNls4routm0zODhILpdT6LV0OZJ0nizLwrZt9X0jIyPKAcvYGQVf7DgdFazzPE9FS4UQGF0zdefOnTQaDU5MnADONkvTMag0Wm81qC8iSO7oo0ePYts21157LYODgyqrJXcpLAblJBBXOmG6rjM0OKSKNNJiKi3nc7kctm0rfZHNZtE1PYklVRZoNBq0220VzpDWVavVwnUS6PrmzZsZHR3l+eefx/XafATrhHtJMuD48eNKzFSr1aRGIGUqyh0lky2WZdFsNpW1I2uCpRUj/QHpiMmcgNz50q8I/ETp1ut1AIV6dhxHJfKbzaYCFeu6zpYtW3jttdc4OXGS3buv6ceyLEureAJi9RICKpUFjh07Rj6fo91uMTMzo3yCNCRdZrUcx1EL5Xkehm7gB8mCZzIZhoeHVfWM1BUyOJfP58lYFrpu0Gw0e7Jm6bqDdrutymelyGu32yqrZlkWZybPrN6SrIBWrVJe19OFbYJms8LgYJ5du7ZTHsh1rZ8ksFapVMhkMpTLZSqVivJopWyPooj5hXkFORkcHMRxHBUhnZ+fZ3x8nJGREYXhNwyTmZlppqamyOfzzMzMYJqmih9JB67Vaqk6MfmzaZq0Wi2y2SynT59WxSHSH1ha27Ca1IdeEQlNTp2h2WoQhJ4CVC1Wo8dq50lICUCz2cSyLCWWLMuikC8gSMqQKpWKKtz44IMPqFarXHXVVWzdupUzk2eYmprC8zyiKKJer6Pr+mI8qCuCluKF0jpIljuFYYBhrE2Spm9mqCzC7nQ6nDlzRkFG5MPLlOLg4CCAss9N08RxHCzLUuWq7U6bU6dO0W63KZfLXHHFFRw8eJBXXnmFqakp7rrrLuVwVatVgiCgUqkon8B13Z4eFOlaBKl3pG6am5vD9wMMI8NahCT6xADBzPQMvu+rZEm1WlV2uCTpYLVaLSYnJ8lkMiqun8lkcByHWq1Gq9WiVqtx5ZVXMj4+zsTEBENDQwwNDfH2229jWRZ79uwhDENqtRoxSZmrZIDc3RJhISs25aK3221lXc3MzHZD54sVnv2kVWNAFC8GsTQRUigWGB0dVeZlvV7vqZiR5mgURVQqleRzXXktgVXtdptisciZM2eYnp5W1lCCBXUYGhpi06ZNFItF6vU6rVZLKVuZrE+3OZCWlxBClblKsSYDdqZp4vmeup/VtPmXo1WtE15s4hMrWex5HrlcTuE75YJEUaSUo7TrG41GD5rNcRzGx8fJ5/MMDQ3hOA6nT5+mXq8zPT0NQLVapVarsX379p5aYOlBp7udpMuP5Hd6nqcCdVEUJUZAuFhHLJ+tX3njvumA9FGX1e7tdlv9XXqyrusyPDxMvV6nUCio6Gcul2NhYYFcLsfWrVv54IMPeO+99xQjc7kc9XqdyclJ9u/fzxVXXMH8/Lza9XIDSPkvcwSwiBeVbRFgsW1BGPZ3xy+lvjJAwj5kbhYWH16GjbPZLGEYqsI7iemPokiZmTt27ODtt9+mWq0yOztLoVBA13VOnTrF3r17ueeee3osH3mddC+hdJwpDEOl8KXOkWZw0mehX6tyNq1qr4jUT8qUlD1/ZLpRigDpBCW4IFcp63REUwjB6OgoI8MjPPzwwzz99NO8+uqreJ7H+Pg44+PjPPDAA5TLZWZmZhgcHGRyclLpHZkjlv6EdOJkSEN+j6yId12Xer1O0O2iIi2mfqInVu3KWk/vNo3BwUEWFhZYWFhQDlan01G2uYzhW5al4j3S9s9ms4kPUCiQy+XwgyTdeMcdd7BlyxZOnjzJpk2b2L17t1ro4eFhXMelUWgoBZxeRCn/5c9S9DiOQyaTVOMPDw/T6TgqkSQL/dZ9ofZylM1mmZ+fZ2RkhI0bNy6GGFLBtHw+rxbcMAxVpS4ZYBiG2pmu61Kr1QjDkA0bNmDbNvPz8+i6rnRGIV8giiMVfkiHOJbmmdOKXr4ajQaNeqPH/PxI1gkDEEOhUEj+t9umRh5nyQRpjUjRIJs0qRQigmqtSrVaVebq1NQUURRh2zb5fJ5SqUSjG1jTNC2polnSgkYyUYbDZaMmSHTR0NAQJ06cYHJyEj/wVfeWj1SdcJwKRQhCPnPTZ5icmuT48ePs2rVLLa48ztLGTr/kwmcyGbX7ZYhaKlIpyiSjfN+n1WwSd/MEQ0ND2FmbwE/6xsmT1263yWQyKnkvvWJd19Xu37NnDzfccGM3KbM2tGoRpvRChlHApo3j/A9feoD5+Tmmp6cxTZNyuUyxmDxcNptlYGCAcrlMuVymVCphWRb5fAHLtFTyJOmEoqsoptQncsfn83n1O9kqLQxDrIylKulN06RQKKjvGxkZUQZBuVxWnvi+vfu44/a7GRkZWWxtmWoa2A/qWz6g0axTKOa55557OXjwIPv372dgYEB5sFL0yHiPaSYFeEHgqwCZtKTOlYlKe9My3JBWmDKVmen2/gnDUOUUZCeXMAx577332Lt3L/v276PZqmGZeTRN7+l30S/qS4xVEzqPP/44Tz75JDt27GB6eppnn32WOI4plUpkMhmVbFevjE3GTEREo9FQ6IU0NHFpq7F0CzKZ8Uq/X/oDEpxl23ZX4evKOTxy5AgzM9Nce+21HD58mL//+7+n2Wz0WE79pFVkgEi9dN5//wNeffU19u+/gVtvvY2XX36Fubk5CvkCvu8rL1RaO0mFjKYQDOnGrFJeS5IiYWkbsqUWT9rel9+ViMEyGcvGcVyOHHmXUmmAT3/6M5w5M8kLL7yI46wdNmiVRJCAOH0pnYHyCEODG7AzJe6959eoVuo8//zzDA0NqVKjQqFAxko8ZN9PTEcZEJO73+yKKGmmyryCDDNICwtQ9QJSrOm6juf7GN0MnJ2x6XQ84iigWCziexM4nZCvfvUBMlaBjFXA0JM2Z1Jhp/PX/aA+nQCw7Ry+HxJFMXv2XMVnP/tZpqameOqpp9A0jcGBwa4zlMDRq7Uqnu+pvLHc+dVKhcnJSVqtlspKpcWRbHEjA28yuSK92zAlvqI4Qtd1xsY28vrrh3j88QPccsutXHPNdRiGSaFQxLazZyVs+kl9A2bJWi7XTUzIG264kR07dvDkk0/yk5/8pItwS3q4ef4iFnSp3JdpQ5lQB3rC2lKpph0s+ffexL/fLYnKcOTIEb797W9jGAb33HMPuq7j+z6NRoNKpbKm0MS+nS0pd6UZF8cRX/rSl5idneXb3/42QRBw3333qQR9NpvtYYJkRKFQoFAoqL7RvT0+F/vOyfoBWcAhr2FZllpQy8rw3nvv8s1v/t8IIfiN3/gNCoVEJ8ng39jY2JqWLK1eLGhJ0npycpLZ2dlut0ONbNakVCrx8MMPA/B3f/d3DAwMcNdddytUnK7rKoSQVsaAwgqVSiUl+9vttoKgy/ZlmzZt6kmiy1jR0NAQJ0+e5C//8i/xvIjf/d3fZdeuXSoqmslkaDQaSTCuGx2VEdWPRD5g6Q3u3LmT0dFRstkcnpcUUDtuk8GBIX7zN36TRqPB97//febm5rjrrruAxXLU9AIIIVRUU3rGUu5rmqbMWQnenZ2dxbZtBWGRzT5efPFFvvvd77Jr16e4/18+wJ49e1SmTN775s2bufvuu8nn88oM7XcJU99KlKrVKnEcK+fLtk2EkKakoFJZ4Iknn+BHP/oRY2NjPPzww8o0lUAuSTLFKBdfLphExqWbb8uC7mKxSBAETE5OcvDgQX7xi19w8803c/+//DKDgyMqXiSdOelPSIcuHafqJ/W9Rkza5KapEYRO8nBCI4pjNKHx1ttv8uSTT/Luu+9y2223cfXVVzM6OqpgKzJG32q1lOiRAT3pYLXbbWzbZmBgQEVZK5UKb731Fm+88Qa+73P//ffzK/f+Wrfh62K3dmDZ5qzScup3DXHfGHDixAlc12X37t3JF4kYOadFyvWYJBrZaXd45plneOGFF8jYGbZu2cLw8HDSKbHbj3RhYUHF6TOZDIV8Hs/3F8ubfF8l5Y8dO8b8/DzFYpHdV17JTZ/5DDt27MTzXCzLRojFWgN5qgzD4NixY7zzzjvcddddDA0Nqa5bH5kBDmmSmJ2tW7eqh5APLvt5Jm1nIJst8IUv3M/dd9/Lu+++y4EDB/jZz15gdGSU8kCZDRs2sH37dgp5nYWFBfK5ElEUc/yDkwoZNzs7y/T0dLficoR77/01brnlFsrlsrqnTKb3cWV9gTRvDx8+zCOPPMLVV1/N8PCwOiUfSQYsxYGej6Q5aVkWV199NTt37mRqaoqjR49y6tQpTp06xdTUFJZlKYxpGIZUKhV27tyJ4zgUCgV27NjBLbfcwo4dOyiXy8qKOt/3p81aCQhYy8rJvjFAKjBZPH2hqKJUiNlstttQu8xVV12FEIJ2u62KOzqdDvPz84yOjqodLISgUCio9vXptsUrMR9lzCibza5Jt9w0rTIuKCG5m2QhnWzKsbRz7dKfJeBK4kOlNWLbNlu2bFGWys6dO9UuTYsIWbyRDtattGuvhLKkJ3SsRTR09ZBxqVCxruvMzc0xNzenMJvLWRPLNdJOlx0td2qWiof0z2nz9GJIiiHbtlXLfXm9fpuhfRNB0o4Ow1DlhtcjSU9X1hovLCz0VGR+ZINxuVwO0zR70HDrkaSn3W63iaKI4eFhBSJL9xTq2/evlh+QTpgIIajVatRqNbZu3aoe8kKNtNPXAC6ouFdC6TjOubJc8vftdptKpUI2m2V4eFiBAS40wuTD0CUxQNrw56P0IIY4jul0OqryEVZHvi53H0t1hFTSchMAZ+WN5b/yXpPmf8aHCkUs3UxLST5/36okFxYWOHXqFJAwQyKj15rSwTYZ3EsvTloHtFotXn/99TVtd9mfpLym8fTTT/PYY49Rq9WSmtzL1J0qXZHTarWoVCo9ekmGvqMo4pVXXuFv//ZvcRxnzXyBvilhiQGVs2UuF8n4URiGHD58mCNHjihRlK4fkC+JF1oruiQGKPl1jheg4j/Srl/6mdV4yOXuYylJ+EkQBLz11lvEcczQ0JD6fC6X6+m23mg0qNVqqs3BpdL51if9/JcsFy60gDIpHkWRUoz92Fkr8XQhQeJ94QtfUMXckmS4RAih+g+l6wr6dV+SLn/bwD6TREwAjIyMnPN98jTI8PZaUV/97LWIpVyIZB2ClPey26KktCkrG0B9LBjgeR5zc3M0m83LygRZGSPzxsuN2JLJ95mZGWZmZhQATI5P72elZN8yYqdPn6ZSqfCpT31KmaCX+zQsRxIIpus6s7OzTExMsGvXLsrlck9Za7+Ccn1jQLopqnR2LneLyOVILrAcINfvEeZLqW8iKIoiarUa0DvDd72R3CTS7JRD4qS3LCGSffv+1bpQGuYB8NOf/pRHHnmkpxB7PVK6eO/555/nr/7qrzh9+rRa+H6HJfqWkDl+/DiNRmPdjxIEVNMO13V5//33e7qs9Dsp07cryz6fsP4nGaUr5+VM+rWivjEgXZC3nnVAmmQLhLWkVWOABF5J8JVp6kRRkHqtXwakQ9JLky/9vu9VYkCMpsVoWoSmRUBELm8yO3eGVrtGEDqsUx0MLBZ5yBqEZA79YpyonyK0L037IBm4Vi6XCYMATROsZUPsiyGZMUtKZPPMzs4quKKmaX2PDfUpGBezddtWMtlEqfnBpYd1+01S/EACT7/xxhsZHh5WKAnZRLxftEqecAz4pHd5u9NOEtp2FtdzMQ0bw7A//FetMkk7X54ECciVveQMw1BFgP2gVTsBYRSSZkDWzhHHkcoHi3Ua+ZbtbOQ+NAxDDQxaCx+mbznhd987wgsvvkCz1VRN8NYjSe/dNE2OHDnCo48+qkLWa+EP9AcVgc4LL7zA448/rsqL1rQN1UWSNDVrtRqPP/44TrenNPSfCX1zxEqlkpoBIFOT65HSUVvP8xgbG+tBcPTbizfkTaRpOdDs+W8kPqtjliBJdOia3q33dbBto+c6/Qa+roR0XVeBt0KhgJUxcb0WEKHrEUEQ9g6SJjnhQvTqtAut4bnIgLO5vLQsc0UM0Hp7xrleMmgnCJMCiTDovcn1lJyRiAjP84jCCNd1gCjx6kVIHC92AEg+oPUI1A8D4u1rMC6OY8IgvKzArAuRzAlLZ8zzPZxOBwiJulbcR65dDaCaoiYtwMS6zQekh8QBeK5Hu9MmCJP4lSb6y4Blt+WlHKc41TlXiIjRkVF27tyZAJFSreDT71/6u8slltLlqkNDQ2iaptDcEjMk0iI2jnsmLS23XitdQxHHcXwhJO+FKQbR6wmHQUilWmFwcKiriKMLesKX41/rMTIAABkjSURBVJTInhSyWXi1WkHTIwYGSlhmBtdzEJpA11L3Fuuslg/bNwbomkkUxTRbNTJWBk230MT5+29eLjElMUOL8EYfiIiJl1ewq8iAvnnCx0+8zwsvPpfkVaNgXVk9aZItcWQb+3feeZtqrZKYngjCMCCOPwJJ+eRSyUtg8vrrb/LjHx9AEyYaBmJtB7eumGSTJ4BXX32Vb37zmxw/PoHvR8SxIAwhigTp57sUrz6NwE6/+tayLPBBYGKaWQUNXI+HQLbAXOxTFJG1i1hmrhuUy/aUvl4qnQum2ddRhr07ZR2ufpekjzI/P9/TpWUt7nl9yoU1JLkrNU1TLTXXkvrGAFknvF6VryQpWjQt6fi+ZcsW9be1uHcDLmz+pRMWKyWJBZW4S9u21y0zZBGJTD/W63WEEGQymb53S+nblWWDpU6ns25D0UBPmEROWZU1AmsBKFtRTvhiT4CmaZw8eZKFhQWuu+66c9ZvrReS3dhlW5ydO3cyNjaG47gYxoXb7XwYWkUG9P5dS7nucRwh+hzU+jDkOE4PjDIMAjK2TbvdSrVWXkqr8yyrNksSsZiUT+S+S7VWZXRklDAK0DWTOO7VNevhVMhiQnlKK5UFTFOQsQ0QAXEskrC0WLzXOBbE8fnv/ULPphoGrspTABCplyYEP3vuWX7wg39keuYMnuckvlp8jtjKZSSZNtV1nYMHD/LDH/6Q+YVZIETXBaapkwRCF58v/Rznel2I+sCANAkmJyepVqtomt6FpaxfiuOYZrPJ1NQUr732Gq1Wm8U0qyCMQoIwUK9oFWNDH6pO+NycjsnlcgwNDVEqlbqu/KV+U39J7kTphOXzue6UD50wdNH18Cx8qKZp6Ku0dZdNyi+ldBdZWXUup1DIUK6ui5Re0lhYWFC9ntvtNrpmoeuLXqaUuenu51JufpiKmnMlx1WXxu6/6epISDbU4OAgui4hNDFBGKCFSUIpnZCJY6F8B8nA5VrgLHcfS2nZpPxSSk+ak86JnEIt+7iloenoMcVikUqlgq4lrSYHyiMYhlDOTnoh0qWjMih2qQw4V+ZNLr5kdLpTrlygZrNJtVrtRkeTuQSGbhBGYc914zjG77ZRlg3/isXiWe9Zeh/LWYEXFEHyRuWNSwx9GkefychM1+JE7ZGRUebm5gijiHy+QC632ARDPrgsBQIUgEvCRFaL0qEGSfL/O50OrutSLpcRQlAqldiwYQNOp0MYRQR+gKFn0Zeiu3UDQxdqEl+6vcHF0ooyYlKMnDp1irffeYd2q8WGsTFcx8GyMuTzWYKgQzLMKkbXdI4ePcrxE8e59tpr2bZtG1EocN2QIEh6+QdBwNDQEHv27GFwcIgwDNTQ53TL+Yv1HdLPous6rVZLzZKRDWPDMBEflcoCb775JkePHsU0Ter1OidPTrDziq3s3Lmd+fl51fUxbd3omkWhMMCOHTvYtWsXxWLxgg2alqIrVFf2OI7j5aYTpUnXBEfeeZvHfvwYlUqVZqvF8NAQjUajeyJsNAM831PFbcViMRmuHMeMjIzSbLbQRDIHLJdLYu2Tk5Ns274d0zT44P0P2Ld/H/fccy+bxzfjea5qyr1IMjFyrnuNkWai0DROTkzw6KOPEscxhUKBMArJWBl1eqempqhUK2hCww98SsUSENNq17Ftm1qtphq/phuEC6ET+BFHjx7lmmuv4V//9r9mYGAgdQoEQvQmbs4FdjOW+2Pa8xVCEHgOLz73DFfu2Mqd//NvJoMW/KA740uj1elg5bMYpql6hEqdIXeG7NmQiLQY0zQQIimAiKOIXxz8BQcOHGB4uMzm8U0kndaXHmu9hwHpPg/JzxEdp46uJwvwTz/4LuVymTvuuBNNS7qhlEol5XjdoF0PoGI/cv6kFItSHMo5x7lcjkKhQLPZxLIsTp08ybf+23/j6Wee4MsPPAhClrQKNM3mfN7yijNiMjp4+PBh/tU3vkEQBNSq1W5X2gRPaXV7A0kIh6w6D4JAjSOXkzBkZbph6ERRzOzsDGMbNrBjxw42b97Mu+8e4b7PfSERF5dQVZNYJwau49JsNtmzZw8Q02q1abVaatS5ZGA2m1Ujs2RljByxK09zWoE7jqM22fYdO/j85+/jnXcOX/R9SlqRH6DrOu12Mig56mp913WTsp5cHjSBJ2LodiEPgmRKURRFambYUmtH0zQlomJQ1lEUpbreXqT7JoSgWCihaYvX2bZtmxI5cgPIJhxy00hIipycJOdeyhB1WgzKoRD1eh2ATttRHQEuhXoYkDbZ0oljgIGBMpX5eXLdHaPs+DjCNDJoUYDWvVHDMFSXlHTDvnTVuaZp2NmsOubz8/M0Gg02j28Goh7U8kopiiI6TgPbzlCrVTl16lRPK+RSsYTjOqp7ShzHZKwMQhNJKVV3akcYRURd0Sl/J68fBAHtdluddM/3us91ab6+YoB0qKQNnshugWUl9rHreeS6O1k2NtJ1naCbsOg4HqJrjp2rhZg0aeV3WJaFJgTValWNHZEOTxRFKn6kKOa8Dypj+5ZpqS4ojUaD0dFRgiDAcR0lbqRVFImIOFi00eV9yQ0jN2W6haW06R3HUTMxQUuBt0RXN/UCnM/LAAmglcfN8zxarSZCFJLdEMf43TEiaYfMzmTw5bHuPlgyMaO3N6ecESzHykomSH8gDENarVZyWrjEoTkiOVkxMYZpMDQ01DO9VX6nEALd0JUfslxf6/RplZtTkny+3hBFbxBuKQPO9Tw9IijdoELukjgGswvdkDshPWXO8zzo2rhyGIKU5+kdk7EySrZK71OeFilvC4UCWTt70bJfPSSL4RLTMNm4caMSNenO6tKBkhvuXAkXuWhyBK6k9PUWY2JJoC4hDdNIhtQt/cw5GJAcNznGaWFhgS1btjI6OqpuIIpjXN/DD4Jk/ktK3ERxTLacKF25yBJdIOcH6Iau5vu2Wq1EJpdK6hphGKqZvxeqRTjf39IbZWBg4KwTIG15IxVvkhtCng75GWn/y/lmaU9eKnK5uGEUdi08CAKfgwffwOl4RFFycq6++mo2bNiQOkndrolhGCK0EKFF5PIW3/3e/8dPf/pTfu/3/i2jo3cRRj6O3+H4mVP4xLQDD6eZTKwwDANNxOimQavVUmaaYRgcOXKETCbDlVdeycSJCU5MnOBTn/oUm8c3U6/X8TxPWRJSRG3dupW5uTn8wFeDeXqPbsjSY700ZqR1ZTMkc2yuu+46oiii2WyqTRHHcRfhnCCiz5w5Q7lcZnp6mlarxY03fpp6vc7BgwcZGBjg+uuv59SpU8qacl1Xmau2bTMzM7M438aymZw8wd/8zX9ldHSETMamWq3wrW/9NX/0R3/EpvFNxFFMqTRIHGsYkATRNGHx1E9/wptvHuKqq/YwMXGC/fv3YWeS0eFC03A9jyAMe2ri6R7BYiHxfP/z//mfVY3t3Nwct912G++99x4bNmzgwIED/M7v/I4avCx3Wnpn+Z6fJNiWRZItQuAXd1Hve9JBLzmUTYoJeQLiOCYCDCFoNBr86Ec/wnVdGo0GJ0+e5POf/zyVSiWJZXVn2KdDGenvUc5mDLqReMmTk5MEgcfv//7vM7ZhC3Hs8hf/5S/48eOP8W9+5990aw9ChOj2jg7DkGarwhNP/Hf27dvHtm3bmJiYWByyHCahZzmza+n8xiiKKBaLvPXWWxw+fJhrrrmGP/7jP2bLli3MzMzwJ3/yJzz00EMEQcDCwsI5i589z0tAsZpQw3kultKKVs4llgw5Vw4jCAK2b9/Of/jf/wMPPPAAr776KjffdDN/+qd/ShiGzM3NqYmuUixJJiiGi26TWEKOHTvGyMgIQ4PDhJHH/MJ8d4joGJ7vIRBE3ftIcEGazoEDB7Btm4cfepinnn6KF198kU6nQ7FYVC64DL9KLze96yrVCrNzs2zbto1f//X/kUajxujoKLfccgvjm8Z5/dDr7Nixg02bNqk+/fPz8z27XDJTCIGhX7wnLHe5HJfSbDbPsl4UE7p67PTp08zMzPDQQw+RzeVotVp8/vNf4K677ubU6ZNs3bqV8fHxnjIryYCewj0hEGj4gadGuP+Xv/y/OHX6FDMzMwwODPLv/td/Rz6fx9BNolhADFoSFazy5BNPsH37dt5//30qlYraQb7vKRkKicyUslT24fQ8T004uvPOO3HdDqdOneLEiRNs2bIFz/c4fPgws7OzyvPsdDpKxjuOQ71eZ2pqSjXWDqNL7zEk58BIk7jZbCpzUzpmAOVymWPHjpHL5di2dRtOx+HQ64cSSDoRExMTACo04TgOjuN0FbOj7lUIQavZIgwDojCiWq2ya9cubr31Vr50/5f4wn1fYHZ2lsNHDndbYvrq2YwwDPnnx/6ZIAx55plnePLJJ9m7dy/tdpvJyUnFfbm7pJWQPgG6rtNsNjl9+jQ333QT2WyWM2fOqLxBs9lkYmKCffv2MT4+TrPZVB6mnLi6tDXMuYYtXIikiATUSfA8T82WhGS6h+u61Go1Tpw4wZ49e/B9n5mZaRzX4apPXYUgw+nTpwn8AF1bLGWV9xTHi8kj27YplUrousnpM8mJ+trXvsbe628iMRxinn7mad5++21uv/32xBkNItDBeOmllzhw4HF+7/f/LZ++4dPouk69Xuc//R//KUmqCxNiFGIsiiI6nU5PQsYwDI4fP061WiVj2zQaDY4cOcKuXbvZOLaRdw6/w/PPP8/9999PrVZT0D/ZJFv6Frlcrkdpyt11MSTThGl/JH09z/NU1mt6epogCLjxxhuZnpnmjTffQAjByOgontdiYmKCjJ3p9sHoHRIkI7tSbGq6RhQHvP/++1iWxdiGMWZmTgLw8isv02g0kgGiGGhaQKx3r/XGG2+wdes2Pn3jZzANiyD0iOJkPvvx48eRIWEZD/d9n06nQ6lU6lmkbdu28Yd/+IeMjo4SBiEPPvggnU6HmdkZdmzfwX/8s//Ixk0blSUhnTaZ7tR1Hdu28X1fLdjFLr4QyZzKWE8QDVJhymuFYUg+n6dcKkE3AzY6Osro6CiWZXHTTTexa9cubDtDEPp88YtfBJbP7xqG0VPcoWsZGs0KL7/8MkePHuXf/2//nmazmXSNiWIe/MqD3H777cQkOCTTyBLHYNx8883c9/nPJvFyL8FxlstlHnroocRr9V1M0ySbzeI4Dvl8nmw3iJa2KAzD4IorrqBWq1GpVBQaotlsYts245vHexIcuq7juq7CjwJqMKc8BZeCro6JIV4svHAcR40llPdc6caeBgYGKBVLdJyOCjGPjY2xsLCAEILx8XHa7XY379GdrARq5r1khOu6NFtVioUiX//61/nKl79CFAuKxVLX49YplwYQAqLuMFHT6OYD9u+/gRiPKOod+XfNNdd1sQHJ8cpkMlSrVTZs2KDET3pxXNdVDpBhGjRbTRUz6nQ6SszI6XZpi0f+zrZtOp1kMQzd6LG7V0pRGBFGiVzWNG0xvtS9Tj6fp9VqqThQpVLpGeQmN0IYhtRqtZ6EEiyivqXesiwrET9hMrN+08ZxTDPHUv8k0SExoGFnzHRCJlbucu8HAvXFMuYhux+eyz5PM0S+R/oKS6Oj50IvXIriTV8jihdNTakLlkY18/m8Ek/yuZYulnzWpQgN+f50q2PTMEHQte9DkipLk3NFbtOie0UJGZWMTk2auBDJ90mnTRZspP+eHpj2YRY+fU0Fk+k+fFpOyxCzhNVA4i0vN6YqPdd+acgjrbfS7TkvhVbEAJl8SNu96R0rLY70zUuFLd8nd1LanAPUMXZdl3a7nZi6JCIqce0vwQqKEu9dfjadIpV+i7wn13XPKkuS4iVMmZ1SEUv5L0+VZEYYhsRdOGMUxSwnJJY6brACBqRD0IVCgUwmw9zcHJs2bVLOSVpOyli/ZVnUajUF+XPdRJlLJ0keb8kgy7ISIFQ3F+wHPlZsXTQDNJHonXo9UfiDg4Nks1na7XYPEg4WYenL9YcOw5Coewocx6HT6RCGocIQyRn3lmVRKpWSLltxwiDHdclY5rIi+az7XclDSa7PzMxQKpWU4my324mp1Q0jy+Odhh3KhHar1WJ2dpZqtUq9XlcPH8exYk673WZoaAiBIGNlujDBlVMcx90OjUmIPJPJUKlUKBaLjI6OMjIyovwZ6bDJyGb6JQ0KufD5fJ7R0VFKpZLa+UIINW2v43R6snkXc98reqemaWzfvp0TJ06oCGGr1erG9QMGBgaTgF6zSafTYWBgoCdYJ5MghXwBTRfouoEf+MzPzZHN5hgYGOD999/nueee47d+67fIZvMJpP0iLSCVQPGTOWC33XYb7777LsPDw2zfvp16vU673SaXy/UgHWSYJe1/SDHj+z7VSoV815N2HId6rU6pXOLQoUP8wz/8A/fffz+FfBEZqTUMfcVJJRHHURxGLpwn8CWEYH5unr/+m7/m6NGjlEol5ufn1e7atGkTcRxz+vRpHMdleHgYXdeYmZmlVCp2UWiVBBtkJEorSQka6kFzuRz3338/v/qrv0o2m8X3vYvu1SOEIAxCla1rtlr88JFHeO0XrzE3O4fv+xSKBTzPJZfLkc/nE7+gUlE6KwgCRkdH0XVdwVTkKZAByUqlytjYGBMTE9x333381m/+T1hWhkUckyDZ2xe+926J0vl3mlSaQeDjOG43bjKjFFTa/U+DX9PebBSFRFFv8rtQKBDFEXEUYxgGo6MburJSxv0v3iqSjljyNYnylOIkiiKC0MX3O8iSqShKBk2Mjo5y+PBhvvOd7/C5z32O/fv3K3EqdYQmRPeuDEzTJpvNMjIymrrnnqVd0f0aK3tzgrPRdZNCwSKOYWhoeOWrcg6K1UKxZL3PTrSslARiyUcF2WyObDbX/U6fmEWlG0URQ0ND5HNlJiYm8DyPbdu2sXPHlUCE5zsYuplSogLX9QmCiEzG7vn9pdBFaTkpMxOv8cNNlpDmp6I+ltAs7VWna6nHjkMs0wJiBUFMUqURECMQeJ7b2zJOmEsW/9LpkipkJLDpw9BSqAesTb+gROf4Z/0ujFrKKXvvvffYt28f5XIZBFgZq6dIL8GormG/IJn7TIclPiylkXer4QWv/HtBaEK9YmIQSSzr0KFD1Ot1Xn31VZqNJq1WC8/1cDqO0nGX+joXrZgB/VisNFPXqmR16WYyDIOsnaPdbjM7O8sVV1yBZVl8cPwDCvnE8dQNPTEW5H/xpb2WXYM1eep1TMnujDl48CAnTpygVqvhOA5PPfWUgth8mFjPheiXngEAzVaLQ4cOce+992JZFrt376bVanH6zGk6TueC1S8fhvo2SW+90NI2C2kzVAYZfc9nfn6e4ZER/vzP/5yvf/3XKeQLDAwOMDg4qLJ0miZbcCb20blJoIleR+yC4NxfFpI5A0lJds5g5849tNt1JLzxiiuupNWuE0eLcH1dk9HZmDg+36kQCNGbDziXHvilF0EJQiEgxiOMFmNXMf0d3iPpl+4EIJLKGxkqScITgcqcLZ033G/62DNA5p+BxOONQ2q1JmEYYJoWxUIRuhgfwzAYGxtLLKM4QQymG3ifs5HrRdzLUvrYM0DKb8dJqmN+9OgPefTRHyZ5ByG49957+ZV7fwU7m0BicrmcypjJZE3aDL3URh3nbVXwcSbP81RG7Nlnn+WtN9/kG9/4Bjt37mRiYoLvfe97zMzM8I1/9Q1c1+XkyZOqPGot6GPPAJnNO3bsGIcOHeLBBx/k+r3XEEUR27ZtQ9d1Dh06hB/4FItFNmzYsGZeOfwSMEAq25/97GeMjIywe/dulXY0TZN9e/dxw/4bklLVjkO1UlV4f4gvOit3sfSxN0MllGZ2dpaNGzcmMJPufJtms4mdzZHLFYnCKKnaJ1YIB8Qijv9iScJazvWSAbqPPQMk4k2CCOxslqDbGCSTyfD/fOfvee7nzyI00dOWRxPJa9H56g997Bkg4fSmafLBBx8kHREzOUrFYd55+x2e+O9PqEIQTddUl0SZstRXqzXWOehjrwPiOMk333777Xz/+9/ne9/7HkPDZTqdDs8//zxf/sqXufP2u/G8DoZuqPln0gwS4hMGfCiSCInbb78dx3F49NEfMjM7yZYtW/jqV7/KbbcllaCiCzlJl9h6vodlWmeVSkkYvKQERe6l35HgRc9Dqmhw1Z50nZLsE6FpGp/97Ge59967iOOAMOpWTEY+Ql/se4EgFXCLV4SFlZHS1G9WfH8fewbIEIPE9xgG2LaJSdLbKIgCLP3sVgUXQ0LQg40FwUod5o89AySoSipjo9vZK/ADNF3DWAIjFMj06MVYPgKtx1ISrDSF87FngOxmKJUxIgYMtFS7AoXXx2RursrsbJXdu0HTMsSx3p0dufTK52fQcl3IlqOPPQPOil7GIulhqkk5n1Q8Ju0SCmzdsp1kNrWGrmnE8VL5vjJayrBz6ZKPvR9wbkoWI3G+PAwjqQ6dmJhIkBDdGoEPE35eCf0SMyChNH5VCMHGjRvJ5XLq59XsYboc/VIk5VdCsrK+UqkAMDg4qH6/GmC0c93Hx54B651+6UXQ5aZPGHCZ6WNvhl4KrbQMdzXoEwYsQxdS3KsKUF6Vq3xCl0yfWEGXmf5/YqSCnxc/fa8AAAAASUVORK5CYII=)
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
In the given figure four identical spheres of equal mass are suspended by wires of equal length
, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 just after collision is
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that
![](data:image/png;base64,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)
Two negatively charges particles having charges
and
and masses
and
respectively are projected one after another into a region with equal initial velocity. The electric field
is along the
-axis, while the direction of projection makes an angle a with the
-axis. If the ranges of the two particles along the
-axis are equal then one can conclude that
![](data:image/png;base64,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)
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?
![](data:image/png;base64,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)
Two blocks
and
(
) are connected with a spring of force constant
and are inclined at a angel
with horizontal. If the system is released from rest, which one of the following statements is/are correct?
![](data:image/png;base64,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)
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then
![](data:image/png;base64,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)
In the given figure, two bodies of mass
and
are connected by massless spring of force constant
and are placed on a smooth surface (shown in figure), then
![](data:image/png;base64,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)
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
Which of the following noble gas was reacted with
by Bartlett to prepare the first noble gas compounds -
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
A set of
identical cubical blocks lies at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is
. The block at one end is given a speed
towards the next one at time
. All collision are completely elastic. Then
![](data:image/png;base64,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)
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,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)
The blocks
and
, each of mass
, are connected by massless spring of natural length
and spring constant
. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block
, also of mass
, moves on the floor with a speed
along the line joining
and
, and collides with
. Then
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARgAAABsCAYAAACxSq3vAAAgAElEQVR4nO192XIcR3b2l1XV1SuWxkYABPd9kSxRM1JoZM1Y4Zlx2OHwC/gF/Ch+DF/51heOCdvh+SM0MZJGokYih1oocwVJcAMBYmn0Vkvmf5F1sk5lV4OASGhGZB0FRLJRXZWVefIs31lSKKUUCiqooIL2gJw/9wAKKqigl5cKAVNQQQXtGRUCpqCCCtozKgRMQQUVtGdUCJiCCipoz6gQMAUVVNCeUSFgCiqooD2jQsAUVFBBe0aFgCmooIL2jAoBU1BBBe0ZFQKmoIIK2jMqBExBBRW0Z1QImIIKKmjPqBAwBRVU0J5RIWAKKqigPSPvzz2AYaSUgpQSjuNACPFc94miCAAghDD3pJ84jiGEgOMUsraggl40/cUKGEALBKUUeE8sIcSuBA5dz7/D70lCR0oJ13WfS5gVVFBBWfqLFTAkFOI4hpTSbHyyNHYqCLgl5DgOXNeFlBJRFCGKImPFKKV2fe+CCipoe/qLFTCAFg4kYHzf37X1opRCGIZ4+PAhqtUqxsfH4Xn6lbe2trC2toZarYZ6vY5KpQKlVCFcCiroBdJfLPBAlodSCpubm/jiiy9w7do1rK6u7vgeUkpsbW3hd7/7HS5duoT19XUAQBzHuHfvHj7++GMsLS2h3+8X7lFBBe0B7diC+SG1O8dIHMdBEAS4ffs2tra2MDExgYMHD6JSqaBer2NkZAQjIyPwPG9gfATwfvfdd2i32zh27Bimpqbw6NEjXL9+HTdv3sTJkycz3yuETEEFvTjakYChDU8/ZFnkXfeiiGMnUkoEQYDf/va32NrawsLCAqampnD48GEcP34cJ06cQKPRgO/7cF0XrusC0MLJ8zxEUYR2u41WqwUpJa5cuYKrV69CCIH5+Xk0Gg3EcQzXdQs3qaCCXiA9U8CQUBFCYGtrC0tLS7hx4wbiOEYcx4iiyERh+I8d/RlGUkqDs3ASQhi3pdPpYGlpyUR8bt68iZs3b+LSpUtoNBoYGxvDxMQEjhw5gjNnzuD1119HtVo1oO3o6CiiKMLy8jLW19exuLgIIQTeffddg8vEcYx+v49SqfTcofGCCipI044FDACEYYj19XXcu3cPURQZK4MLCW4BPO8mFULA8zz0+310u130ej10Oh10Oh0AQLlcNhEg13XR7XaNoOJRp5GREbTbbdy/fx+O46DVamHfvn04f/48arWasXjiOH6u8RZUUEFZ2lUUyXEcVKtVNJtNEzomq4ILIsJDnhX1od9T+JiI7hPHMUqlEtrtNtrtNpaWlgAAzWYTjUYDU1NTmJ6eRrPZxPj4OBYWFjA3N4dyuWysF8/zMDk5iVarhcXFRTx8+BCVSgXHjh3D/v37zTPp+buNVBVUUEHDaVcg7+joKM6dO4dTp049cxO+qE0qpcTDhw/R6XSwvLyMubk5nDx5EocOHcKRI0cwNzeH0dHRTJ6L4zjGkvJ9H4cPH8b169fx7bffYnp6Gv/wD/+AM2fOGKHIM3sLKqigF0e7smDIZaFNDKTWBgd+t8MwdiJ46D4UBarVajh58iSOHDmCWq2GiYkJNBoNNBoNVCoVk9tCRK4OWUdzc3OYnJzEyMgIjh49ikOHDqHZbGaes5vx/ViI3Fdaj7x3y8PJhs3Bbq4dRq8SiE57guY/Lyud08s4L88UMMMmgeMv/LPnJb7p6adareLo0aMYGRnJRIpo0TjuYo/XcRxMTk7i7NmzqFarOHLkCGZnZ1Eul3Pf78dMvPyB/s1B+rzrh63ZToXRsGu3e9bLNOc7IZp/m1fzaDfz/n3GQc/4odZAqO85esqSpXR7G3fZTSq/GUyyCPQ5B43J7YmiCHEcG0sKgBmDjeUQRVGEXq+HMAzhOA5qtVpu3syPnewNzBWAbVXylANOedfS9XnpCcOut8dkr+XLNvd5xIU7YZXcus7Lv9orAcPXeTuL9kXTc5UK0IZ+3oFup2X5ZgE0GMtdIm6CDhuH67qo1Wo7cuF+zJRnvb2oiN5uaZgwetVAdP6+ea6Sbf3vVX7Z91H+L4K+t4DhmsiWxLutduZ/55OZB7rmadZhv+PENejLigNw0BpILZg8q84uHrU/z7s+b22Hrbe9rpROoJRCqVR6KeffJp5CQRY4Ud68P48L+izKUzQ/hMv6XBZMFEXo9/smJ4b/7JT4y5EJaVc329dyIeF5HnzfR6VSMYzLBQgfUxzHL631AiAzb0opdDodbGxsIAgCs0bDaDdC19a6wwQMWbi0Pr7vw/O8l1bA28QFfBzH6PV62NraQr/fHwqYP0tY27TdXPLfccC5XC6bzPe93g87LhUABl90dXUVDx48wObmpsFjSEDYvj19P08D0oaghLp+v2/wEv58AnepfKBUKmFkZATT09M4dOgQJicnUa1WMzk63IUi1+plZG7Cp6SU8DwPUkosLy/j8uXL+Prrr7G+vo4gCDJCO08hbGeBcgFPVgkP73MtTIw8OjpqkhqPHj2KycnJVwbw5VZ+EAS4c+cOrl69iqWlJfR6PdPsjK71PA+lUinz/by/A4NuU55lwon2p+/7WFhYwOuvv46FhQXU6/UX8q7D6JkgL0lhAGZjt1otXLp0CV9++SUWFxcBAKVSydTy8KxeImJEvvHpcwJceUawEALlchlhGBphMzIyAqUUer2euUe328XGxgbOnTuH999/Hz/5yU8ApIlzZKK+zIxMFASB2fQXL17EH/7wB1y9ehWjo6MZ3CpPyOcRrSUHZ2mNyCKi9cxzZ2lde70eyuUyTp06hV/84hc4fPgwfN8HsPv+Pj8mor5D7XYbH374Ib744gs8fPgQMzMzAy4Rd+HDMAQAs5+AfMFvWy/bbWUhBKIoQrfbxfr6Os6ePYv33nsP7777biYx9UXTjl0kkrYbGxu4du0afv/736Pb7WLfvn1oNBomqmObz8D2zCOEGPBRiWFLpRJ6vR76/T4cx8H4+LhZAMdxEIYhVldXcevWLSwuLmLfvn04cOCAWcBXjVzXRRAEePLkCS5evIilpSXMzMzg5MmTqFarhmG5YLCZlGtdu06M1ojXoNHnto9P943jGK1WC0tLS1hcXESpVEKz2cTk5OSANfWyrZnjONjc3MTXX3+NL7/80lT0Hz58eMCdJ8ufrB0AxhLNmxu+TrQmvP0rt/5pj9FaLC4uYnV11SSenjhxApVKZU/m4JkChpiKXnRlZQVffvklbty4gQ8++AC//vWvMTo6mhEOdsEgn8Cd1vvQxJGAEUKYxlC0OP1+H2tra1hcXMR///d/Y3l52Qgans37sjHuMHJdF/1+H9evX8f169cxPz+Pf/zHf8T8/HzG9ObCXwscAEgtSrJGeQmI7UrxEPcwMJ5vjitXruDixYv47LPP8M4772BsbMzkIr2MwoVodXUVH3/8MTY2NvD222/jl7/8JRqNhtkjRLQvPM8bEDB5QkYIYazAOI4RhiGCIDCulp18Svug3+9jeXnZ7JeLFy9iYWFhzwTMjuwi7sZsbm7i4cOH+Ku/+iucOnUK5XIZy8vL2NraMiY6Ec+1oD+5oKEfmhz6IbcIgAFxqeKZcJ4oihCGIcrlMk6ePImTJ0/C9308fvzYaF1uyr8q1G63cf36dUxOTuLMmTM4evQoHMfJ4GO0Fhyr4oKY5o7wK8K++FoST+TlP5FyoJQCpRQOHz6Mo0ePolQqYX19Hb1ebyDa9bKRUgpBEGBrawsXLlzA2bNnUa/XdxQdtYXJsDnmwoeECj2T/2xubqLT6cBxHMzMzOCtt97C+Pg4rly5gm63u2d7ZMcuEmmkIAjQ7XZx5MgR1Os1k2Pi+6XE1RGQMgaUAqwIETCo7YgR7RckTUrAF98YPLGONPPo6CjW19extbU1tF/Ny07cyqDNT5aIni8BmhbblQEoP0Oi34/Muriuk3GZ+LPStVSQMusS0/ooJREEfZTLZYyMNFCrVQ2Q/32ijj82IvdkZGQEtVot42ZyZWwXD9N37fQKIsIfgTQfjSvhMAwH8Bm6HxUtO46Ddru9p8J9VwImlZgSpZKXyA+JWq0MIRKXSABSRlBINCL9IGU8TsOwGloY7j9GUTSA8SilM4pJ0PT7/WemY7+MxEHzarVq3NIwDBHLCIALIdK5N2shBNisJwKcMk4VtJHrQjgCwgEE9HI6jv7Rc+xmhIU0lo+AlAJCAK7rwPd9lMtlY03xsb+Ma0VzzPmXb+ZhUVUi27Kzf8f3A1covOnaMOFNAsl2pV407aqaGqBokJu4ITGUihAEEQSZzK6LWMqEEQUc14UjSAOmGpRoWCiOpC19xrEB6hEThqH5E4DJNbDzYF4F4m5JuVxmEb0IURggFgqOIyASy8LzPLieD98vDUQzvFJWi9Jcum4aMXKEgIJ+nl/yjRsWhEGiPWM4rkDJ9+C4da2UfAHHTRPP6P4crHwZBY1SCq1WC51OxwgFXjTMI6xANjFxWJSIoqxZa1EZDLRUKmVgCb6OSunOCGNjY6jVans65zsWMLy/ijbFIkgltVZT0MwrAAgFIRQEBBxH/7iuAyC1ZDjZ/r/9u7y/59VzcJyAWzevEtkaDkCS6FbSFofraJdHJLiK5yYGZvo9zayAlNzayXuYSpSIgoKEAqAQA5AAtBUUhgGUkgjDKIlgbCbNwrJNyV5GoUJEPEh5KEAaks7LZbHdICBN8bDpWV0LBsH8FBPt9Xro9XoIgiATWXzRtKOOdvSnw7RfHGuW0pJTM66bvLDD/nQTpoYSoP9symOyPOHA3TSuYWlMpEV5m4JXjWzLLdWWJGC0Rem4lJM0cAcjZJ5NCVMqBSUlFNJ8GYBMfP0MpaSxel8VyuNh+oxjLsDwUgEeZrZpNwLBDrL0+330+30EQfDnx2C49CMXSSnSkImAcZIWCk5q6vIGUEB+QeJurQ0OkNnRDF5xzcfwqhNhY0IkIp79mUe7TR/XuIsEVCrQzOfJRpJKJlauHguFxV8Vsl0UG4MiGmap5H2+GwudCxc7634vaUcWDM+upU0bS5lEDhKLxREQTnZDZ3xLpf1/Lamz99+NBLXrlUi62wKGR5JeZhP8mSQEgjCEiKSJCDmOC89zMy0v0svFUIYepFQr2t8HtCsrY6nTEPoBgiBEHEsoqbCLvfGjJyF0cijNUxiGAy1i+d6yv7tdcGSnQoZ/n3AanmawV7QjC8bGSYQAoCQcIeC6XoK1pNZKBiBM/pNKIo4lHCfNYORuF58wuxMbfW6PiaJM/O8AXpnSgDzi80cAr1Iy4wrZuMt290rXPflRElJREV+29IPzCT9hwnFSUJdwCP49ehbHAcIwNIWBjuOgUqmgWq2aDaGUwsbGBrrdrsERXNdFvV7H2NiYeV6/38f6+rpRkq7rYnJy0vAIZduura1ha2sLvu+bs7bq9bp5l36/j1arBUBvVt/3Ua/XM9EaPn4Cc6XUAtb3fdMsjZLsbHDXTl7k85qXaGd/h7tbNnE3i0BfUsx7iYPtKkyd/C35AUQC4EqZRgaGDVRKMgvTEBoxURiGZvF5lSeX8sMaFuWlm/MsyZc1MrEdcX87iiII6HXyPDeDV+UmfCX/keXqOA6ggCAIsba2hpJfQrVaSRizZNaDW4s031JKxDJOnu2lyicf7zeMT9mm165dw9bWFgCgVqthZmYGk5OTKJfL6PV6uHPnDtbW1tDr9cw9ms0mFhYWMD4+jiiK8PTpU9y6dctgDZVKBcePH0ez2YTneeh0OlhcXDRFu77vY2pqCgcPHsSxY8fguq4p6n3w4AGUUqhUKpiYmMCBAwcwNjZm2rbyOSAFSbljpVLJJIwCGIikcXzRjqwBMDVEXDlLKVGr1YzgHdaaw36Gbf3/2S0YPkBhmIP8+OHfUUpBQbtR+sUkgNiAsZubm/jqq6+wurqKOI5RqVRw+vRp7N+/H41GIzcqRAKEA72kJYhByfTn2NGrImT4O9O8ua6ThC49I7iHWYb8PsSI/V5f1zd9fhEzMzM4fPgwpmemM/fKm18ScLSxtJARgNJ5mPba0po+efIEX375Jf7nf/4H7XbbWAAHDhzA+fPn0Ww28fTpU3zzzTdYWVlBFEXm9Anqu3zixAkjPL799lt0Oh0IITA6OoozZ87g9OnTqFQquHXrFr788kusra2ZcTQaDZw/f95YTpcvX8Ynn3yCu3fvQimFZrOJw4cP47XXXsOJEyeMQOMChrd0JauNZzbzqCdfBxISXAHw+jL6PmW8nzhxAocPH8bY2Jh5dp6i5+tNc/1DRFufK8uG3B7yLcnlycM+dH6GC8cpIQgCfPvtt/jNb36Da9euIQgCU6h34MABvPvuu/jVr36F0dFRCJHWMdHk0+IRYEU/du3Mq0jcZdRaswylQghgRwJXJf/RPVzXxeLDRXz4uw/x0Ucf4c0338T4eBMHDhzCdkAtCXqllMlfKpfL8Lz8ZlOO4yCOYzx48AD/+7//i+vXr5sTO8vlsnGJvv76awRBYNqenj17FtPT0xgdHcXi4iJWVlbw9OlTXLx4EQBQr9fx93//9wZzCMMQN2/exGeffWb4dmFhAW+//TZmZ2cRhiGWlpawvr6O//qv/0KlUkGr1UKj0cDPf/5zs5Gpo0AYhqjX65iYmMi4KLTJuTW3G97k67S+vo7Lly/j3/7t33D06FFUq1X0ej20Wi18/vnnOHfuHH79619jenoavu/nzi/HOWkugL0/C+x7CxilACVTADj9PB9YVYnWklLi8uXL+Oijj3D16lUcOXLEmL3dbhc3btzA5cuXMTY2hnfeeQf1ej0jYLgEps+G5RW8qpQKGO33h6GEnR3wLKtOu1UuOu0O7ty5g6+++grdbhebm5vY3NyE55UQx+E2661MyjqAjDLIw9PCMMTTp0/x8ccf49GjR5iZmcF7772Her0O3/fR6/Vw9epV3L17F6urq+Y8LDrNs1armeLJu3fvotVqwXEcNJtNXLhwwbgRVEt37949rK+vo1wu48KFCzhz5gyOHTtmrKE//elPuHnzJlzXNRbL22+/jUajgSiK8OTJE3z++eemmn/fvn0ZV4nP77Bo5rP4lb6/vr6OR48eodvt4tChQ1hYWIBSuhD45s2bWF1dxePHj9FsNocrDvYsEvgA9rxWb1cChm9iIbK+PpEtufl3wzBCv9/Bp59+iitXrmDfvn34p3/6Jxw7dgy+7yOKIvz7v/87rl+/jkuXLuHcuXOoVqsZ85kX4vEK1GHPfVWJzPFSqYRYhhBiF7kO2quF67h49PAR7ty9g42NDRw6dAiO4+Dp06c6JA0BqXT9ku37y0TAUOmGabwehGnInGEMvV4P9+/fxyeffIL5+Xm89dZb+MlPfgIhdB+TlZUVlMtlTExMAIDB6cbHx3HgwAF4nocHDx6gWq2iXC6jVquh2+0a4HdqasrUZRHWR/1RHMcx1wghcPv2bXOfUqlkfkdtLwDgwIEDUErh2rVruHfvnjmjywZ9iZ7Fm3wu6N90n42NDfT7fZw8eRK/+MUvcPbsWVOf9x//8R8GiyLhvZ0FwyEE+nwvYYQdR5FsE89xHCgMFm0ByAWatAkscfv2bayvr+PkyZP453/+Z+zbt8+kNbuui/fffx8zMzPY2NjIuFtAfkib+6s2tvCqChseddCCxoVS+dGjgfCn1C6SlLq04KtvvsLjx49x/PhxHDt2DLdv38b9+0vo9dsJsKhM8hx3DbzERYuiKFNw6ZU8E03hz2+1Wrh37x5arRaazSbm5ubMeq+uruLatWv45ptvcObMGfi+j6tXr2JjYwMbGxvodDrwfR8rKyvY2trCxMQE/uZv/gZXr17F4uIiPvnkE/z85z+H4zi4fv067t69i/Pnz2NiYgKXL1/G8vIyHj58aA4U7Ha7GBsbwy9/+UvMzc3hu+++M0Dw3NycAVbfffdduK6LW7du4dq1a+acLt6YngQLz9vioees0s5Ga+l3VAX9xhtvYN++fajVaiYbd3l5Gaurq3Acx+S3UDuTvPvZGI3tAbzoPbOrc5E4sEqb2S77BzAgGPR9HARBiGvXrqFSqeDgwYOYm5vLNN5RSmFhYQFjY2MIwxDj4+MZrUPP5QtDz6QWhMP6nrxKRNadBr2BklcCRDbaBiSulOOm7pMSkNBuZ6/fxdbWFm7fvo1KpYKf/vSncB0X9+7dQ6fTNpaJdn3TyAeQWLFIG4lRUpeUEt1uF1/88QssP15GozFi8LcnT57g9u3baDabOHjwIKampoyA6Xa7pkp+cnLS8MhHH32E9fV1PHjwAKOjo1heXobneTh16hQOHDiAtbU1PH78GPfv30e32zWuVrVaxezsrMEzLl68iM3NTayvr6Ner6PX66Fer+O1115Ds9nE3bt3sbGxgaWlJUxMTKBWqwHQVtT4+Dg8z8OVK1fw5MkTNJtNE+WSUmJpaQnLy8s4c+bMQC6KTTxszQHilZUV3L59G47j4D//8z8NnLC1tYXl5WXs378fp06dMmH1YUS/47VJ9Ay7feeLoh0LGNrMmR+KIjHhMmxw5GcvLS2hXC5jZmYGlUolkxehlC7Cos513HLikpcEDI8iDcNgXkUhw6MECkgEiAAHZTPazfyelAOwubmJP/7xczx+vIyFhQXMzs6htbkJGcfoBwE2NzcxNtbUVfVIIx5SSshYmvUk8JbCtABw995dtNsdVKtVtNttVCoVtNttbG5uYv/+/ZiZmTFaGtDpDNzdmZ2dRb1ex8WLF7GxsYHl5WX4vo+1tTU4jmN+X6/XUS6X8eTJExOmbrfbEEIYd8t1XVy+fBm9Xs+MhQpmJyYmUK1WUalUoJRutkYhcbLIRkdHMTIyglarZTosVioVM//Ly8vo9/umcRpFO4dhMlxxkuVDltrMzAzW1tYyQpfyhMid4+HtDB8wZWzjZtyK+cEtGP7idtNtYiBXpY2JhmMhurJ3c3MTExMTJjJAvV14QyMpZSbd3B4LPZv/SX1FCVS0fdpXlhQBebr9gp3/oqASuZNmZcexxJMnK/jNb34DIVzMzUk8fKhBxtbWFoJAb6Sx0SYq5aquWxL6OWEUIgojI1gADSpWKhXTE8VzPZQSVymKIrOJm80m5ufnM9FDcrOoQZXj6JB7o9GAlBJbW1totVrwPA/dbjcX+6M0hjAM0Wq10O12jWKjqAtvp9DpdEzfI3perVYzOVs8s73RaGB2dhYLCwsG8yqXyxgfHzdh7nv37mFra8skBvLwMFecHM+kvUbCtVwu45133jGtT+M4RqfTwUcffYTl5WU8ePAA9XrdYERkxfJgiG0d/RAwwq6jSCQMaCIcJ3Vd3CRjUw0JX3qei/HxcZNgR4ATvXCn08GlS5cghMDp06cxMTGRmyJNPzyyRAKm0+lksiH3spDrx0CpCRzCcYQBxOl3ND+a6QWEW8L9+/fx7Tdf48mTJ/D9Kr799iru3bsHIYDFxUWMj49jY2MTsdQuGNUhQd/BMHIURQiCwCgTIQRqtRrOn3sd58+/hrm5+UwvH9oEjUYjo2UrlQoqlQqePn2KlZUVtFotw4OEM1EGbr/fN+4U3ZPAT9r8tjLr9XpG4CiVnm7R6/VQq9UQBIERcPbGbDQaOHXqFA4dOmQsE95npdFo4E9/+lMGd+JV1Xw96Pm8cHdjYwNxHGNqagoXLlww4XlAuzoPHz7E/fv3sbq6ikOHDqW1XywgYpf65Fkze0W77gcDZEFfzUyJ/5i0ApAqf1N7XsmAZg8ePEC32zVmXavVwtWrV/H73/8e4+PjOHLkyFCXh5t/NA5iGt5w6lUlrpW0gIkRx5Ep6eCUtr4AAIF+0MPV767iu//7DidOnMDpU2cxPt6EgrYmxsbGsLGxjvv3l3Dq5CnEkvoCpdrYcRwomXZQo1T+IAgg4xijo6OYmprGvn37EIZhRslwU502EpUJrK2t4f79+5ienka5XDbWcLPZRKPRwL59+3D//n3cvn0bR48eRafTQavVQrvdRhRFqNfraDQapoXk06dPsbq6ina7bZSZ53mo1+vo9/tYXV3F6Oio2agU3iVBE8ex6ejYaDQyTbdpM4+NjaHRaAxYCvxa7hLZCXbLy8tot9tmXNQDhrKdHz16hFarZTrU2XuD/9j1Tzav7AXtOIpkZwfGcYzYwkeAxOxDFr2mojjPK+HQoUMG3b906RKmp6chhMDy8jI+/fRT3Lt3L2nBmSYM8ckHBssGTFRLpdmnfNFeJaI6GbJctEkfJRosxa6y2Bo0wCslVlZXcO3aNTxeXsavf/UrvPez9zE9PY04DuGV9AFqX3zxR9xZXES7s4XJeAKxjM2zXScB/yHhudQ7KDY4RBTRWUpZnID4i0B9ACanpFKpYHx8HADw8OFD41K1220sLCwY4HVubg4rKytYXFw04Gqn08HIyIhxc5rNpolM3bp1y7gvJFx838fExAQ2Nzdx48YNUK2S53mmUTm3gDhWSGS/D3UYBJCxvOxoEYAMT0dRhEePHmF1dRX9fh9XrlwxJQHtdhs3b97E0tISpqamMDs7a+Z6mOvDrX4a+7DSghdFO7ZgeNWlSZpKTgz0vDSmLuMYJXZiHE1cFIdwXeDkyZP46quv8PHHH+Nf//Vfce7cOQRBgMePH+PJkyf4u7/7O3zwwQeYmZkx3zVaMUc6c38WgLGIXlUh43keRkZGDBO2Wi0oxPC8tLbLrnchodDvd/Dtt1fx8OFDNOoNvPHGGxhNCgeF8CAgUK/pAr/bt29jc1O7SRQJpNojWhff91HySwj6AVpbLc0bSRYpFUDyNAMehQRS7ToyMoL5+XkcO3YMa2truHLlCmq1mqkJoqLD2dlZ3L9/H3fu3MGnn36KlZUV+L6P9957D3Nzc6hWq6bU4enTp3jw4AHu3LmDcrmcyXuZmprCjRs38OGHH+Kbb75BHMdoNps4evQoGo1GJlrGybbyOd/RZiYBZStM7l5xAUEW2a1bt/DVV1+ZeabIz09/+lP89V//NY4cOWKEuOM4qNVqmakhM4wAAB9lSURBVMZspuyDAc6Ok/bm3SvaMcirBYlnTNdyuQy/7BtglczFkpc9soS+7witWUulCj744ANMTEzg888/N/7qqVOn8Ld/+7e4cOECFhYW0O/3B/xT+562cOHVofzzV0nAAFnm1n/mdw1MhUwC2kNhcnIC77//PiqVCmb3zaHkuZAqShqFKRw8eAAQ7+HkyVOYm51LBLoLHqEifjGRqsQ1k0ohDANj+Q4bu02uq7G7Cxcu4LPPPsP9+/fRbrdx+vRpHD9+HBMTE5BSYmxsDCMjI+h0Ovjiiy8wPj6O06dP48iRI6hWq6aQ8cKFC7h48SIePHgAIQTefPNNnD9/3gCz4+PjGBsbg5QSGxsbmJ+fx6lTpzA/P5853uNZIWGuEAlEJsFg98IlYcvrk8rlMo4fPw4hdLkAYVUECYyMjODYsWM4evRopkrbtvyBbIqJ3oclg5PtJX2PampeJ6FN3SBIUGrhZCRz5vtOknOhHBw8eBC+72NsbMyc5dJoNDA/P4+5uTn4vo8gCHIbEusFy3a145bMq2ax5BG3/FzX1a1N7TlJSj3SHBg9d9Mz05iZnkG1VkelUkY/6AORzqURjsLE5ASqtRqOHO5jdHQ0c8s8HqExkHWgP9/5u9A9a7UaTpw4gc3NTZPvcf78eXOmTxzHqNfrRhg8ePAA+/fvx+nTpzE1NWU2VK1Ww8mTJ7G2tmbA4TfffBMHDx40YDRZKxrk1ketUl3Udi5FngAnt4T/ZISvEBmLhqwNcnWPHz+O+fn5TJ4KAJONPDIygmq1ZhQ/BV3s2hDuFvFMXrJs9op2JGA4aEWofL/vII5TNNykSA+JIImkRl8ljDw/P4/Dhw+bl5NS99wgKT2s23mei6SYySi30Y6vAvFQJ21uyBgi6ZoLJIwPxfxwbZ24rouJiQn4pQo8t4Qw6pkqZFS0kvB9X2MKECbc6/vDD16TUp8hTriJcPKapj6bPM/DzMwM3n33Xbz22muIoshk1XLNfPToUYyMjGB1dRXNZtPk1NDcCCEwOzuLn/3sZzh37hwAYP/+/UZICSHQbDZx9uxZjI2NoVqtmpya78tX5NLwyI7JeGZlLgCMAKZo0vz8/EBqAV1n/6nXkuCBvH2QRAotfHQvaddRJHoJx3Egk0rqSqUMh8C9WCJ24gE3iV5Eh0p16rqdpqxRep1U4TjDi7aU0pGLOE4FDAevOL1K1gzPeTAguOtCKgcQ0lgO5LJql1K3vojiyLRF0HOf5rAAWnEIsJR3QUeeCB0xstYrjmNzQqFf8gGVfjYsyphHnO/K5TKmp6cxOTlprCMiso6q1Sr279+P2dlZ43LYeJ3jOJiamjItFrhbQjQyMoLDhw+bUHJeEeNOxp4qwzRcTBYMKWUeQQMAmkp+Fpg9PnJD6fs8EJLvZupobxxL9Hr6XCpADa2+flG0o5aZ9JJkyrlu2mpPKS00eAMdjo+knwFKRtC9YWCafwshWZhT++lan+p/C0vCOo5KNK4D4QBK6sbSjpP2PeET/pdGu8Eevu/9CcDjbUR5kl22OZgWDhxfA/TZRkIIE5Ey85kIihixsURiGUMokbsRpJToB31j+kupknypwQ3xLEzDdiloQ/K15pYBxx9sIUJzwCM6fByUHWtHSXe3TqQMQ1SrZXieQBB0E7dJIQyV5mcvcaVkjDDsJy4MAd+6AbsQyLiWQgCep7EzqbSyTYVgoryVPsMMUPpaJQChEIQhYhlCQcJ1BRyXzrhSgNAtWCAEHPH8zah2ZcGkZhhl9GZRcp6RSKE6AJkOadkFcyGESoSMBhkVFc4BEK5LCRrpcxIBI4SAkAJSOnCSQj69eQZNzr8UQcMFbx497zhp7jMCRggjYACaIycR3mKg9wvHDPim4+PmoWUgwXKsa4x7pnSdmJeEZ5WScD33e21YIdKoJBd6XDDYc8z50v4dV4J0H/u7HHPZfbRFAZBQiFGp+nBdIAx7cFwvEQoKUSzgxhqIlzJCGAYAfAjhwXHocEMC6rN39zyBOAZULKFUBH2wnjLRPIN3iSRfTRFEoQBEAGJASAghIRw6bkhCyggQSZ9t8Xxh7B3nwfAOXbq4LWFSkRU+nushVKH5LN3gWnhEUZScx+OmGepQEI6W9nxpRFpIw0hBQTMqlITjJNZR4jYJkc0l2Ksai+9LeQLmRYyNzze5Jvy+FM2huiMhBByhs675mMiNoZIL/n27zeN2AtMAzFKi3+tDeh7iKIKu0nYGhMIwsufmWZs8D68Ydi8SqnnXDAtWfB9yHMB19B6IZQQnscAhNM/rLGsHgIRUEaRyoCAA4ep9IROrwhqn67rmLCqRnEeWWk150SF9jedRHpK+Tu87mX4fcbL3np92VOzIGUkmL0smHJQYAHa51ovjGFIkYbo40klZMVtIDH6fKC8jl3Jw4jjWkQ+HwOekickrTNwPZ5/Cc7U76ZDVQtgAcrAQpSNGebVgu8mQ5jkdeiNTprfYa1zxL4b0WtApHDEUlAklUz6QXb/nedRPOnU581qiCCTubMLyVBbDsRxOfA/bDac0AB1DKW0x6Qp7d8Bi+j60q1MF8gqnBi/WjByrLEBlHzXC+2MMozyfnupCeO6LluSvCNfukPja6KQ2GJeWoilDLQc1PBq4U+KWRBiG6bPNM19+ZaASC5zmmruivAE4t5rssgkgfx8oKIRRaAQUZQjzcHR2LM8QMLEESmnBK51j9ry0qzyY1HqILJM70XRJbgVnTrvgir8wR9HzJiRvYqmAjofGtSUFbKca7ftsN3k8cvE81/w5iEcugNTUdxI4a5gVwq3OYdG4YR3o84RVqpG9TJP2OGnR+EOnEtjYyg/yTIZ7AdrqoAMK7cb0RFzh8tyXvDA1RZF4/gxPUbCv5/gnQQjUpIpDCRrLeb45onfy8vCJTMjMAsh0mE1bH66jK6ijOO21SpLUSFbH1RW2wjFp5HaPXX6MBs9xESIJg+pR6UWyhJHneqbPiAKSyclfCE4GhLTIFmrDQEQ+P3lW2LBNNGyD5hHHVezr7WfysVF7A12g50GpIPG3h9+Ph3Q91wPcJDrEtClfV1org+UkzErfKZVKJoQNJK0cgghhqBUET/CyLSobO9ot5c37MAH4ooRN7tjhwEkybHu9HsIohHDSKnO7dIMD7Xyd+JEv/Ica3ZOypXml+efvTJgarR21M6XGWDsR+sOUdBZrTfec67rwhjF8HgNTH47x8XEsLy9jc3MTrueh5HtpJq8j0G63TYMhITTG4noefLcMpWAORXccR5cWuG6SV+HAEQoR0iNIlFLmoC96wUqlYnx813URRzEePX6EXreLycnpzNh3Cvjxz7lJa19va5TtGHS3EZJhn+30PkII1Ot1HDt2DDdu3MDTp0/x5MkTTE42AWhAj3rlcgvHdRxz6gDP93AFM7uTRlNUEGiK9kBlABK9fs/keJD7K4Rut7C+vo5Ot2P6wlBVMICMJfu88zgM0B8mwF4UDXtmo6HzaS5fvozx8XEcO3YMtVot01fJczWWQkovN1KGrFCk/cgNAIPpJJajAjJCSt9UW0b37t7F5uYmZmZmMD42iXK5lmQBazCaIld57zhM0Ni/F0LAo9PquASzJRMxC/2+0Wjgxo0b+L9r1zA6NoLGSA0qyW8gAUN+JjUMchwHnqvrVsIogJRxOqFSQSs6B1ASURQijALD7LaLRcJFQJetP11bw5U/XUEYxhgdHce9e/dM451hmb0kREkzk5bO68+R992dbP6duAGEbQ1LptruHramc10X/X4fSulcmOvXb+DDD3+Hc+fOoFRyoEC9QrKnMeh1c+A4WQxAWyUJACgV+kEfvl9GpVJGqeQlv9NHwUZxapk4jotymRK4dH/e7/7vO9y8eRMKCt1uF48ePTK9TshlsCN/L1Ig8HvwOc17zjCwlHhmmBKy7y8EsLGxhkq5jOXlZQBAc7yJhQMLidUttKJNSmxEwteDxHGrVPjoRFM+Rjq3TDBLSH9fpyUAQRhic2MDn138HI8ePcLk5CQ2NjYhknCsUlLzCVwI4cEWMvz9bQXMyw+iKNKZ21euXFG8GIsupCQk0nY04M3NTSwu3sZvf/v/4LrA3PwMZuf26VqTJPpQr9fNcQi1Wk1niQYhZCzhl/2UsSmMmbQStIFkKnPn41NKAUL7s51OBysrK7hz5x6W7j3A7Ow8zp9/DbOzs0bABEnFN198ElCe56Hf76Pf75vrGo1GpjqYb2JiMMIiOMPlMdlOBUwQBAPjpHsMEzzAIL5VrVZRKpXQ7/fx3XffYWlpCXEc46233sDIaAO+X0qOMKVCtxDtdgcAkuRJvcblBIAMozAZgx5HKWnXUC6X4fsuoihCp9PNdIhznPTcKil1L5hOp4Nvv/kGG5ubmJycwk/eegf1egNBEKLT6ZhUfOpwx3GB3bgx21mBOtM8W/Rnb1K6lp+1xRUr4UkkhI2LyPK/+Np4noCCRHurhT9+8TnW19cxNjaG119/HUiiea7rZCqpXbeUGb+WD9kG7iSEtra2EEVhEkG131nwO0Al+Gin08GDhw9w9+4dNJtNvPHGG5ib249SyUWaHS8hhAfX8bVnkUR6lVKmpoynrej5TRuFET9PT09D/Mu//IviwB69CPlwtNiO4yY1SNTtqw2pIvi+LrqiA7LIKuh2u6aZEB14RdqVt1QgS4d8SFp8DiiSFRNFEWq1GkZHRxGGmjk11iAh4KFaraNeb8DzPFObRC9vS9tSyUe57KetJ5LQtw4TpiXxtHFoUmksfK7yizIzLGLeIw9kpQ2srBT6PAFDz/T9Mij9nMbj+9qy4JiGTLJDFfT9taCk+zgolXzQsb5xHJnTFznuEsfS4Dflchnlsg/f9xAEIaKISgp4AV36fL3eev2VVPA8H83mNOJYt6bc2trC2NgYqD2kXU9mLFdFs5lq82FyJ89U1yUPwrwnueBppzmySNNncjedBB3xh405AFowyVgnuekiXgkImfBA2lybxqISiyF9HwHH8QzP6GfDrJeTWJmULJkmlWb5TSkMCOc4lkaRArq7JPE4uVY8gVZKgShSOg2FvT/nxRQPIs+mbva5lBInTpyAt2/fPjNIIUSS0JNqeWJgCqvRhqzVqpAqQhj2EcdR6lc7DsIklEybs1arQSl9UFQQBOaAKpLcdChWt9s1JrPBbxijk5amjmPdbg9K6fOGXacEx9EumFJAt6s1c7VaZQybMiVVgpOGVkpPFFkvqeAJjFAkl402W7rYg2AxaRGaVwhhijJztoRhbk6DIG96P2qxkLo7CpVqBX7JT+YrMpu+09lCFIeQSS6SZj4keErZCO84jjIRDgL0+YYvl8uoVCoolTyjEIRwmFWkAWYhyNKDUQyO4yAKJSqVOsIwMgKGTo8g5udj6Pf7CIMQcTJme87AQgCCzZE9X76vD2ULwzDpGxwCEOZ8pXST2u5T9rM0iJAcSg/AdRz4fhlhGBilFAQBHBdwXV1MSgWXpN1tCyDlT7I+skGNVDml1nQ6dse8M/FntmJb306D8Hq/0OkJT58+heelvbbTiJQuZYDiZyrpPUNjT3No0iOdwzA0fHH8+HGIP/zhI+V5HpzkS2SxkKlMVK1V0ag3oAB0OxqskypCv9/D1lbL9NsQQiAirZoIBWrSE4Yher2eAWlps1ETHuqnS/1muE/OLRvDeKE+EtUvlxEEOlXa87RZ1+t14bguRkdG0et1NYMaxoHZhDpRzzG1UX5Zf18mWceE1FMZAlUD0ybXmkUwBgfTOonGSRZPybQ/LF2HJNLPMR1ubUkpk+hYWoUcx9Isou6Hq33saq0Kv+QjimM8XV0BANRq1aQOJcVdeNIWF2IcRPd931xLn1NPW9L6qRuDRLAr4xIBaUe6zc1NI2D6/RCVSg1SKtNYe3RkBK7nQSZ9Unzf16a4X0J7SzfgjmUMz6p3I2VIIkCw9xFCR3DcROuTRR6Euik5bVZaB7LuKNOYkgJjKRNsQtdnKZnU6ThpU7NSAgtIKRFGEcIEiyr5HkolFwCVVaTuPilsbulxvJMEietq65inZ2Svy2JDSslEOUYZnkpTOrQVViqVzFrxJlgkVLVVq5LTW6Xhw3JSTe/7JZPxrcfiIY5Tqz+KIhw8eBDi62++ZC6SSjQigYYaGBKOg1JJAz6k7dKFzvYrpXtxwEy/WBoe48AtMS4Pz3Gsg5gp9aXTFPRsuDsbMqaJUorCeQqp9NfvUy77TCxwgI93ymMCIFFzMTOftTvpGV+ZjA0tPJXRxp5XAqDQ7/WShkup6RuG5M5phjK1Qsba4tpamHcKAr24nldCvV4zLpHWhI7x1xVUkqafrgsxLPXdsdsGcJyChB4Jffo9RZAcd9CKI+FBVglZqXpNYNYiDCN4HtVFIbPGruui2+1CSo1VVMpl+Oz0CPodaVVydaMoQskroZTgTZ7n6Y0i08LacrkCz3MzG0LzdgzXdRK8xTPWgL5vcs5UImijKEYUhYlLCGNVastcl804jm6KTt0GaH+kfJGGoMm94NY7WeBBEKDf75u9Vi6XM+428SLfF5x41JWeR+tLPZlc10UpMTaUUon1qtDv99Dv68CM53moVKoJvKDnU7fI9dDt9o273+/3cfToUXga+FKWP08+I0ekiTm17242nxAZVyq7IdKXpwXM+rNerm9HL843hPHJo0hvFjXYX1TKQWSbTEk+JBJk/X7f+Lmkzbg7QJ87jgvfT3EjyKQwTABCcD86dXOojai+Z4wgSI67lTHbYLT4gEhSs1M/OE2GIl851RZppa+2IiIEScWyfr4Dx0lyYuJIa10gd55pzYjpiRFJ4/P555YkaUupJByVKg4ijl2RUKKNyK/zfS+Zg/R9dT1U36wF8V0sNX4ipUiSPWHuF0UhyLWnsHkY9hFFobmGg/tRFCAIFKhfMceblNId+gir4XxbqVRRqZRThdEPEEWheUdOKc9nExzT+UiPKMnysTS/HywlyObE0HtxnqH7ceKRH/474i26DwHbpVLJJEgqpT2ZMAxQKnnmR4gIUSQBOHCTMZFLbTr36cfQhiLzKzs4u4ERdc3Si5KmM/OXIaakl+JRIC69uYnIvzuMpFLa9WImJXcrsoAokMFB+H2G4CF5go7u77oOpARcV+VYF+m/CZ9J7zdY+MnzDXT7CZFhEGIYEiLkjpAG44d7kaAdBMYjauuSuwHIUqT5oLXheJNtwmfmBkjaZeRHuni0LY+4crGfQWOzQUUebdTX0fNS4FoIz4xJF/OlKQjEc2lD9NiMl9ZNW4gsggjeyB7muWSFputsubjMRaH5yrpx6e/5v/leCsO0HIASSgd4DqkdTuuZhwtm90aaq0QtOex7p0LNBVAyriYpTxLYgICSBAlk383jNyOA1I7128xFzMP9wqymSkv9ef6KjcjzRYDFoLkTSQug0rwPO9OYX0ebj+Me9uTZk843Iv2eb/g8prDBOmJoWkDSPCQs0mfy7w7OsT02PkY+JiDN9uTvTfNOmijrq+v3IkuI4y32OPh88fvza+y14mY+d6kBZMZJv7NdZsqhIuCf3iXPquXuAb0Xx0gAGDeArxu57PR37sYT9mb3laHxlMtlUOU5aWv7HbO4hsrMB13Dgx0kOIlvNGbVNy4RVypkwRhQNsGGbP7OI5obsu4pCEOfES+QMOdWM80zRYg1byl0gwBeiZq5pxafRwvFTS57s9DkEjBlwNyEOTi2wjcDDYxeil6IGJR/nwNWw4QFf1G+ybjvaZuGNFE2bSdg7N9xZuH35/NkLyBPOuLWW96i883N34nPBQlxIE2oo/mjlpSc4blLCiDDHPQ9AtvTKFIanjWtMtn7cZyGr6ttOdHnXPjx8gDO4CR4eQQDSIvw+NxyV8XewFypcWuFcAeKapKAIheAUgzofjRW3qGfYxcAzHeVUiYlguOFfE1tWICexa1PTjxdgwQMt2x93zfBEh744LVNeRgMF6K2VUhjpL2ShQkGOwfS5+m1+t+e6yKGxmWMYqUXpoFyhubSkiaHS7Y8IDDP7Kbv00TYviZdY0/IdoKBFomkP/fXiQFo8/Dqa058MexwPDEvfxd7Tvh47PvaVhO3ZPg705/0ewqTc2snb0NRTpHrpJ3rOAaWBbuzWpMURNbVGHxXzpQAzLrbOBE9hxPHa/j7513LeYePmdbHdpv4zzCrj9+DBA7NkY1vcX6MZVqQabdT4OtFWAWQCl7+TOJJzhv23rItyjiO03VN9golT9r8wueDKyV7LTnxZ3Hi/M+FsC30aQ649aTfSbdLUVLjinw8HoVA7eM++I3sRUjB0XSgXIvxBYnjeABk5ELCtgLyLBfOiMMYkzQYZwoaUx7oxZmRJ9vxZ/BFsi0CW6jajG4zCk9monnh47A1DM+stp9BQpO0q7AsF3sOYxMhiVAul42Q45aV7QrxOaR5aLfbmbmx3VNuodn35C6c/e78uWZ+9QXaHWYMz3EdW+jzyB79m2t5MycqrcfiCZm2suAClCcA0mb0PA/lxJXjAiDP1Rz2vtz9Ij4kfiFXkb7L18oWyLTh6d55Aoau3e7ffJ6yLVfze87oMWgMRs9jmqgrhIAXR9FQpqAJ5uCafV2eVOQLxrOC84DVYb6iLfS2mxT6jO5P5jBNsm1qpxMD47bxqImtKfnE543DFi42ws/nkZvqnGltF4+bvfZ9ueXGf7hJzsdD70Xmd7/fz+AUNvHqdhKKXGiSm0zmMo07TwHw++Q9z1YkGpdP75Nn8ZFg5Jm/3O3jm5Luy7PE+bNpnm1Lg/7kVch0HT2XnikcBy7yW5NwPqM/7Z4vnD9rtVrGTaQxkhIlIl7i3oFtldnK2QhxBlq7rmuKL2n8NjhvrytXOkY5ujobmt6d+NEjqc8lPp8EYjCfJd1xTWUTXxRaPAIZKcvPnvDcASemvC2JqczcZhbbBKeF5lnB9jj5+3meB9dx0draSvqiZsFue6JtC4Z/DsBgTbagoAQ2fj1pJ8pLoXevVWvwSmmiFY968Pe13yvvM24B8E3LlYHtlvB3I+yLC03+vO2ECxF3Y9ML0+sz2YoJ0VhtzIKqsm3FNUxh5ZVzEH5lrzEXEvxeJGjpnXRnfhge42OhTWYrYC5s6VruelJ+C094pT1kU94hcCmmkpYgDFsP/kz6Lu8Nk6cMMla87kwGnbPlQUnH/J7wLY/O/FVKQcbSHNLF/SibmZXKKJkB4otNSXQ0+DwLhm9kPXidHTsoGATiKEJQGdRGnOG5C0IbakB7JszMXRgvydRN6zW8pI0EzAKkc6AGNlke8feja7lgMsI9ihGEAeIohkjCgeVyxQgmyizWY2DNqJVuZ6Go122uaaxfVo8laSikdE5OHMWZTc21MN8MAgK1qo42UGsBI5SsJmO6lanOjRBO1oUCoNtmbsdA1vwBOnJIrp6Anh8/afmgNXbWGmR3YImSg/d2E83Lh6PoYD/rwDrX0YfYkTIIw9C4MWkZicxYAhw348+kz6IoMmtAGezcZSdw3/NKmTEKZBuAUTGi7kyQZCkrkt4wSZH8eBkBkZy6qfN+9B7lpSHKZLjTfTi2RmvuCBeO8AC45vv0LqIftBRxhaACLCTrr0yGDNtEtqbK5QvQ5drlZabawCrrRD+98RLhRTkHjrXwSrfjpBoiuhUJPGIMCP583Z4geY3kWrbZk3oiYno9uXoTe55ulgUjCNKzhWgmtLaJkPa5SvJu6HsgPCFlAiFY1bF5NxbKpPUQjnk313EySfE0jxqY1A3PPdcDpZY/i/TzBjvXAZQGQCd3JnMDmlNlRmCEikqPOQH0OqRmtv6elHFyTVLZbPNB/ig1b1BdTqZGh7SxSMaUbArDvCkJMLeH/U8h4T1JdU5J+wSjEHRyH4DkHCmtbLQAiHTWq6XYtGDSOUjacvXS+UsncfDfzDWnMVF9HLfw+Utp/jEcpMeqaG52JsAB6FYpybOoKZwWhA7SHUu9mZI8OaUYn7pwHQ+AZ5SgiThKGQxVv1Tnot/fTTZ0Kmi2ewUujkga6g1na9hhbQ0EIFR6I7qZYTPLfGPMB5Z2rh+hMn8dKhSBZPL0s1LrRejjP+hdLDN/YPwib26SIrRYn7KYmqtpHVPmniDMgZm3wkyCeS4JCSmlZmZn+2bNNpPnXkOlEsbKchgb8zUhrIL+nl5FbRdpLFLKxPfXvLRDAwZRHJPWSQQTMvel51H2OY3XfusoitMD35jycRIhT/cj4ZlcAVh8xgWJhhHS4kfzf5VNzhskZQTdwO/JVWRzK6x155fSNZRVrd9lSJdFlj1u7pHciPapgraCsq5muq7pPNjj0H18OfYohIBQ1NMwbxpIMCSDzj5k5xIyR0ps83t+3fYbYTjZz3j2fRTbNBkRKtjf6ffPcBGHvaNSJLT190lLpi4MwN/bWBe00QfuzzNgATrMbPjasE1grhqcK2VxT/a6PIyHPufXiMzGyPLSdmPMklFymTng36WNyFZNDP7eBj1pHLzmK0vD15DeJbWg8mi7ffKs/bBbSnmA3KFBwZZde07pnHKFkSP8nknMMyBMS20HIBRUUEEFPQe9mJOlCiqooIJyqBAwBRVU0J5RIWAKKqigPaNCwBRUUEF7RoWAKaiggvaMCgFTUEEF7RkVAqagggraMyoETEEFFbRnVAiYggoqaM+oEDAFFVTQnlEhYAoqqKA9o0LAFFRQQXtGhYApqKCC9owKAVNQQQXtGRUCpqCCCtozKgRMQQUVtGdUCJiCCipoz6gQMAUVVNCe0f8HH12+bJWXAGEAAAAASUVORK5CYII=)
Find the velocity of centre of the system shown in the figure.
![](data:image/png;base64,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)
Find the velocity of centre of the system shown in the figure.
![](data:image/png;base64,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)
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,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)
Two blocks
and
are connected by a massless string (shown in figure). A force of 30 N is applied on block
. The distance travelled by centre of mass in 2 s starting from rest is
![](data:image/png;base64,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)
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?
![](data:image/png;base64,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)
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is
If
then descending order of ![a comma b comma c](data:image/png;base64,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)
is