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JEE Main & Advanced Sample Paper JEE Main Sample Paper-36

  • question_answer
    A pendulum consists of a wooden bob of mass m and length \['\ell '\]. A bullet of mass \[{{m}_{1}}\] is fired towards the pendulum with a speed \[{{v}_{1}}\]. The bullet emerges out of the bob with a speed \[{{v}_{1}}/3,\] and the bob just completes motion along a vertical circle. Then \[{{v}_{1}}\] is

    A)  \[\left( \frac{m}{{{m}_{1}}} \right)\sqrt{5g\ell }\]           

    B)  \[\frac{3}{2}\left( \frac{m}{{{m}_{1}}} \right)\sqrt{5g\ell }\]

    C)  \[\frac{2}{3}\left( \frac{{{m}_{1}}}{m} \right)\sqrt{5g\ell }\]        

    D)  \[\left( \frac{{{m}_{1}}}{m} \right)\sqrt{g\ell }\]

    Correct Answer: B

    Solution :

     Using conservation of momentum,\[{{m}_{1}}{{v}_{1}}+0={{m}_{1}}\frac{{{v}_{1}}}{3}+mv\Rightarrow {{m}_{1}}{{v}_{1}}-\frac{{{m}_{1}}{{v}_{1}}}{3}=mv\](\[v=\sqrt{5gl}\] to complete motion along vertical circle)\[\frac{2{{m}_{1}}{{v}_{1}}}{3}=mv\Rightarrow v=\frac{2}{3}\frac{{{m}_{1}}{{v}_{1}}}{m}\] or \[{{v}_{1}}=\frac{3}{2}\frac{m}{{{m}_{1}}}\sqrt{5g\ell }\]


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