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JEE Main & Advanced Sample Paper JEE Main Sample Paper-24

  • question_answer
    A bob of mass m, suspended by a string of length\[{{l}_{1}}\], is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length\[{{l}_{2}}\], which initially at rest. Both the string are massless and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio \[\frac{{{l}_{1}}}{{{l}_{2}}}\] is:

    A)  1                    

    B)  3

    C)  4                                

    D)  5

    Correct Answer: D

    Solution :

    velocity of first bob at highest point,\[{{v}_{1}}=\sqrt{gR}=\,\sqrt{g{{l}_{1}}}\] (to just complete the vertical circle) Velocity of second bob just after elastic collision = Velocity of second bob at the bottom most point \[=\sqrt{5g{{l}_{2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\frac{{{l}_{1}}}{{{l}_{2}}}=5\]


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