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JEE Main & Advanced Sample Paper JEE Main Sample Paper-27

  • 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 is initially at rest. Both the strings are massless and inextensible. If the second bob, after collision acquires the maximum speed so that it will oscillate in the vertical plane, the ratio \[\frac{{{l}_{1}}}{{{l}_{2}}}\] is

    A)  1                    

    B)  3

    C)  4                                

    D)  2

    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 first bob just before elastic collision = velocity of second bob at the bottom most point \[=\sqrt{2g{{l}_{2}}}\]\[\Rightarrow \,\,\frac{{{l}_{1}}}{{{l}_{2}}}=2\]


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