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JEE Main & Advanced Physics Two Dimensional Motion Question Bank Critical Thinking

  • question_answer
    A particle \[P\] is sliding down a frictionless hemispherical bowl. It passes the point  \[A\] at \[t=0\]. At this instant of time, the horizontal component of its velocity is \[v\]. A bead \[Q\] of the same mass as \[P\] is ejected from \[A\] at \[t=0\] along the horizontal string \[AB\] (see figure) with the speed \[v\]. Friction between the bead and the string may be neglected. Let \[{{t}_{P}}\] and \[{{t}_{Q}}\] be the respective time taken by \[P\] and \[Q\] to reach the point \[B\]. Then                               [IIT 1993]   

    A)             \[{{t}_{P}}<{{t}_{Q}}\]

    B)               \[{{t}_{P}}={{t}_{Q}}\]

    C)             \[{{t}_{P}}>{{t}_{Q}}\]

    D)               All of these

    Correct Answer: A

    Solution :

                    For particle P, motion between A and C will be an accelerated one while between C and B a retarded one. But in any case horizontal component of it?s velocity will be greater than or equal to v on the other hand in case of particle Q, it is always equal to v. horizontal displacement of both the particles are equal, so \[{{t}_{P}}<{{t}_{Q}}\].


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