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

  • question_answer
    A particle of mass \[m\] is moving in a circular path of constant radius \[r\] such that its centripetal acceleration \[{{a}_{c}}\] is varying with time t as, \[{{a}_{c}}={{k}^{2}}r{{t}^{2}}\], The power delivered to the particle by the forces acting on it is                  [IIT 1994]

    A)             \[2\pi m{{k}^{2}}{{r}^{2}}t\]

    B)               \[m{{k}^{2}}{{r}^{2}}t\]

    C)             \[\frac{m{{k}^{4}}{{r}^{2}}{{t}^{5}}}{3}\]

    D)               Zero

    Correct Answer: B

    Solution :

                    Here the tangential acceleration also exits which requires power. Given that \[{{a}_{C}}={{k}^{2}}r{{t}^{2}}\] and \[{{a}_{C}}=\frac{{{v}^{2}}}{r}\]\ \[\frac{{{v}^{2}}}{r}={{k}^{2}}r{{t}^{2}}\]  or \[{{v}^{2}}={{k}^{2}}{{r}^{2}}{{t}^{2}}\] or \[v=krt\] Tangential acceleration \[a=\frac{dv}{dt}=kr\] Now force \[F=m\times a=mkr\] So power \[P=F\times v=mkr\times krt=m{{k}^{2}}{{r}^{2}}t\]


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