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JEE Main & Advanced JEE Main Paper (Held On 10 April 2016)

  • question_answer
    A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by \[{{n}^{2}}R\,{{t}^{2}}\]where n is a constant. The power delivered to the particle by the force acting on it, is:   JEE Main Online Paper (Held On 10 April 2016)

    A) \[M\,\,n\,{{R}^{2}}\,{{t}^{2}}\]                    

    B) \[\frac{1}{2}M{{n}^{2}}{{R}^{2}}{{t}^{2}}\]

    C) \[M\,{{n}^{2}}{{R}^{2}}t\]                              

    D) \[M\,n\,{{R}^{2}}\,t\]

    Correct Answer: C

    Solution :

                 \[\frac{{{V}^{2}}}{R}={{n}^{2}}R{{t}^{2}}\] \[\Rightarrow {{V}^{2}}={{n}^{2}}{{R}^{2}}{{t}^{2}}\] \[\Rightarrow V=nRt\] \[\Rightarrow \frac{dV}{dt}=nR\] \[P={{F}_{t}}V\] \[m=\frac{mdV}{dt}V\] \[=mnR.\,nRt\] \[P={{n}^{2}}{{R}^{2}}t\,m\]


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