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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

  • 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 \[{{a}_{c}}={{k}^{2}}r{{t}^{2}},\] where A; is a constant. The power delivered to the particle by the force acting on it is

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

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

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

    D)       Zero

    Correct Answer: B

    Solution :

    [b] \[{{a}_{c}}={{k}^{2}}r{{t}^{2}}\Rightarrow \frac{{{v}^{2}}}{r}={{k}^{2}}r{{t}^{2}}\] \[\Rightarrow \,\,\,{{v}^{2}}={{k}^{2}}{{r}^{2}}{{t}^{2}}\Rightarrow v=krt\Rightarrow {{a}_{r}}=\frac{dv}{dt}=kr\] \[P=\int{m\,\,{{\overset{\to }{\mathop{a}}\,}_{r}}}\overset{\to }{\mathop{v}}\,=m(kr).\,(krt)=m{{k}^{2}}{{r}^{2}}t\] 


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