A particle of mass \(m\) is moving in a circular path of constant radius \(I\) such that its centripetal acceleration \((a)\) is varying with time \(t\) as \(a=k^{2} rt^{2}\). where \(k\) is a constant. The 10.Power delivered to the particle by the force acting on it is given as

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Answer & Solution

Correct Answer

(C) \(mk ^{2} r ^{2} t\)

Step-by-step Solution

Detailed explanation

\(a = k ^{2} rt ^{2}=\frac{ V ^{2}}{ r }\)

\(V = krt\)

\(a _{ t }=\frac{ dv }{ dt }= kr\)

\(F _{ t }= ma _{ t }= mkr\)

\(P =\overrightarrow{ F }. \overrightarrow{ V }\)

\(= F \cos \theta V = F _{ t } V = mkr ( krt )\)

\(P = mk ^{2} r ^{2} t\)

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