JEE Mains · Physics · STD 11 - 5. work,energy,power and collision
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 \(n^2Rt^2\) where \(n\) is a constant. The Power delivered to the particle by the force acting on it, is
- A \(\frac{1}{2}\,M\,{n^2}\,{R^2}{t^2}\)
- B \(M\,{n^2}{R^2}{t^2}\)
- C \(M\,n\,{R^2}{t^2}\)
- D \(M\,n\,{R^2}t\)
Answer & Solution
Correct Answer
(B) \(M\,{n^2}{R^2}{t^2}\)
Step-by-step Solution
Detailed explanation
\(v = \sqrt{a_c R}\) \(v = \sqrt{(n^2Rt^2)R} = \sqrt{n^2R^2t^2} = nRt\) \(a_t = \frac{dv}{dt} = \frac{d}{dt}(nRt) = nR\) \(P = F_t v = (Ma_t)v = (MnR)(nRt)\) \(P = Mn^2R^2t\)
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