Question

A particle of mass ‘m’ is moving in circular path of constant radius ‘r’ such that centripetal acceleration is varying with time ‘t’ as K² r t² where K is a constant. The power delivered to the particle by the force acting on it is

(A) m² K² r² t² 

(B) mK² r² t 

(C) m K² r t² 

(D) m K r² t

Answer 1

Answer is (B) mK² r² t

Centripetal acceleration

\(\frac{v^2}{r}\) = K²t²r

∴ v = K t r 

acceleration, a = \(\frac{dv}{dt}\) = \(\frac{d}{dt}\)(Ktr) = kr

F = m x a

and P = F x v = mKr x Ktr = mK² t r²