First slide

Power

Question

A particle of mass M is moving along a circular path of consultant radius R. The centripetal acceleration varies as a $a = K^{2} {Rt}^{2}$ , where K is constant and t is the time elapsed. What is the power delivered to the particle by the force acting on it ?

Difficult

A

$\frac{M}{4} K^{2} R^{2} t$
B

$\frac{M}{2} K^{2} R^{2} t$
C

${MK}^{2} R^{2} t$
D

$2 {MK}^{2} R^{2} t$

Solution

$For circular motion, a = (v^{2} / R) Here K^{2} {Rt}^{2} = v^{2} / R or v^{2} = K^{2} R^{2} t^{2} D i f f e r e n t i a t i n g, 2 v \frac{d v}{d t} = k^{2} R^{2} (2 t) \Rightarrow a_{t} = k R T h e r e f o r e P o w e r = F_{t} . v = M . k R . k R t = M k^{2} R^{2} t \begin{aligned} \end{aligned}$

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