Question

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 = k² rt², where k is a constant. The power delivered to the particle by the force acting on it is –

• A. 2p mk² r²
• B. mk² r²t
• C. $\frac{(mK^{4}r^{2}t^{5})}{3}$
• D. Zero

Answer 1

Answer: (B)

mk² r²t

Answer 2

a_c = k² rt²

or $\frac{v^{2}}{r}$= k² rt²

or v = krt

Therefore, tangential acceleration, a_t =$\frac{dv}{dt}$= kr

or Tangential force,

F_t = ma_t = mkr

Only tangential force does work.

Power = F_t v = (mkr) (krt)

or Power = mk² r² t