Question

A particle of mass m is moving in a circular path of constant radius r such that is centripetal acceleration a is varying with time t as a_c = k²rt, where k is a constant. The power delivered to the particle by force acting on it is

• A. 2πmk²r²
• B. mk²r²t
• C. $\frac{mk^{4}r^{2}t^{5}}{3}$
• D. Zero

Answer 1

Answer: (B)

mk²r²t

Answer 2

a_c = k²rt²

i.e., $\frac{v^{2}}{r} = k^{2}rt^{2}$ or v = krt

Also a_t$\frac{dV}{dt} = kr$

∴ F = ma_t= mkr

Then, power = Fv = mkr(krt) = mk²r²t