Question

A car of mass m moving along a circular track of radius r with a speed v which varies with time t as v=kt, k being a constant Then,

• A. The instantaneous power delivered by the centripetal force is $\frac{m{k}^3{t}^3}{r}$
• B. The power delivered by the centripetal force is zero
• C. The instantaneous power delivered by the tangential force is $m{k}^{2}t$
• D. The power delivered by the tangential force is zero.

Answer 1

Answer: (B), (C)

The correct options are
B The power delivered by the centripetal force is zero
C The instantaneous power delivered by the tangential force is $m{k}^{2}t$

Centripetal forces $F_c=\frac{m{v}^2}{r}=\frac{m{k}^2{t}^2}{r}$
$P=\underset{F_c}{\to }.\underset{v}{\to }=0$
$F_t=m\left(\frac{dv}{dt}\right)=m\frac{d}{dt}\left(kt\right)=mk$
$P=\underset{F_t}{\to }.\underset{v}{\to }=m{k}^{2}t$