Question

A body of mass $m$ is moving with a constant speed $v$ in a circle of radius $r$ . Find the work done by the centripetal force in moving the body over half the circumference of the circle.

• A. $\frac{m v^{2}}{\pi r^{2}}$
• B. zero
• C. $\frac{m v^{2}}{r^{2}}$
• D. $\frac{\pi r^{2}}{m v^{2}}$

Answer 1

Answer: (B)

In uniform circular motion speed and kinetic energy remains constant, work done is independent on path.
Here the centripetal force and instantaneous displacement are perpendicular to each other $W=\overset{ \rightarrow }{F}\cdot \overset{ \rightarrow }{s}=Fs cos\,\theta ^{\circ}\left(\theta = 90^{\circ}\right)=0$
therefore the work done by centripetal force is is zero.