Question

A body of mass $m$ is performing a $UCM$ in a circle of radius $r$ with speed $v$. The work done by the centripetal force in moving it through $\left(\frac{2}{3}\right)rd$ of the circular path is

• A. zero
• B. $mv^{2}\pi r$
• C. $\frac{2\pi mv^{2}r}{3}$
• D. $\frac{2mv^{2}\pi}{3}$

Answer 1

Answer: (A)

When a body perform uniform circular motion, then centripetal force acts always in perpendicular direction to its velocity, hence work done by centripetal force is always zero. Hence, work done by centripetal force is zero, when it through $\left(\frac{2}{3}\right)$ rd of the circular path.