Question

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

• A. $m{v}^{2}r$
• B. $zero$
• C. $m{v}^2/r$
• D. $r^2/m{v}^2$

Answer 1

The correct option is B $zero$

Since, centripetal acceleration
$a_c=\frac{v^2}{r}=r\omega$, because $v=r\omega$.

Work done, $W=\overrightarrow{F}\cdot \overrightarrow{r}$, where $\overrightarrow{r}$ is the displacement vector.
As particle is under uniform circular motion, $\overrightarrow{F}\perp \overrightarrow{r}$. So, $W=\overrightarrow{F}\cdot \overrightarrow{r}=0$