Question

The work done by a centripetal force in a circular motion :

• A. increases by decreasing the radius of the circle
• B. decreases by increasing the radius of the circle
• C. increases by increasing the mass of the body
• D. is always zero

Answer 1

The correct option is D is always zero

Centripetal Force, $\overrightarrow{F}=\frac{m{v}^2}{r}\hat{r}$

Therefore, the direction of force is in the radial direction.

Workdone, $W=\int \overrightarrow{F}\cdot d\overrightarrow{s}$

where, $d\overrightarrow{s}$ is the displacement.

Since, the particle always moves in a direction perpendicular to the radial direction in circular motion. Therefore, the dot product is always zero and hence, the work done by centripetal force in a circular motion is always zero.