Question

A rigid body of mass m is moving in a circle of radius r with a constant speed v.The force on the body is $\frac{m{v}^2}{r}$ and is directed towards the centre. What is the work done by this 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)

Zero

The work done is zero when the direction of the force is perpendicular to the direction of motion. Force is directed towards the center and the displacement, which means the shortest distance between two points is a straight line from one point of circle to another point over half the circumference.

Hence the angle formed between force and displacement is ${90}^0$.