Question

Why is the work done on an object moving with uniform circular motion zero?

Answer 1

Hint
If the particle moves in the circle with a uniform speed ,we call it a uniform circular motion. In this case ,$\dfrac{{dv}}{{dt}} = 0$ (here v is Speed). In uniform circular motion speed remains constant but due to change in direction velocity becomes variable hence due to change in velocity we get an acceleration which is called centripetal acceleration.

Complete step by step solution
Work done on an object is the force applied and the displacement covered in the direction of the force applied.
Mathematically-
$W = FS\cos \theta$.
Force in uniform circular motion is always perpendicular to the displacement and hence the angle between $F$ and $S$ is $90^0$ always.
After putting the value of $\theta$.
$W = 0$.
Hence, The work done in a uniform circular motion is always zero.

Note
If a particle moves in a circle of radius r with constant speed $v$, its acceleration is$\dfrac{{{v^2}}}{r}$ directed towards the centre. This acceleration is called centripetal acceleration. In uniform circular motion speed remains constant the direction continuously changes and hence the “velocity” changes and there is acceleration during the motion.