Question

A body of mass m is moving in a circle of radius $r$ with a constant speed $v.$ The force on the body is $\frac{mv^{2}}{r}$ 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. $\frac{mv^{2}}{\pi r^{2}}$
• B. Zero
• C. $\frac{mv^{2}}{r^{2}}$
• D. $\frac{\pi r^{2}}{mv^{2}}$

Answer 1

Answer: (B)

Work done by centripetal force is always zero, because force and instantaneous displacement are always perpendicular
$W= \vec{F} .\vec{s}=Fs\, \cos \theta$
$=Fs\, \cos\, \left(90^{\circ}\right)=0$