Question

A sphere of mass m is tied to one end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done in full horizontal circle is
A. 0
B. $({\dfrac{mv^2}{l}})^2$
C. 3
D. 2

Answer 1

Hint: To solve this problem, we should know about circular motion. Basic concepts regarding the circular motion and work done by a system moving in a circular motion. Here a sphere of mass is tied on a string and it is rotated in a circular path. We have to calculate the work done in a full horizontal circle.

Complete step by step solution:
Here a sphere of mass m is tied on a string of length l and it is rotated through the other end along a horizontal circular path and we have to calculate work done by the system in full horizontal circle.The particle moving in circular motion means centripetal force acting on the system.

Centripetal force is the force acting on a particle executing uniform circular motion and it is acting inwards. It restricts the movement of particles in a circle but it is not at all responsible for the displacement of particles. If no displacement takes place, then from definition of work centripetal force can’t do work. Therefore, work done by a centripetal force in uniform circular motion is equal to zero and the answer is: the work done in full horizontal circle is zero.

Therefore, the correct answer is option A.

Note: Usually, we go for the general equation for work done in these kinds of problems. We have that work done is equal to the product of force and distance travelled. But here answer is zero since work done by centripetal force in uniform circular motion is always equal to zero