An object of mass m follows a circular path of radius r with a constant speed v in uniform circular motion. Then, the work done by the centripetal force for the object to move once in a full circle is

CONCEPT:

• Circular Motion: The movement of an object along a circumference of a circle or rotation along a circular path is called circular motion.
• Uniform circular motion: The circular motion in which the speed of the particle remains constant is called uniform circular motion. In a uniform circular motion, force supplies the centripetal acceleration.
  • The kinetic energy and the speed of the body remain constant.

If the Force F acts on a body and it gets displaced by a displacement of S, the work done in that case is given by:

Work done (W) = FS Cos θ

• Centripetal Force: It is a force required to move a body uniformly in a circle. This force acts along the radius and towards the center of the circle.

\({\bf{Centripetal}}\;{\bf{Force}}\;\left( {\bf{F}} \right) = \frac{{m{v^2}}}{r}\)

• The centripetal force required for circular motion along the surface of the road, towards the center of the turn. The Static friction between tire and road provides the necessary centripetal force.

CALCULATION:

It is given that,

Mass = m, radius = r

• Now, here, please note that the movement is uniform circular in motion. The angle between force and displacement is 90°. The force and displacement are perpendicular to each other

⇒ cos 90° = 0

Work done (W) = FS Cos 90° = 0 J

• So, no matter what is the mass, radius, or velocity, the work done by centripetal force would be zero. So option 2 is correct.