A body of mass m moving around a circle of radius r with a uniform speed v experiences a centripetal force F. The work done by the centripetal force on it is

Analyze the question: The body moves in a circle at constant speed. We want the work done by the centripetal force during this motion.

Concept: Work done by a force is

W = F d cos θ

where θ is the angle between the force and the direction of displacement (the direction of motion).

Solution:

• The centripetal force always points toward the centre of the circle.
• The body's velocity (and its small displacement at every instant) is along the tangent to the circle.
• A tangent is perpendicular to the radius, so the angle between the force and the displacement is θ = 90°.
• Therefore W = F d cos 90° = F d (0) = 0.

This also agrees with energy considerations. The speed is uniform, so the kinetic energy (½mv²) does not change. By the work-energy theorem, the net work done is the change in kinetic energy, which is zero.

Checking the other options:

• A. Fv has the units of power (watts), not work (joules).
• C. Fmr has the wrong units.
• D. Fr/m has the wrong units.

Answer: B.

Tip: Whenever a force is always perpendicular to the motion, as with centripetal force in uniform circular motion or the magnetic force on a moving charge, it does no work. It changes the direction of motion but not the speed.