# The work done by centripetal force is? (a) positive (b) zero (c) negative (d) unity

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The work done by the centripetal force is zero. A body must be moved with centripetal force in order to move in a circle at a constant speed. Centripetal force is the force that causes a body to move in a circular path. Examples of centripetal force orbiting planets, washing machine dryers, etc.

### Work Done by Centripetal Force

The force acts on the body in a radius-toward-center direction. Formulae for centripetal force is F = mv2/r2 where F = m = mass of the body, Centripetal force, v = velocity of the body, and r = radius.

• Since centripetal force is orthogonal to velocity and thus instantaneous displacement, the work it performs is always zero.
• This is so that the centripetal force, which acts along the radius of curvature and toward its centre, makes a 90° angle with the displacement of the body, which occurs along the circumference (tangent), which is perpendicular to the radius.
• Given that force times, displacement equals work done, ie. W = FS cos θ
• And the angle between the F and S is 90°
• W = FS cos 90° = 0

Summary:

## The work done by centripetal force is? (a) positive (b) zero (c) negative (d) unity

The work done by the centripetal force is always zero. It is because it makes an angle of 90° angle with the displacement of the body. The force that makes a body follow a curved path is called centripetal force.

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