Question

When a body moves with a constant speed along a circle

• A. no work is done on it
• B. no acceleration is produced in it
• C. its velocity remains constant
• D. no force acts on it

Answer 1

The Correct Option is A

A body moving with a constant speed along a circular path experiences unique physical conditions due to its motion. Let's analyze the options and determine why "no work is done on it" is the correct answer:

1. Understanding Circular Motion: In circular motion, a body moves along a circle with a constant speed. Though the speed is constant, the direction of the velocity vector changes continuously. This change in direction means that the velocity of the body is not constant, but rather the speed is constant.
2. Analysis of Options:
   • No work is done on it: This option is correct because work done is defined as W = \mathbf{F} \cdot \mathbf{d} \cdot \cos(\theta), where F is the force applied, d is the displacement, and \theta is the angle between the force and displacement vectors. For a body moving in a circle with constant speed, the force exerted (centripetal force) is perpendicular to the displacement at any point in time. This means \theta = 90^\circ, and since \cos(90^\circ) = 0, no work is done on the body.
   • No acceleration is produced in it: This is incorrect as circular motion involves continuous change in the direction of velocity, thus the body does experience centripetal acceleration towards the center of the circle. This acceleration changes the direction of the velocity but not its magnitude.
   • Its velocity remains constant: This is incorrect as the velocity (a vector quantity) changes direction continuously in circular motion, although the speed (magnitude of velocity) remains constant.
   • No force acts on it: This is incorrect because a centripetal force is necessary to keep the body moving in a circle, causing it to continually change direction.

In conclusion, in circular motion with constant speed, no work is done on the body, aligning with the physics that the force is perpendicular to the displacement. Therefore, the correct answer is no work is done on it.