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Chapter 4: Problem 3

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that (A) Its velocity is constant. (B) Its acceleration is constant. (C) Its kinetic energy is constant. (D) It moves in a straight line.

Short Answer

Expert verified
The kinetic energy of the particle is constant. Therefore, the correct answer is option (C).

Step by step solution

01

Understand the motion

A force acting on the particle is of constant magnitude and always perpendicular to the velocity. The motion takes place in a plane. This description corresponds to circular motion. In circular motion, the velocity keeps changing direction, with speed remaining constant because the force working on it is constantly perpendicular to the velocity.
02

Analyze options A and B

Option A suggests that velocity of the particle is constant which is not true as in circular motion, velocity keeps changing direction. Option B suggests that the acceleration is constant. This is also false because although the magnitude of the acceleration is constant in circular motion, the direction of acceleration isn't constant.
03

Analyze option D

Option D indicates that the particle moves in a straight line, which is not correct. As concluded, the motion of a particle under a perpendicular constant force is circular.
04

Conclude option C

Option C suggests that the kinetic energy is constant. Work-Energy theorem states that the work done on an object is equal to the change in its kinetic energy. However, in this case, since the force is always perpendicular to the direction of motion, it does no work on the particle. Hence, the kinetic energy of the particle remains constant.

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