Question

A particle performing uniform circular motion has:
(a) Radial velocity and Radial acceleration
(b) Radial velocity and Transverse acceleration
(c) Transverse velocity and Radial acceleration
(d) Transverse velocity and Transverse acceleration

Answer 1

Initially, we define what is uniform circular motion and quantities associated with them. Then we will see which quantities are zero and which are not. Then we see why some of these quantities are zero and if there is any condition where they will be non-zero.

Complete step by step solution:
We define circular motion as the motion of a body or an object along the circumference of a circle or rotation along a circular path. And it can be uniform when the angular rate of rotation is constant.
For any moving object, there are three quantities, a force, velocity and acceleration. When a force is applied to the object, it causes the body to move and a moving body has a velocity with which it moves. The change in velocity is called acceleration. If a body has velocity, it has acceleration unless it is moving with the same velocity without acceleration or speeding up. Now discuss the option given in question.
(a) Radial velocity and Radial acceleration
In uniform circular motion has zero radial velocity and non-zero Radial acceleration.

(b) Radial velocity and Transverse acceleration
In uniform circular motion has zero radial velocity and zero Transverse acceleration.

(c) Transverse velocity and Radial acceleration
In uniform circular motion has Transverse velocity and non-zero Radial acceleration.

(d) Transverse velocity and Transverse acceleration
In uniform circular motion has Transverse velocity and zero Transverse acceleration.

In conclusion, the right answer is option (C) Transverse velocity and Radial acceleration.

Note:
The acceleration of a body moving in a circular path or undergoing circular motion is called centripetal acceleration. This acceleration is also called radial acceleration. The radial velocity of an object as for a given point is the rate at which the distance between the item and the point changes.