Question

For a particle in uniform circular motion:
(A) Both velocity and acceleration are constant
(B) Acceleration and speed are constant but velocity changes
(C) Both acceleration and velocity changes
(D) Speed is constant

Answer 1

Hint: To answer this question, we have to analyse the uniform circular motion and observe the variation of different quantities given in the options with respect to the time. For differentiating velocity from the speed, the direction must be taken into account.

Formula used: The formula which is used in this question is given by
$\Rightarrow{a_c} = \dfrac{{m{v^2}}}{R}$, here ${a_c}$ is the centripetal acceleration of an object of mass $m$ which moves with a speed of $v$ along a circle of radius $R$.

Complete step by step solution:
Uniform circular motion is the motion in which the speed of the particle, which is performing the circular motion, is a constant. So, the speed, or the magnitude of the velocity in uniform circular motion remains constant.
Now, the acceleration of a particle in the circular motion has two components, one is tangential and the other is radial or normal. Since the speed of the particle, which is in the tangential direction, is a constant in uniform circular motion, so the tangential acceleration must be zero. Now, the magnitude of the radial acceleration, also known as the centripetal acceleration is given by
$\Rightarrow{a_c} = \dfrac{{m{v^2}}}{R}$
As the speed $v$ is constant, so the magnitude centripetal acceleration should also be constant.
As this acceleration is always directed towards the centre of the circle, so its direction keeps on changing. Thus the acceleration is not a constant.
Also, the velocity of the particle is always along the tangent of the circle. So, its direction also keeps changing. Therefore the velocity is also not constant.
So the options A and B are incorrect.
Hence, the correct answers are the options C and D.

Note:
There are different terminologies, speed and velocity, respectively for the magnitude and vector considerations of the velocity. But there is no such separate terminology for the acceleration. So, we must take care of the fact that we have to consider the direction of acceleration along with its magnitude when the variation of the acceleration is being discussed.