Question

A body is moving in a circular path with a constant speed. It has
A. A constant velocity
B. A constant acceleration
C. An acceleration of constant, magnitude
D. An acceleration which varies with time in magnitude

Answer 1

Hint:A body is moving in a circular path with constant speed means body is covering equal distance in equal interval of time. The body moves in a circular path having constant speed because speed does not depend on direction as it is a scalar quantity and in circular motion direction of body changes. Whereas linear velocity is vector quantity and also linear acceleration so both depend on direction but magnitude remains same. Also there is a direct relationship between acceleration and speed of the body.

Formula used:
Linear velocity is given as,
$v=\dfrac{\Delta s}{\Delta t}$
where v is linear velocity and $\Delta s$ is change in linear displacement, $\Delta t$is change in time or can say rate change in linear displacement such as$\dfrac{\Delta s}{\Delta t}$
Linear acceleration is defined as,
\[a=\dfrac{\Delta v}{\Delta t}\]
where a is acceleration. The $\Delta s$ is change in velocity and $\Delta t$ is change in time or can say rate change in linear velocity such as $\dfrac{\Delta s}{\Delta t}$.
Also there is direct relation between in linear acceleration and constant speed such as,
$a=\dfrac{{{v}^{2}}}{r}$
Where v is constant speed of body in circular path of radius r where a is uniform acceleration at linear velocity.

Complete step by step solution:
At the point when a body is moving in a circular movement with constant speed, its bearing ceaselessly changes and consequently velocity(v), momentum(p), and speed increase change since they are vectors and their direction changes

Assuming that the body is in uniform circular motion, the acceleration is not constant. It is on the grounds that the course of acceleration is evolving. The acceleration going through uniform circular motion is given by
$a=\dfrac{{{v}^{2}}}{r}$
Acceleration is a vector amount, and in this way estimating its shift includes both magnitude and the direction is continuously pointing towards the centre of the circle, and consequently the bearing of acceleration is continuously changing. So the acceleration doesn't stay consistent. At every point of the circle, the magnitude of acceleration is the same.

Hence, option C is the correct answer.

Note: In the above explanation with the constant speed the acceleration is constant in magnitude but varies with the direction as in the circular motion direction changes and the velocity and acceleration a vector quantity and thus they change with change in direction but magnitude will remain same as constant speed.