Question

A body is revolving with a constant speed along a circle. If its direction of motion is reversed but the speed remains the same, then which of the following statement is true:
A. The centripetal force will not suffer any change in magnitude
B. The centripetal force will have its direction reversed
C. The centripetal force will not suffer any change in direction
D. The centripetal force would be doubled

Answer 1

Hint:In this question the concept of centripetal force will be used. Centripetal force is always directed towards the centre and does not depend upon direction of rotation. Centripetal force is directly dependent on mass and directly dependent on square of velocity and inversely proportional to radius.

Formula used:
\[F=\dfrac{m{{v}^{2}}}{r}\]
here \[\left( F \right)\] Denotes centripetal force, \[\left( m \right)\] denotes mass of the body,\[\left( v \right)\]denotes speed of the body and \[\left( r \right)\]denotes radius of circular path of the body.

Complete step by step solution:
Centripetal force is also equal to \[F=m{{w}^{2}}r\]; where \[\left( w \right)\] represents angular velocity but here we will used the formula \[F=\dfrac{m{{v}^{2}}}{r}\] for centripetal force. In this question the speed of the body remains same which means magnitude of centripetal force will also remain the same. And hence option (D) is not at all correct.

Also the change in direction of rotation of a particle does not affect direction of centripetal force as it is always directed towards the centre. (Radial vector) and hence option (B) is not correct.

Therefore option A and option C are correct.

Note: Please make sure that centripetal force is a vector quantity but it is a radial vector i.e. no matter what is the direction of motion of the body it will always be directed towards the centre only. Moreover, when a car travels through a curve on a circular horizontal road, the centripetal force created by friction between the vehicle's tyres and the road surface helps the automobile to navigate the bend.