question_answer

The centripetal acceleration of particle of mass \[m\]moving with a velocity v in a circular orbit of radius r is:

A)  \[{{v}^{2}}/s\]along the radius, towards the centre

B)  \[{{v}^{2}}/r\]along the radius, away from the centre

C)  \[m{{v}^{2}}/r\]along the radius, away the centre

D)  \[m{{v}^{2}}/r\]along the radius, towards the centre

Correct Answer: A

Solution :

 When a particle performs a uniform circular motion, its direction changes continuously though its speed remains constant, thus its velocity changes continuously, that is there is an acceleration in circular motion. The direction of this acceleration is always towards the centre of the circle. Hence, it is called centripetal acceleration, given by \[{{a}_{c}}=\frac{{{v}^{2}}}{r}\] Note: Non-uniform circular motion has tangential acceleration\[({{a}_{t}})\]and resultant acceleration is \[a=\sqrt{a_{c}^{2}+a_{t}^{2}}.\]