Q. A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is ( P O Q   = 40 ° )

 

Dear student, 

It is given that the particle is moving in the circle with a uniform velocity v. As such the magnitude of velocity remains the same but the direction changes. We know the direction of velocity of a particle moving in a circle is along the tangent of that point. Since OP and OQ are at 40° with each other, their velocity vectors at P and Q will also be at the same angle to each other.

Hence,
v=v cos 40--vcos 40=2v cos 40 =1.53 v
Regards

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