A particle of mass 'm' is moving on a circular path of radius 'r' with velocity 'v', then centripetal force acting on it is F. if the velocity of particle increases by 2 times and radius of circular path increases by 4 times then new centripetal force F' will be?

F' = 2 F

F' = F

F' = 1/2

F' = 4 F

Explanation

When the velocity increases by 2 times and the radius increases by 4 times, the centripetal force remains the same.

This is because the increase in velocity squared (2^2 = 4) is balanced by the increase in radius (4r), resulting in no net change in the centripetal force.

So, the correct answer is:

F' = F