Question

A particle of mass M moves in a circular path of radius R under the action of a force F = Mv2 / R. The work done by force F during its motion over half of the circumference of the circular path is

Zero
(Mv2 / R) x πR
(Mv2 / 2) x 2πR
none of these​

Answer 1

workdone is the dot product of force and displacement.

here it is given that, A particle of mass M moves in a circular path of radius R under the action of a force F = Mv²/R.

displacement of particle during its motion over half of the circumference of the circular path = diameter of circular path = 2R

now we have to think about direction. you should remember that displacement of particle is perpendicular to direction of centripetal force. or you can say that in circular motion, there is no displacement in the direction of centripetal force.

so, angle between force and displacement = 90°

now workdone = mv²/R × 2R cos90° = 0

hence, answer is zero.