Question

A body moves in a vertical circle of radius r from the lowest point to highest point. What is the amount of work done by gravity? (Assume mass of the body to be 'm' kg and acceleration due to gravity to be $gm{s}^{-2}$)

• A. 2mgr
• B. -2mgr
• C. mgr
• D. mgr

Answer 1

The correct option is B -2mgr

As the body moves in a vertical circle from its lowest to the highest point, net displacement is equal to 2r. The only force acting is gravity in vertically downward direction i.e. opposite to the direction of displacement. $cos\theta ={180}^0$
Since $cos{180}^0=-1$, work done will be negative.
Work done = force due to gravity $\times$ displacement $\times -1$ = mg $\times$ -2r = -2mgr.