An object of mass m slides down a hill of height h of arbitrary shape and after travelling a certain horizontal path stops because of friction. The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion. The work that a force must perform to return the object to its initial position along the same path is

Options

A. (a) `mgh`
B. (b) `-mgh`
C. (c) `-2mgh`
D. (d) `2mgh`

Answer

D

Explanation

The initial potential energy of the object is `mgh`, which has been used up for work against the force of friction. In returning the body to its initial position, the force performs the same work against friction. In addition, it imparts to the object the initial potential energy. As a result, the total work will be `2mgh`.