Question

A body of mass $M$ was slowly hauled up a rough hill by a force $F$ which at each point was directed along a tangent to the path of the hill. The work done by this force

• A. depends on vertical component only.
• B. does not depend on coefficient of friction.
• C. depends on horizontal component only.
• D. depends on both horizontal and vertical components of displacement.

Answer 1

The correct option is D depends on both horizontal and vertical components of displacement.

Let the work done by the force $F$ be $W_F$.
Work done by the friction force on the rough hill, $W_{\text{Friction}}=-\mu mgs$
where $s$ is displacement along the surface of the hill.
Work done by gravity force, $W_G=-mgh$

Apply Work-Energy theorem:
$W_F+W_G+W_{\text{Friction}}=\Delta KE$
($\because$ the block is slowly hauled, final and initial velocity = 0)
$W_F-mgh-\mu mgs=0$
$W_F=mgh+\mu mgs$
Hence it depends on horizontal and vertical components of displacement.