Question

A body of mass m was slowly hauled up the hill as shown in fig. by a force $F$ which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill is h, the length of its base is l and the coefficient of friction $k$

• A. $mgh$
• B. $mg(h+kl)$
• C. $mg(h-kl)$
• D. $Noneofthese$

Answer 1

The correct option is A $mgh$

Applying work energy theorem

Change in kinetic energy$=$work done by all forces

$=W_{mg}+W_{ext}$

work by gravity$=-mgh$ ($-$ve sign is because work is done against gravity)

Work by F is $W_{ext}$

Change in kinetic energy$=0$

so,

$W_{ext}-mgh=0$

$W_{ext}=mgh$

So work by force F is mgh, this work will not depend on the angle of incline...