Question

An object of mass $m$ slides down a hill of arbitrary shape and after travelling a certain horizontal path stops because of friction. The total vertical height descended is $h.$ 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 tangential force must perform to return the object to its initial position along the same path is :

• A. $mgh$
• B. $-mgh$
• C. $-2mgh$
• D. $2mgh$

Answer 1

The correct option is A $mgh$

$h^{\prime }=h$
$△PE=mg△h$
now work done by friction =$△PE$
$friction=f_s$

now work done by $f_s=△PE$
$f_s.d=mgh$

So the work done against gravity to make the body reach its highest point is $mgh$