Physics - W.E.P. Question with Solution | TestHub

First, consider the motion on the smooth curved track. By conservation of mechanical energy, the potential energy at height $h$ is converted into kinetic energy at the bottom of the track.$$mgh=\frac{1}{2}m{v}^2⟹v=\sqrt{2gh}$$

Next, consider the motion on the rough horizontal surface. The work-energy theorem states that the work done by non-conservative forces equals the change in kinetic energy. Here, the only non-conservative force is friction.$$W_{friction}=\Delta KE$$ $$-\mu mgd=0-\frac{1}{2}m{v}^2$$ Substituting $v^2=2gh$: $$-\mu mgd=-\frac{1}{2}m(2gh)=-mgh$$ $$d=\frac{h}{\mu }$$