Question

Consider a frictionless ramp on which a smooth object is made to slide down from an initial height $h$. The distance $d$ necessary to stop the object on a flat track (of coefficient of friction $\mu$), kept at the ramp end is

• A. $h/\mu$
• B. $\mu h$
• C. ${\mu }^{2}h$
• D. $h^2\mu$

Answer 1

The correct option is A $h/\mu$

Let the distance it slides on the rough surface be $d$.
Work done by friction $W_f=-\mu mgd$
Work done by gravitational force $W_g=mgh$
From work-energy theorem, $W_f+W_g=\Delta K.E=0$
$\therefore$ $-\mu mgd+mgh=0$
Or $mgh=\mu mgd$
$⟹d=\frac{h}{\mu }$