Question

A body of mass m, having momentum p is moving on a rough horizontal surface. If it is stopped in a distance $x$, the coefficient of friction between the body and the surface is given by:

• A. $\mu =\frac{p^2}{2g{m}^{2}x}$
• B. $\mu =\frac{p^2}{g{m}^{2}x}$
• C. $\mu =\frac{p}{2gmx}$
• D. $\mu =\frac{p}{2g{m}^{2}x}$

Answer 1

The correct option is A

$\mu =\frac{p^2}{2g{m}^{2}x}$

$|W_f|=\frac{1}{2}m{v}^2-0=\frac{1}{2}m{v}^2=\frac{p^2}{2m}$

$\therefore \mu mgx=\frac{p^2}{2m}\Rightarrow \mu =\frac{p^2}{2g{m}^{2}x}$