Question

A block B is pushed momentarily along a horizontal surface with an initial velocity $v$. If $\mu$ is the coefficient of sliding friction between $B$ and the surface, block B will come to rest after a time :

(A) $\frac{v}{g \mu}$

(B) $\frac{g \mu}{v}$

(C) $\frac{g}{v}$

(D) $\frac{v}{g}$

Answer 1

Block B will come to rest, if force applied to it will vanish due to frictional force acting between block B and surface, i.e, foce applied = frictional force

i.e., $\mu \mathrm{mg}=\mathrm{ma}$ or $\mu \mathrm{mg}=\mathrm{m}\left(\frac{\mathrm{v}}{\mathrm{t}}\right)$

or $\quad \mathrm{t}=\frac{\mathrm{v}}{\mu \mathrm{g}}$

So, The correct option of this question is (A).