Question

'A' block 'B' is pushed momentarily along a horizontal surface with an initial velocity '$\upsilon$'. If '$\mu$' is the coefficient of 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

The correct option is A $\frac{v}{g\mu }$

Let after time $t$, block B comes into rest ($v_f=0$)

By using: $v_f=v_i-at$ (acceleration $=-a$ , due to retardation)

$0=v-at$ (given $v_i=v$)

$t=\frac{v}{a}$ ...........eq1

Now, block B comes into rest due to frictional force.

Hence, external push $=$ frictional force

$F=\mu mg$

$ma=\mu mg$

$a=\mu g$

Putting the value of $a$ in eq 1, we get:

$t=\frac{v}{g\mu }$