A block B is pushed momentarily along a horizontal surface with a… - Vidyadip

MCQ

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
$\frac{{g{\mu _k}}}{V}$
B
$\;\frac{g}{V}$
C
$\;\frac{V}{g}$
✓
$\;\frac{V}{{g{\mu _k}}}$

✓

Answer

Correct option: D.

$\;\frac{V}{{g{\mu _k}}}$

d
Given $u = V$, final velocity $= 0$.
Using $v = u + at$

$\begin{array}{l}
\therefore \,0 = V - at\,\,or,\,\, - a = \frac{{0 - V}}{t} = - \frac{V}{t}\\
\,\,\,\,f = \mu R = \mu mg\,\left( {f\,is\,the\,force\,of\,friction} \right)\\
\therefore {\rm{Retardation,}}\,{\rm{a}}\,{\rm{ = }}\mu {\rm{g}}\,\therefore {\rm{t}}\, = \frac{V}{a} = \frac{V}{{\mu g}}.
\end{array}$

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