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Q.

A body is moving up an inclined plane of angle θ with an initial kinetic energy E. The coefficient of friction between the plane and body is µ . The work done against friction before the body comes to rest is

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a

\large \frac{{\mu \cos \theta }}{{E\cos \theta + \sin \theta }}

b

\large 2\mu E\cos \theta

c

\large \frac{{\mu E\cos \theta }}{{\mu \cos \theta - \sin \theta }}

d

\large \frac{{\mu E\cos \theta }}{{\mu \cos \theta + \sin \theta }}

answer is D.

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Detailed Solution

$\large E = \frac{1}{2}m{v^2},S = \frac{{{V^2}}}{{2a}}\;and\;a = g(\sin \theta + \mu \cos \theta )$
$\large w = {F_s}S = (mg\cos \theta \mu )\frac{{{v^2}}}{{2a}}$
$\large w = \frac{{\frac{1}{2}m{v^2}\mu \cos \theta }}{{g(\sin \theta + \mu \cos \theta )}}$
$\large w = E\mu \cos \theta /(\sin \theta + \mu \cos \theta )$

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