Question

A body of mass $10Kg$ is moved with a uniform speed on a rough horizontal surface, for a distance of $2m$. The work done is $150J$. The surface is inclined to the horizontal at $30$. The same body is moved over the inclined plane for a distance of $2m$. The work done against friction will be: (Take $g=10m{s}^{-}2$):

• A. $250J$
• B. $50J$
• C. $150J$
• D. $75\sqrt{3}J$

Answer 1

The correct option is D $75\sqrt{3}J$

Given,

Mass $M=10kg$

Work done,$W=150J$

Displcement on horizontal = displacement on incline $=d=2m$

Friction force on horizontal plane,$F_r=\mu mg$

Friction force on incline plane,${F_r}^{\prime }=\mu mg\cos \theta$

Speed is uniform means net acting force is equal to friction force

Work done,$W=F_r.d=\mu mg.d$

$\Rightarrow \mu =\frac{W}{mg.d}=\frac{150}{10\times 10\times 2}=0.75$

Work done on incline plane, $W={F_r}^{\prime }d=\mu mg\cos \theta .d$

$\Rightarrow W=0.75\times 10\times 10\times \cos {30}^o\times 2$

$\Rightarrow W=75\sqrt{3}J$

Work done against friction is $75\sqrt{3}J$