Question

The force required just to move a body up an inclined plane is double the force required just to prevent the body sliding down. If the coefficient of friction is 0.25. then the angle of inclination of the plane will be :

• A. $ta{n}^{-1}\left(\frac{3}{4}\right)$
• B. $ta{n}^{-1}\left(\frac{1}{4}\right)$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

The correct option is B $ta{n}^{-1}\left(\frac{1}{4}\right)$

Coefficient of friction is given as $\mu =0.25$

Frictional force acting on the block $f=\mu mg\cos \theta$

Gravitational force acting along the inclined plane is $mg\sin \theta$

For no sliding, $f=mg\sin \theta$

$\therefore$ $\mu mg\cos \theta$ $=mg\sin \theta$

$⟹$ $\tan \theta =\mu =0.25=\frac{1}{4}$

$⟹$ $\theta ={\tan }^{-1}\left(\frac{1}{4}\right)$