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 a fraction is 0.25, the angle of inclination of the plane is

• A. ${36.8}^{\circ }$
• B. ${45}^{\circ }$
• C. ${30}^{\circ }$
• D. ${42.6}^{\circ }$

Answer 1

The correct option is A ${36.8}^{\circ }$

Force required just to move a body up an inclined plane(F) = $mg\sin \theta +\mu mg\cos \theta$

Force required just to prevent the body sliding down(f)= $mg\sin \theta -\mu mg\cos \theta$

According to question,

F = 2f

$\Rightarrow$ $mg\sin \theta +\mu mg\cos \theta$ $=2(mg\sin \theta -\mu mg\cos \theta )$

$\Rightarrow mg\sin \theta =3\mu mg\cos \theta$

$\Rightarrow \tan \theta =3\mu =0.75$

$\Rightarrow \theta ={\tan }^{-1}\left(0.75\right)={36.8}^0$

Therefore, A is correct option.