Question

The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $\theta$ is the angle of friction and $\theta$ is the angle which the plane makes with the horizontal, then :

• A. $\tan \phi=2 \tan \theta$
• B. $\tan \phi=3 \tan \theta$
• C. $\tan \phi=\tan \theta$
• D. $\tan \theta=3 \tan \phi$

Answer 1

Answer: (D)

$\tan \theta=3 \tan \phi$

Answer 2

Here, $m g(\sin \phi+\mu \cos \phi)=2 m g(\sin \phi-\mu \cos \phi)$ $\Rightarrow$ $\tan \phi=3 \mu$ As $\mu=\tan \theta$ So, $\tan \phi=3 \tan \theta$