Question

An object placed on an inclined plane starts sliding when the angle of inclination becomes $\propto$. The coefficient of static friction between the block and object is $\frac{1}{\sqrt{3}}$ then$\propto is$

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

When an object starts sliding at some angle, then there two forces will acts i.e. force of gravity and frictional force such that,

$F=mg\sin \alpha$

$N=mg\cos \alpha$

$F=kN$

Where k is coefficient of static friction.

$mg\sin \alpha =kmg\cos \alpha$

$\frac{\sin \alpha }{\cos \alpha }=\frac{1}{\sqrt{3}}$

$\tan \alpha =\tan 30$

$\alpha ={30}^0$