Question

A cube of side $a$ is placed on an inclined plane of inclination $\theta .$ What is the maximum value of $\theta$ for which the cube will not topple?

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

When the cube is just about to topple, normal reaction will shift towards face $\text{AD}$.



Torque equilibrium about point $\text{A}$ :
$mg\sin \theta \times \left(\frac{a}{2}\right)=mg\cos \theta \times \left(\frac{a}{2}\right)$
{$mg\sin \theta$ and $mg\cos \theta$ are horizontal and vertical components w.r.t inclined surface respectively}
$\Rightarrow \sin \theta =\cos \theta$
$\Rightarrow \theta ={45}^o$