Question

An equilateral uniform prism of mass m rests on a rough horizontal surface with the coefficient of friction $\mu$ and a horizontal force $F$ is applied. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is :

• A. $\frac{mg}{\sqrt{3}}$
• B. $\frac{mg}{4}$
• C. $\frac{\mu mg}{\sqrt{3}}$
• D. $\frac{\mu mg}{4}$

Answer 1

The correct option is A $\frac{mg}{\sqrt{3}}$

From the figure,

AP= $asin\left({60}^o\right)=a\frac{\sqrt{3}}{2}$

For prism to be toppled, the Normal reaction should pass through the toppling point 'O' as shown in the figure.

Taking moments about point 'O',

Clockwise moments= Anticlockwise Moments,

$F\times a\frac{\sqrt{3}}{2}=mg\times \frac{a}{2}$

$\Rightarrow F=\frac{mg}{\sqrt{3}}$