Question

An equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force F is applied on the prism as shown in Fig. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, 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 $\frac{mg}{\sqrt{3}}$

The tendency of rotating will be about point C. For the minimum force, the torque of F about C has to be equal to the torque of mg about C.
$F\left(a\frac{\sqrt{3}}{2}\right)=mg\left(\frac{a}{2}\right)\Rightarrow F=\frac{mg}{\sqrt{3}}$