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 the figure. 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 $\frac{mg}{\sqrt{n}}$ . Find $n$.

Answer 1

Force applied to plate at top most corner and plate is about to topple about bottom right corner.

The tendency of rotating will be about the bottom right corner

For minimum force, the torque of $F$ about bottom right corner has to be equal to the torque of mg.

$\therefore F\left(a\frac{\sqrt{3}}{2}\right)=mg\left(\frac{a}{2}\right)$

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

Comparing with $\frac{mg}{\sqrt{3}}$

We get \$n=3$

FINAL ANSWER: $3$