An equilateral prism of mass m rests on a rough horizontal surface, with a coefficient of friction μ . A horizontal force F is applied to the prism, as shown in the figure. If the coefficient of frict

Question

An equilateral prism of mass m rests on a rough horizontal surface, with a coefficient of friction μ . A horizontal force F is applied to 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

TestHub · Accepted Answer

The prism will topple after normal reaction shifts to the rightmost part of the prism.

Hence, at that time, equating torque about the toppling point ( rightmost point of the prism) due to force $F$ and force due to gravity $m g$

$F \times (\frac{a \sqrt{3}}{2}) = m g \frac{a}{2}$

$\Rightarrow F = \frac{m g}{\sqrt{3}}$

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