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. 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:
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. 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:
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For toppling problems, take moments about the edge that acts as the pivot.
Updated On: Mar 24, 2026
- \(\dfrac{mg}{\sqrt{3}}\)
- \(\dfrac{mg}{4}\)
- \(\dfrac{\mu mg}{\sqrt{3}}\)
- \(\dfrac{\mu mg}{4}\)
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The Correct Option is A
Solution and Explanation
Step 1: At the point of toppling, prism rotates about the bottom edge.
Step 2: Taking moments about the edge: \[ F \times \frac{a}{2} = mg \times \frac{a}{2\sqrt{3}} \]
Step 3: \[ F = \frac{mg}{\sqrt{3}} \]
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