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Question

An equilateral uniform prism of mass m rests on a rough horizontal surface with coefficient of friction μ 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
mg3
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B
mg4
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C
μmg3
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D
μmg4
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Solution

The correct option is A mg3
From the figure,


AP=asin60o=a32
For just topple condition, normal reaction will shift to O.
Since friction act through horizontal line passing through O, there is no torque due to it.
Net torque about point O=0,
Fa32=mg×(a2)
F=mg3

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