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Question

A force F is applied on the top of a cube as shown in figure. The coefficient of friction between the cube and the ground is μ. If F is gradually increased, the cube will topple before sliding if


A
μ>14
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B
μ<12
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C
μ>12
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D
μ<1
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Solution

The correct option is C μ>12
Equilibrium of an object is broken when the object is on the point of toppling,
hence we draw the FBD and write the force and torque equation.
Let m be the mass of the cube and a the side of cube. The cube will slide if :
F>μmg ...(i) (By applying the force balancing equation).

It will topple if torque of F about P, is greater than torque of mg about P i.e.,
Fa>(a2)mg
or F>12mg ...(ii) (By applying the torque balancing equation).

From Eqs. (i) and (ii), we see that cube will topple before sliding if

μmg>12mg
μ>12

Hence option C is the correct answer

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