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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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