A uniform cube of side a and mass m rests on | vedclass

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(B) To find the minimum force $F$ required to tilt the cube,we consider the torque about the edge of the cube about which it is about to tilt (let thi

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$\frac{2mg}{3}$

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(B) To find the minimum force $F$ required to tilt the cube,we consider the torque about the edge of the cube about which it is about to tilt (let this point be $O$).For the cube to tilt,the torque due to the applied force $F$ must be greater than or equal to the restoring torque due to the weight $mg$ of the cube.The torque due to the force $F$ about the edge $O$ is $	au_F = F 	imes \frac{3a}{4}$.The torque due to the weight $mg$ about the edge $O$ is $	au_{mg} = mg 	imes \frac{a}{2}$ (since the weight acts at the center of mass,which is at a horizontal distance of $\frac{a}{2}$ from the edge).For the cube to begin to tilt,we set $	au_F = 	au_{mg}$:$F 	imes \frac{3a}{4} = mg 	imes \frac{a}{2}$$F = mg 	imes \frac{a}{2} 	imes \frac{4}{3a}$$F = \frac{2mg}{3}$.

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