A cubic block of side L rests on a rough surf | vedclass

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(C) To find the minimum force required to topple the block,we consider the torque about the edge $O$ (the pivot point) about which the block will topp

Vedclass · Accepted Answer

$\frac{mg}{2}$

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(C) To find the minimum force required to topple the block,we consider the torque about the edge $O$ (the pivot point) about which the block will topple.Step $1$: Identify the forces acting on the block.- The applied horizontal force $F$ acts at the top edge,at a height $L$ from the base.- The weight $mg$ of the block acts at the center of gravity,which is at a horizontal distance $L/2$ from the pivot point $O$.- The normal force $N$ shifts to the edge $O$ at the point of toppling.Step $2$: Apply the condition for toppling.For the block to be on the verge of toppling,the torque due to the applied force $F$ about the pivot point $O$ must be equal to the torque due to the weight $mg$ about the same point.Torque due to $F$ (clockwise) = $F 	imes L$Torque due to weight $mg$ (anticlockwise) = $mg 	imes \frac{L}{2}$Equating the torques:$F 	imes L = mg 	imes \frac{L}{2}$$F = \frac{mg}{2}$Thus,the minimum force required to topple the block is $\frac{mg}{2}$.

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