Question
A cubical block of side $$L$$ rests on a rough horizontal surface with coefficient of friction $${\mu .}$$ A horizontal force $$F$$ is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is
A cubical block of side $$L$$ rests on a rough horizontal surface with coefficient of friction $${\mu .}$$ A horizontal force $$F$$ is applied on the block as shown. If the coefficient of friction is sufficiently high so that the block does not slide before toppling, the minimum force required to topple the block is
A.
infinitesimal
B.
$$\frac{{mg}}{4}$$
C.
$$\frac{{mg}}{2}$$
D.
$$mg\left( {1 - \mu } \right)$$
Answer :
$$\frac{{mg}}{2}$$
Solution :
The applied force shifts the normal reaction to one corner as shown. At this situation, the cubical block starts topping about $$O.$$ Taking torque about $$O$$
$$\eqalign{ & F \times L = mg \times \frac{L}{2} \cr & \Rightarrow F = \frac{{mg}}{2} \cr} $$
The applied force shifts the normal reaction to one corner as shown. At this situation, the cubical block starts topping about $$O.$$ Taking torque about $$O$$
$$\eqalign{ & F \times L = mg \times \frac{L}{2} \cr & \Rightarrow F = \frac{{mg}}{2} \cr} $$
