A cubical block of side L rests on a rough horizontal surface with coefficient of friction μ. 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

Question

A cubical block of side L rests on a rough horizontal surface with coefficient of friction μ. 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) mg/4 (C) mg/2 (D) mg(1-μ)

Tardigrade Admin · Accepted Answer

At the critical condition, normal reaction N will pass through point P. In this condition

τ_{N} = 0 = τ_{f r}

(about P) the block will topple when

τ_{F} > τ_{m g}

or

F L > (m g) \frac{L}{2}

∴ F > \frac{m g}{2}

Therefore, the minimum force required to topple the block is

F = \frac{m g}{2}

infinitesimal

mg/4

mg/2

mg(1−μ)

At the critical condition, normal reaction N will pass through point P. In this condition τN​=0=τfr​ (about P) the block will topple when τF​>τmg​ or FL>(mg)2L​ ∴F>2mg​ Therefore, the minimum force required to topple the block is F=2mg​

$m g (1 - μ)$