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A block with a square base measuring $a \times a$ and height h, is placed on an inclined plane. The coefficient of friction is $\mu$. The angle of inclination $(\theta)$ of the plane is gradually increased. The block will

(a) topple before sliding if $\mu > \large\frac{a}{h}$ (b) topple before sliding of $\mu < a/h$ (c) slide before toppling if $\mu >\large\frac{a}{h}$ (d) slide before topping if $\mu < \large\frac{a}{h}$

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1 Answer

Condition for sliding $\mu =\tan \theta$
At the instant of toppling normal force acts along the edge AB and friction acts along AD.
Taking moments about A
$mg \sin \theta \times \large\frac{h}{2}$$ = mg \cos \theta. \large\frac{a}{2}$
$\tan \theta= \large\frac{a}{h}$
if $\mu > \large\frac{a}{h},$ it will topple before sliding
if $\mu < \large\frac{a}{h}$ it will slide before toppling.
answered Dec 6, 2013 by meena.p
edited Jun 24, 2014 by lmohan717

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