First slide

Toppling

Question

A right circular solid cylinder of radius 10 cm and height $20 \sqrt{3} c m$ is placed on a rough inclined surface having angle of inclination $θ$ with horizontal. Upto what maximum value of $θ$ , will the cylinder not topple? Assume that there is sufficient friction between the cylinder and the inclined surface to prevent slipping.

Moderate

A

$45^{o}$
B

$60^{o}$
C

$30^{o}$
D

$37^{o}$

Solution

The cylinder will not topple if $mgsinθ \times \frac{h}{2} < mg cosθ \times r$
$\Rightarrow tan θ < \frac{2 r}{h}$
$\Rightarrow θ_{\max} = \tan^{- 1} \frac{2 \times 10}{20 \sqrt{3}} = \tan^{- 1} (\frac{1}{\sqrt{3}}) = 30^{o}$

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