First slide

Angle of repose

Question

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is $(g = 10 {ms}^{- 2})$ .

Moderate

A

0.80 m
B

0.60 m
C

0.45 m
D

0.20 m

Solution

For balancing $mgsin θ = f$
$mg \sin θ = μ mgcos θ$

$\tan θ = μ \tan θ = \frac{3}{4} h = R - Rcos θ$

$\begin{array}{l} = R - R (\frac{4}{5}) = \frac{R}{5} \\ h = \frac{R}{5} = 0 .2 m \end{array}$

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