First slide

Static friction

Question

An insect crawling up a fixed hemispherical bowl of radius .R. If the coefficient of friction is $\frac{1}{3},$ then the insect can only crawl upto a height of

Moderate

A

0.051 R
B

0.51 R
C

0.0051 R
D

0.95 R

Solution

See fig.
The insect will crawl up the bowl till the component of its weight down the plane just equals the force of limiting friction
$\begin{array}{l} F = Wsin α and N = Wcos α \\ μ = \tan α = F / N = 1 / 3 \end{array}$
$But \tan (\frac{π}{2} - α) = \cot α = \frac{x}{\sqrt{(R^{2} - x^{2})}}$
$so that X = 3 / \sqrt{10} = 0 \cdot 949 R$
$Now h = R - x = 0 \cdot 051 R .$

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