An insect crawls up a hemispherical surface very slowly. The Coefficient of friction between the insect and surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angel $α$ with the vertical, the maximum possible value of cot $α$ is given by:

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answer is 3.

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Detailed Solution

For the insect to be in equilibrium,
$\begin{aligned} F_{f :} = mgsin α \\ μN = mgsin α \end{aligned} \begin{array}{l} μ (mgcos α) = mgsin α \\ \cot α = \frac{1}{μ} = 3 \end{array}$

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