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Q.

An insect crawls up a hemispherical surface very slowly [see fig.]. The coefficient of friction
between the insect and the surface is 1/3. If the line joining the centre of the hemi-spherical surface to the insect makes an angle α with the vertical, the max. possible value of c is given by

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a

sec α = 3

b

cot α = 3

c

cosec α = 3

d

None

answer is A.

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Detailed Solution

$\begin{array}{ll} mgsin α = μmgcos α \\ \tan α = μ or \cot α = \frac{1}{μ} = 3 . \end{array}$

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An insect crawls up a hemispherical surface very slowly [see fig.]. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemi-spherical surface to the insect makes an angle α with the vertical, the max. possible value of c is given by