An insect crawls up a hemispherical surface as shown (see the figure) the coefficient of friction between the insect and the surface is $\frac{1}{3}$ . If the line joining the centre of the hemispherical surface to the insect makes an angle $θ$ with the vertical, the maximum possible value of $θ$ is given by

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$\tan^{- 1} (3)$

$\cos^{- 1} (3)$

$\cot^{- 1} (3)$

$\sin^{- 1} (3)$

answer is B.

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Detailed Solution

$N = m g \cos θ$ ...(1)

$μ N = m g \sin θ$ ......... (2)

From (1) and (2) we get

$\cot θ = \frac{1}{μ} = 3 \Rightarrow θ = \cot^{- 1} (3)$

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