An insect crawls up a hemispherical surface very slowly (see figure). coefficient of friction betwee

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4-1.Newton's Laws of Motion

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An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha $ with the vertical, the maximum possible value $\alpha $ is given by

A

$cot\,\alpha \, = \,3$

B

$tan \,\alpha \, = \,3$

C

$sec\,\alpha \, = \,3$

D

$cosec \,\alpha \, = \,3$

Solution

$\mu R=m g \sin \alpha$

or $\mu \mathrm{mg}$ cos $\alpha=\mathrm{mg} \sin \alpha$

$\cot \alpha=\frac{1}{\mu}=3$

Standard 11

Physics

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