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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 ex with the vertical, the maximum possible value of α is given by

 

a
cotα=3
b
tanα=3
c
secα=3
d
cosecα=3

detailed solution

Correct option is A

α = angle of reposemgsinα=μmg cosα⇒  tanα=μ=13∴    cotα=3

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