An insect crawls up a hemispherical surface very slowly The coefficient of friction between the surface and the insect `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 of `alpha` is given by :

Options

A. `cotalpha=3`
B. `tanalpha=3`
C. `secalpha=3`
D. `cosecalpha=3`

Answer

A

Explanation

Here F is the force of friction `F=mgsin alpha" "…(i)`
Also `F=muN`

where N = normal reaction
But `N=mgcosalpha`
`therefore F=mumgcosalpha" "…(ii)`
From (i) and (ii), `mumgcosalpha=mgsinalpha`
or `cotalpha=(1)/(mu)=(1)/((1)/(3))=3`