An insect craws 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 center 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

`N=mg cos alpha`
`f=mumg cos alpha`
`mu mg cos alpha=mg sin alpha`
`mu mg cos alpha=mg sin alpha`
`cot alpha=(1)/(mu)=(1)/(1//3)=3`