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. `cot alpha = 3`
B. `tan alpha = 3`
C. `sec alpha = 3`
D. `cosec alpha = 3`

Answer

A

Explanation

The two force acting on the insert are any and N let as resolve `mg ` into two component
`mg cos alpha` balance `N`
`mg sin alpha `is balance by the frictional force
`N = mg cos alpha`
`f = mg sin alpha`
`But f = mu N = mu mg cos alpha rArr cot alpha = (1)/(mu) rArr cot alpha = 3`