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 three forces acting on the insect are mg, N and friction f. Let us resolve mg into two components: `m g cos alpha` balance N
`m g sin alpha` is balanced by the frictional force
`N=m g cos alpha f =m g sin alpha` but `f=muN =mu m g cos alpha`
`rarr cot alpha=1 / mu rarr cot alpha =3`