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

Explanation

From FBD friction `f = mg sin alpha`

`N = mg cos alpha(f)/(N) = tan alpha`
For the maximum value of `alpha` the friction limiting friction , so
`mu = tan alpha rArr cos alpha = 3`