Question

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

A. `cot alpha =3`
B. `sec alpha =3`
C. `cosalpha =3`
D. None

Answer 1

Correct Answer - a
As is clear from
`F = mg sin alpha`
`R = mg cos alpha`
`(F)/(R) = tan alpha`
`mu = tan alpha = (1)/(3)`
`cot alpha =3`
.