An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre 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

For the insect to be in equilibrium,
`F_("fr") = mg sin alpha`
`mu N = mg sin alpha `
`mu (mg cos alpha ) = mg sin alpha`
cot `alpha = (1)/(mu) = 3`