An insect crawls up a hemispherical surface very slowly. 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 a with the vertical, the maximum possible value of `alpha` so that the insect does not slip is given by

Options

A. `cotalpha=3`
B. `secalpha=3`
C. `cosecalpha3`
D. `cosalpha=3`

Answer

A

Explanation

The insect crawls up the bowl upto a certain height h only till the component of its weight along the bowl is balanced by limiting frictional force.
Force limiting condition at point A
`R- mg cos alpha " "...(i)`
`F_(1)= mg sin alpha " "...(ii)`
Dividing eq. (ii) by (i)
`tan alpha=(1)/(cot alpha)=(F_(1))/(R)= mu [ As F_(1)=muR]`
`rArr tan alpha= mu =(1)/(3) [ :. mu=(1)/(3)` (given)]