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An insect craws up a hemispherical surfa...

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

(a)`cot alpha =3`

B

`tan alpha =3`

C

`sec alpha =3`

D

`cosec alpha =3`

Text Solution

Verified by Experts

The correct Answer is:
a
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`
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