Question

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the surface and the insect is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with vertical, the maximum possible value of $\alpha$ is given by :

• A. $\cot \alpha =3$
• B. $\tan \alpha =3$
• C. $\sec \alpha =3$
• D. $cosec\alpha =3$

Answer 1

The correct option is A $\cot \alpha =3$

According to fig .

$N=mgcos\alpha$....(I)

frictional force $f=mgsin\alpha$......(II)

from equation (I) and (II),

$tan\alpha =\frac{f}{N}$

Also,

$tan\alpha =\mu$

given that,

$\mu =\frac{1}{3}$

Therefore,

$tan\alpha =\frac{1}{3}$

or

$cot\alpha =3$

Therefore, the correct option will be