Question

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is $\frac{1}{3}$. If the 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

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

Answer 1

The correct option is A

$cot\alpha =3$

For equilibrium, $mgsin\alpha =\mu N=\mu mgcos\alpha \Rightarrow tan\alpha =\mu =\frac{1}{3}\therefore cot\alpha =3$