Question

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:

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

Answer 1

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

From FBD

$N=mgcos\alpha ,f=mgsin\alpha$

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

$\mu =tan\alpha$

$cot\alpha =3$