Question

An insect crawls up a hemispherical surface. 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. cot $\alpha =3$
• B. tan $\alpha =3$
• C. sec $\alpha =3$
• D. cosc $\alpha =3$

Answer 1

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

For equilibrium., $\mu mg\cos \alpha =mg\sin \alpha$
$\Rightarrow \tan \alpha =\mu =\frac{1}{3}$
$\therefore \cot \alpha =3$