Question

An insect crawls up a hemispherical surface very slowly (see the figure-$3.114$ ). 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. $\text{cosec} \alpha=3$

Answer 1

Answer: (A)

For equilibrium of insect we use
$m g \sin \alpha=f$
$m g \sin \alpha=\mu N=\mu m g \cos \alpha$
$\tan \alpha=\mu=\frac{1}{3}$
$\cot \alpha=3$