Q.
An insect crawls up a hemispherical surface very slowly, 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) $\cot\alpha = 3$
B) $\sec\alpha = 3$
C) $cosec\ \alpha = 3$
D) None of these
Explanation
(a) As is clear from figure
[image:5_image208.jpeg]
$F = mg\sin\alpha$
$R = mg\cos\alpha$
$\frac{F}{R} = \tan\alpha$
$ie\ \ \mu = \tan\alpha = \frac{1}{3}$
$\therefore\ \cot{a = 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.