Question

An insect crawls up a hemispherical surface very slowly as shown in figure. The coefficient of friction between the insect and the surface is $\frac{1}{3}$. 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

Answer 1

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

$mgsin\alpha =\mu mgcos\alpha \therefore tan\alpha =\mu$
or $cot\alpha =$$\frac{1}{\mu }$$=3$