Laws of Motion 3 Question 11

11. An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect 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

(2001, 2M)

(a) $\cot \alpha=3$

(b) $\tan \alpha=3$

(c) $\sec \alpha=3$

(d) $\operatorname{cosec} \alpha=3$

Show Answer

Answer:

Correct Answer: 11. (a)

Solution:

  1. Equilibrium of insect gives

$$ \begin{aligned} N & =m g \cos \alpha \\ \mu N & =m g \sin \alpha \end{aligned} $$

From Eqs. (i) and (ii), we get

$$ \cot \alpha=\frac{1}{\mu}=3 $$



NCERT Chapter Video Solution

Dual Pane