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) $\operatorname{cosec} \alpha=3$
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Answer:
Correct Answer: 11. (a)
Solution:
- 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
$$ \cot \alpha=\frac{1}{\mu}=3 $$
