Question

The coefficient of friction between a hemispherical bowl and an insect is$\sqrt{0.44}$ and the radius of the bowl is $0.6m$. The maximum height to which an insect can crawl in the bowl will be

• A. 0.4 m
• B. 0.2 m
• C. 0.3 m
• D. 0.1 m

Answer 1

Answer: (D)

0.1 m

The problem is same as a block sliding on an inclined plane where friction is there.
$mg\sin \theta =\mu mg\cos \theta$
$\Rightarrow \tan \theta =\mu$
$\cos \theta =\frac{1}{\sqrt{1+{\tan }^2\theta }}=\frac{1}{\sqrt{1+{\mu }^2}}$
$h=r[1-\frac{1}{\sqrt{{\mu }^2+1}}]$
$=0.6\times [1-\frac{1}{\sqrt{1+0.44}}]=0.1m$