Question:
An insect is at the bottom of a hemispherical ditch of radius $1 \mathrm{~m}$. It crawls up the ditch but starts slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is $0.75$, then $\mathrm{h}$ is :
Correct Option: 4,
Solution:
For balancing $m g \sin \theta=f$
$m g \sin \theta=\mu m g \cos \theta$
$\tan \theta=\mu$
$\tan \theta=\frac{3}{4}$
$h=R-R \cos \theta$
$=\mathrm{R}-\mathrm{R}\left(\frac{4}{5}\right)=\frac{\mathrm{R}}{5}$
$\mathrm{h}=\frac{\mathrm{R}}{5}=0.2 \mathrm{~m}$
$\therefore$ correct option is $(4)$
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