1. Tardigrade
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  4. An insect is at the bottom of a hemispherical ditch of radius 1 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 h is: (g=10 m s-2)

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Q. An insect is at the bottom of a hemispherical ditch of radius $1 m$. 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 $h$ is : $\left(g=10 \,m s^{-2}\right)$

JEE MainJEE Main 2020Laws of Motion

Solution:

image
For balancing $\operatorname{mg} \sin \theta= f$
$mg \sin \theta=\mu mg \cos \theta$
$\tan \theta=\mu$
$\tan \theta=\frac{3}{4}$
image
$h = R - R \cos \theta$
$=R-R\left(\frac{4}{5}\right)=\frac{R}{5}$
$h =\frac{ R }{5}=0.2 m$