Question

An insect is at the bottom of a hemispherical ditch of radius $1\text{m}$. It crawls up the ditch but start 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 : ($g=10{\text{ms}}^{-2}$)

• A. $0.20\text{m}$
• B. $0.45\text{m}$
• C. $0.60\text{m}$
• D. $0.80\text{m}$

Answer 1

The correct option is A $0.20\text{m}$

FBD of the insect can be shown as below


From FBD, for balancing,
$mg\sin \theta =f=\mu mg\cos \theta$
$\Rightarrow \tan \theta =\mu =0.75=\frac{3}{4}$
From the shown geometry we have,
$h=R-R\cos \theta =R-R\left(\frac{4}{5}\right)=\frac{R}{5}$
$\therefore h=\frac{R}{5}=0.2\text{m}[\because \text{radius},R=1\text{m}]$