Insect in a bowl

Classical Mechanics Level 2

There is a hemispherical bowl with centre O on a table inside which, there is an insect. The bug (which is quite desperate to get out) starts climbing the wall of the vessel. If the coefficient of friction between the surface of the bowl and that of the insect is $\frac{1}{3}$ , then the maximum inclination $\theta$ of OB with the vertical is given by-

\theta = \cot ^{ -1 }{ 3 }

\theta = \cos ^{ -1 }{ 3 }

\theta = \sin ^{ -1 }{ 3 }

\theta = \tan ^{ -1 }{ 3 }

4 solutions

Rishav Koirala
Apr 2, 2014

The frictional force acts tangentially to the surface of the vessel at B. $mg$ $sin (\theta)$ = $\mu$ $mg$ $\cos (\theta)$ , where $\mu$ is the coefficient of friction , $\frac {1}{3}$ . This equation gives $\mu$ = $\frac {1}{3}$ = $\tan (\theta)$ . Then, $\cot (\theta)$ $= 3$

same approach

kaivalya swami - 7 years, 2 months ago

angle of tan = coeff. of friction

shuvam jaiswal - 7 years ago

freak!!!!!!!!!.......... i just thought mgsin@=Umgcos@ but i thought it wud be just one sine component.............. :(

Archit Murkunde - 7 years, 1 month ago

right way..

Apoorv Lokhande - 7 years ago

Apoorv Lokhande
May 15, 2014

It's a question from IITJEE-2001, asked for 2 marks..!! cool..!

Aashish Kafle
Apr 21, 2014

we know\mu =tan \theta. as \theta is angle of repose.So \theta=\cot ^{-1 }{3 } .

Jaivir Singh
Apr 18, 2014

tan ( angle ) = coefficient of friction

Insect in a bowl

4 solutions

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