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  • An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle  \thetawith the vertical, the maximum possible value of  \theta is given by

 

 

Option: 1

cot^{-1}3
 


Option: 2

tan^{-1}3


Option: 3

sec^{-1}3

 


Option: 4

cosec^{-1}3


Answers (1)

best_answer

As the insect crawls up, limiting friction friction force decreases and the component of weight along the suface (driving force) will decrease. Let's assume the insect can crawl upto angle \theta before it starts slipping. At that moment the frictional force will be limiting friction force as shown in the figure.

       

         Let m=mass of the insect, r=radius of the bowl, μ= coefficient of friction for limiting condition at point A

          \\ \mathrm{R=m g \cos \theta }\\ \mathrm{Limiting\ friction-}\\ \mathrm{f_{l}=\mu R=\mu mgcos\theta\ ...(1)}\\ \mathrm{For\ equilibrium-}\\ \mathrm{f_{l}=m g \sin \theta \ ...(2)} \\

 From equation (1) and (2)-

\\ \mathrm{m g \cos \theta=\mu mgcos\theta\ }\\ \mathrm{cot\theta=\frac{1}{\mu}=3}\\\\ \mathrm{ \theta=cot^{-1}3}

 ?

Posted by

Ritika Jonwal

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