Insects and Mechanics !!!!

Classical Mechanics Level pending

A bug crawls up a hemispherical surface, starting from the bottom up to a point where it starts to slide back towards the starting point. If the angle made by the staring point and the topmost point towards the center is α, and the coefficient of friction is 1/3, then which of the options is true ??

sec α = 3 cot α = 3 cosec α = 3 tan α = 3

Vaibhav Prasad by Vaibhav Prasad , 21, India

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1 solution

Md Zuhair
Aug 26, 2016

Here we will get that The Insect crawls up the Bowl. This is the F B D FBD

Now We can see that m g c o s mgcos α \alpha μ \mu = m g s i n mgsin α \alpha

Hence t a n ( α tan ( \alpha ) = μ \mu

or

c o t ( α ) cot (\alpha) = 1/ μ \mu

Hence

c o t ( α ) cot (\alpha) = 3. (Ans) ..

i hope this is clear enough.

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