^Insect crawling in a hemisphere

^Insect crawling in a hemisphere

Consider an insect crawling up a rough hemisphere. As the insect crawl up the force pulling it down the

hemisphere i.e. mgsinθ increases where as normal

reaction N = mgcosθ & thus limiting friction on it decreases. Let at a height h, mgsinθ is just balanced by limiting friction.

After this height insect tends to slip back. Thus at maximum height reached by the insect.

mgsinθ = msmgsinθ  or  = tanθ,


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