A uniform circular chain of radius `r` and mass `m` rests over a sphere of radius `R` as shown in figure. Friction is absent everywhere and system is in equilibrium . Find the tension in the chain.

Answer

`T=(mg)/(2pi)(r)/(sqrt(R^(2)-r^(2)))`

Explanation

Consider the `dm` mass of chain subtending angle at `d apha` centre

`N cos theta =(dm)/(d alpha). (g)/(T)`
`tan theta =(m)/(2pi).(g)/(T), tan theta =(sqrt(R^(2)-r^(2)))/(r)=(m)/(2pi)(g)/(T)`
`T=(mg)/(2pi)(r)/(sqrt(R^(2)-r^(2))) Ans.`