A chain of mass 'm' and radius 'r' is placed onto a cone of semi vertical angle `theta`. Cone rotated with angular velocity `omega`. Find the tension in the chain if it does not slide on the cone.

Answer

`(M)/(2pi)(omega^(2)R+g cot theta)`

Explanation

From F.B.D of chain element
`N sin theta = Delta mg = lamda R (2 alpha)g`…(i)
`2T sin alpha - N cos theta = Delta m omega^(2) R = lamda R (2 alpha)omega^(2) R` ….(ii)
for small `alpha, sin alpha = alpha`
From (i) and (ii)
`2 T alpha - (lamda R(2 alpha)g)/(sin theta) xx cos theta = lamda R(2 alpha) omega^(2)R`
`rArr 2 T alpha = lamda R(2 alpha) omega^(2) R + lamda R (2 alpha) g cot theta`
`rArr T = lamda omega^(2) R^(2) + lamda R cot theta`
`=lamda R [omega^(2) R + g cot theta]`
`= (MR)/(2 pi)[omega^(2) R + g cot theta]`