Question

A rod of length L is pivoted at one end and is rotated with as uniform angular velocity in a horizontal plane. Let `T_1 and T_2` be the tensions at the points L//4 and 3L//4 away from the pivoted ends.

Answer 1

`dm=(M)/(L)dx`
`df=dmomega^(2)x`
`T=intdF=(Momega^(2))/(L)int_(r )^(L)xdx`
`=(Momega^(2))/(L)|(x^2))/(2)|_(r )^(L)`
`=(1)/(2)(Momega^(2))/(L)(L^(2)-r^(2))`
`=(1)/(2)Momega^(2)L[1-(r )/(L))^(2)]`
`r=(L)/(4),T_(1)=(15)/(32)Momega^(2)L`
`r=(3L)/(4),T_(2)=(7)/(32)Momega^(2)L`