A thin uniform rod of length `l` and masses `m` rotates uniformly with an angularly velocity `omega` in a horizontal plane about a verticle axis passing through one of its ends determine the tension in the rot as a funtion of the distance x from the rotation axis

Options

A. `(1)/(2)momega^(2)x`
B. `(1)/(2)momega^(2)((x^(2))/(L))`
C. `(1)/(2)momega^(2)L(1-(x)/(L))`
D. `(1)/(2)(momega^(2))/(L)(L^(2)-x^(2))`

Answer

D

Explanation

`dm=(m)/(L)dx`
`dF=dmomega^(2)x`
`T=(m)/(L)omega^(2)int_(x)^(L)xdx`
`=(momega^(2))/(L)|(x^(2))/(2)|_(x)^(L)`
`=(1)/(2)(momega^(2))/(L)(L^(2)-x^(2))`