A uniform rod of mass `m` and length `l` is fixed from Point `A`, which is at a distance `l//4` from one end as shown in the figure. The rod is free to rotate in a vertical plane. The rod is released from the horizontal position.

What is the reaction at the hinge, when kinetic energy of the rod is maximum?

Options

A. `4/7`
B. `5/7mg`
C. `13/7mg`
D. `11/7mg`

Answer

C

Explanation

`KE` of the rod is maximum when it is in the vertical position. From coservation of energy we get

`(mgl)/4=1/2[(ml^(2))/12+(ml^(2))/16]omega^(2)`
`(omega^(2)l)/4=(6g)/7`
`R_(y)=mg+m((6g)/7)`
`=(13mg)/7`