A thin uniform rigid rod of mass `m` and length `l` is in mechanical equilibrium under the constraints of horizontal and vertical rough surfaces. Then select correct option(s):

Options

A. the net torque of normal reaction about `O` is equal to `(mgl)/2 cos theta`
B. the net torque due to friction about `O` is zero
C. the net torque due to normal reaction is numerically equal to the net torque due to the frictional force about the `CM` of the rod
D. all of the above

Answer

A, B, C, D

Explanation

`N_(1)=mg-f_(2).....(1), N_(2)=f_(1).....(2)`
Now taking moment about `A`
`N_(2)xxlsin theta+f_(2)xxlcos theta=mgl/2xxcos theta......(3)`
Take moment about point `B`
`N_(1)xxIcos theta=mgxxl/2 cos theta+f_(1)xxl sin theta....(4)`
`tau_(0)`(of normals)=
`N_(1)l cos theta+N_(2)xxl sin theta=(mg)/2`
`l cos theta+(mg)/2 cot theta=2mglcos theta//2`
`B,C &D`are easily explain