A rigid rod of length 2L is acted upon by some forces. All forces labelled F have the same magnitude. Which cases have a non-zero net torque acting on the rod about its centre?

Options

A. I and II only
B. II and III only
C. I and III only
D. The net torque is zero in all cases

Answer

A

Explanation

By sign convention anticlockwise moment (or torque) is taken as positive while clock wise moment(or torque) is taken as negative .
In case I , net torque about its centre is
`tau = F xx L + F xx L = 2 FL`

In case II , net torque about its centre is
`tau = F xx L + F xx (L)/(2) + F xx L = (5)/(2) FL`

In case III , net torque about its centre is
`t=- F xx L + F xx (L)/(2)- F xx (L)/(2) + F xx L = 0`