A rigid rod of length `2 L` 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 ?
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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

(a) By sign convention anticlockwise moment (or torque) is taken as position while clockwise moment (or torque) is taken as negative.
In case `I`, net torque about its centre is.
`tau = F xx L + F xx L = 2FL`
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.
`tau = -F xx L xx (L)/(2) - F xx (L)/(2) + F xx L = 0`.
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