Question

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?

• 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 1

Answer: (A)

I and II only

Answer 2

By sign convention anticlockwise moment (or torque) is taken as positive while clockwise moment (or torque) is taken as negative.

In case I, net torque about its centre is

$\tau = F \times L + F \times L = 2FL$

In case II, net torque about its centre is

$\tau = F \times L + F \times \frac{1}{2} + F \times L = \frac{5}{2}FL$

In case III, net torque about its centre is

$\tau = - F \times L + F \times \frac{L}{2} - F \times \frac{L}{2} + F \times L = 0$