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)

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

In case II, net torque about its centre is
$\tau=F \times L+F \times \frac{L}{2}+F \times L=\frac{5}{2} F L$

In case III, net torque about its centre is
$\tau=-F \times L+F \times \frac{L}{2}-F \times \frac{L}{2}+F \times L=0$