Question

A uniform rod PQ has mass M; length L. In Fig X-Y plane is vertical. The rod is pivoted at point O. The rod is at rest in a vertical position. It is given a flick and let go. The torque due to weight of rod about point O is

(1) zero

(2) a uniform torque

(3) a non-uniform torque of constant magnitude

(4) a non-uniform torque of constant direction

Answer 1

(4) a non-uniform torque of constant direction

Due to flick imparted to rod the rod rotates in a vertical plane (X-Y plane) about axis through end O. Let θ be the instantaneous angle rod makes with vertical as shown in Fig. Then

w = The weight of rod = - (mg)\(\hat{j}\) 

r = The instantaneous position vector of C.G.

The instantaneous torque about O due to weight of rod is

The magnitude of torque changes with time t because θvaries with time. However direction of \(\tau\) is same at all times