Question

A massless rigid rod of length 'l' suspended vertically from a rigid support at one end has a mass ‘m’ at its mid-point and another identical mass at its free end. The velocity that must be imparted to the lower mass which may just make the rod horizontal is

(1) \(\sqrt{\frac{12}{5}}gl\)

(2) \(\sqrt{2gl}+\sqrt{gl}\)

(3) \(\sqrt{2gl}\)

(4) \(2\sqrt{2gl}\)

Answer 1

 (1) \(\sqrt{\frac{12}{5}}gl\) 

In Fig. shown; A and B are the two masses. The masses will have same angular velocity but different linear velocity.

Using energy conservation principle; Gain in gravitational P.E. = Loss in Kinetic energy