A rod of length 1m is sliding in a corner as shown in. At an instant when the rod makes an angle of 60 degrees with the horizontal plane, the velocity of point A on the rod is 1m/s. The angular velocity of the rod at this instant is

Match 4 correct pairs between List $$I$$ and List $$II$$. No credit will be given for partially correct matching

List $$I$$
(a) Collision of particles
(b) Stability
(C) Satellite motion
(D) Spinning top

List $$II$$
(1) Euler’s equation of motion
(2) Minimum kinetic energy
(3) Minimum potential energy
(4) Impulse-momentum principle
(5) Conservation of moment of momentum

A spring scale indicates a tension $$T$$ in the right hand cable of the pulley system shown in figure below. Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass $$m$$ is