Question

A ring of mass can slide over a smooth vertical rod. A light string attached to the ring passing over a smooth fixed pulley at a distance of from the rod is shown in the figure. At the other end of the string, mass is attached, lying over a smooth fixed inclined plane of inclination angle . The ring is held in level with the pulley and released. Determine the velocity of ring (in ) when the string makes an angle with the horizontal. ]

Answer 1

Let is the vertical distance covered by the ring. Then

distance moved by block
Now, from constraint relation
...(ii)
velocity of ring,
velocity of the block at this instant
From work-energy theorem, we get
...(iii)
On solving equations (i) and (ii), we get