A thin circular coin of mass 5 gm and radius 4 3 cm is initially in a horizontal x y -plane. The coin is tossed vertically up ( + z direction) by applying an impulse of π 2 × 10 - 2 N - s at a distance 2 3 cm from its center. The coin spins about its diameter and moves along the + z direction. By the time the coin reaches back to its initial position, it completes n rotations. The value of n is _____. [Give

Step-by-step solution

By impulse - momentum theorem: J = M V C M ⇒   V C M = J M = π 2 100 × 5 1000 = 2 π   m   s - 1 ⇒ Total time of journey = 2 V C M g = 2 g × 2 π ⇒   ∆ t = 2 π 5   s Also, by angular impulse - momentum theorem: J × R 2 = I ω ⇒ J × R 2 = M R 2 4 ω ⇒   ω = J × R 2 M R 2 4 = J M R × 2 = π 2 100 × 2 5 1000 × 4 3 × 1 100 = 150 2 π   rad   s - 1 ⇒ Number