A solid ball of radius 0 . 2 m and mass 1 kg lying at rest on a smooth horizontal surface is given an instantaneous impulse of 50 N s at point P as shown. The number of rotations made by the ball about its diameter before hitting the ground is

Question

A solid ball of radius 0 . 2 m and mass 1 kg lying at rest on a smooth horizontal surface is given an instantaneous impulse of 50 N s at point P as shown. The number of rotations made by the ball about its diameter before hitting the ground is, 625 3 2 π, 2500 3 2 π, 3125 3 2 π, 1250 3 2 π

MARKS App · Accepted Answer

Impulse = change in momentum Along vertical V V = 50 cos ⁡ 30 ° 1 m s = 25 3 m s - 1 Along horizontal V H = 50 cos ⁡ 60 ° 1 m s = 25 m s - 1 Time of flight T = 2 V V g = 5 3 s Also ω = 50 × 0.2 2 5 m r 2 rad s - 1 = 625 rad s - 1 2 π n = ω T ⇒ n = ω T 2 π = 3125 3 2 π

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