In an hour-glass approximately 100 grains of sand fall per second (starting from rest); and it takes 2   s for each sand particle to reach the bottom of the hour-glass. If the average mass of each sand particle is 0 . 2   g , then the average force exerted by the falling sand on the bottom of the hour-glass is close to

Step-by-step solution

Force = Rate of change of momentum Velocity with which a sand particle strikes the bottom of hour-glass, v = u + g t ⇒ v = 0 + 10 × 2 = 20 ms - 1 Change in momentum of particle = p f - p i = 0 - m v = - 0 . 2 × 10 - 3 × 20 Momentum imparted to base by the particle = 4 × 10 - 3 kg · ms - 1 Total change of momentum imparted per second by all 100 particles = 4 × 10 - 8 kg · ms - 1 × 100 s - 1 = 0 . 4 kg · ms - 1 So, force on bottom = 0 . 4 N