Q54 / 57 · KVPY 2019 (SA) · Physics

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
 

  • Correct answer
    A
    0.4 N
     
  • B
    0.8 N
     
  • C
    1.2 N
     
  • D
    1.6 N

Solution

 Force = Rate of change of momentum

Figure

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
=pf-pi=0-mv

=-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

Hence, the correct answer is option: 'A'.

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