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A stream of glass beads, each with a mass of 15 gram, comes out of a horizontal tube at a rate of 100 per second. The beads fall a height of 5m to a balance pan and bounce back to their original height. How much mass (in kg) must be placed in the other pan of the balance to keep the pointer at zero? $(g = 10 m s^{- 2})$

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answer is 3.

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Detailed Solution

$Δ \bar{p}$ (change in momentum per collision) $= 2 m \sqrt{2 g h} = 2 \times 15 \times 10^{- 3} (10) = 0.3 k g m s^{- 1}$

Then in $Δ {\bar{p}}_{100} (i n 1 second) = 30 k g m s^{- 1}$

Force exerted = 30N
So, weight required =30N. So, mass = 3kg

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