First slide

Second law

Question

A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. If the mass of each marble is 5 g. What will be velocity with which the marbles are striking the disc? Assume that, the marble strikes the disc normally and rebound downwards with the same speed.

Moderate

A

$2.98 {ms}^{- 1}$
B

$0.98 {ms}^{- 1}$
C

$0.49 {ms}^{- 1}$
D

$1.96 {ms}^{- 1}$

Solution

$F = \frac{Δp}{Δt} = \frac{Δ (mnv)}{Δt}$
Here, m = mass of one marble $= 5 g = 5 \times 10^{- 3} kg$
$\frac{n}{∆ t} =$ number of molecules striking per second = 10
$∴$ $Mg = m (\frac{n}{Δt}) | Δv |$ $(∵ |∆ v| = 2 v)$
Here, M = mass of disc
$(10 \times 10^{- 3}) (9.8) = (5 \times 10^{- 3}) (10) 2 v$
or $v = 0.98 {ms}^{- 1}$

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