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 marble are striking the disc? Assume that, the marble strikes the disc normally and rebound downwards with the same speed.

• A

  $2.98 \mathrm{~m} / \mathrm{s}$
• Correct answer
  B

  $0.98 \mathrm{~m} / \mathrm{s}$
• C

  $0.49 \mathrm{~m} / \mathrm{s}$
• D

  $1.96 \mathrm{~m} / \mathrm{s}$

Solution

$F=\frac{\Delta p}{\Delta t}=\frac{\Delta(m n v)}{\Delta t}$
Here, $m=$ mass of one marble $=5 \mathrm{~g}$ $\begin{aligned} \frac{n}{\Delta t} & =\text { number of molecules striking per second } \\ & =10 \\ \therefore M g & =m\left(\frac{n}{\Delta t}\right)|\Delta v|\end{aligned}$ Here, $M=$ mass of disc $\begin{aligned}\left(10 \times 10^{-3}\right)(9.80) & =\left(5 \times 10^{-3}\right)(10) 2 v \\ \text { or } \quad v & =0.98 \mathrm{~m} / \mathrm{s}\end{aligned}$

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