$10^{23}$ molecules of a gas, each having a mass of $3 \times 10^{-27} \mathrm{~kg}$ strike per second per…

$10^{23}$ molecules of a gas, each having a mass of $3 \times 10^{-27} \mathrm{~kg}$ strike per second per sq.cm of a rigid wall at an angle of $60^{\circ}$ with the normal and rebound with a velocity of $500 \mathrm{~m} / \mathrm{s}$. The pressure exerted by the gas molecules on the wall is
  1. $2000 \mathrm{~N} / \mathrm{m}^2$
  2. $500 \mathrm{~N} / \mathrm{m}^2$
  3. $1000 \mathrm{~N} / \mathrm{m}^2$
  4. $1500 \mathrm{~N} / \mathrm{m}^2$

Solution

According to the Newton's second law of motion: $\begin{aligned} & \text { Pressure exerted on the wall }=\frac{\text { Rate of change of mometum } \times \text { no. of molecules }}{\text { Area }} \\ & \Rightarrow P=\frac{\left(2 m V \cos 60^{\circ}\right) \times N}{A}=\frac{2 \times 3 \times 10^{-27} \times 5 \times 10^{-2} \times \cos 60^{\circ} \times 10^{23}}{10^{-4}} \\ & \therefore P=1500 \mathrm{~N} / \mathrm{m}^2\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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