Q 11-12-158JEE MainJEE Main 2018 (8 Apr)Medium
The mass of a hydrogen molecule is $3.32\times10^{-27}$ kg. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2\ \text{cm}^2$ at an angle of $45^\circ$ to the normal, and rebound elastically with a speed of $10^3\ \text{m s}^{-1}$, then the pressure on the wall is nearly:
Answer: (B) $2.35\times10^3\ \text{N m}^{-2}$
Only the normal component of momentum reverses. Change per molecule:
$$\Delta p = 2mv\cos45^\circ = 2\times3.32\times10^{-27}\times10^3\times0.707 = 4.69\times10^{-24}\ \text{kg m s}^{-1}$$
Force $=\Delta p\times(\text{molecules per second}) = 4.69\times10^{-24}\times10^{23} = 0.469$ N.
$$P = \frac{0.469}{2\times10^{-4}} \approx 2.35\times10^3\ \text{N m}^{-2}$$
Solution by Sreeraj P, M.Sc Physics