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Question:

The mass of a hydrogen molecule is 3.32 × 10⁻²⁷ kg. If 10²³ hydrogen molecules strike, per second, a fixed wall of area 2 cm² at an angle of 45° to the normal, and rebound elastically with a speed of 10³ m/s, then the pressure on the wall is nearly.

4.70 × 10² N/m²

4.70 × 10³ N/m²

2.35 × 10³ N/m²

2.35 × 10² N/m²

Solution:

Given : u = 10³ m/s
m = 3.32 × 10⁻²⁷ kg
n = 10²³ H₂ molecules per sec.
Change in momentum along y-axis of one H₂ molecule
ΔP = mucos45° - (-mucos45°)
⇒ ΔP = 2mucos45°
Total change in momentum along y-axis of all H₂ molecule in one second
ΔPT = 2nmucos45°
Area of the wall A = 2 cm² = 2 × 10⁻⁴ m²
Net pressure P = ΔPT/A = 2 × 10²³ × 3.32 × 10⁻²⁷ × 10³ × 0.707 / 2 × 10⁻⁴ = 2.35 × 10³ N/m²