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Question

The mass of hydrogen molecule is 3.32×1027 kg. If 1023 hydrogen molecules strike 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. Calculate the pressure exerted on the wall.

A
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B
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C
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Solution

The correct option is A
The molecules strike the wall along AO and rebound along OB such that

AON=BON=45
Because the collision of molecules with the wall is elastic, hence
¯P1=¯P2=p=mv=3.32×1027×103
=3.32×1024Kg ms1.
Now change in momentum normal to the wall per molecule
(Δp)n=¯P2n¯P1n=2pn=2pcos45=2p
Number of collision per sec or collision frequency, f=1023 per sec.
Hence, change in momentum per sec = change in momentum per molecule × collision frequency
or ΔpΔt=(Δp)n×f
According to Newton's second law of motion, force exerted by the molecules on the wall
F=ΔpΔt=(Δp)n×f=2pf=1.414×3.32×1024×1023=0.4695NNow, area of the wall A=2cm2=2×104m2Pressure on the wall,P=FA=0.46952×104=2.347×103N/m2.

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