The mass of a hydrogen molecule is $3.32 \times 10^{-27}$ kg. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2$ cm$^2$ at an angle of $45^{\circ}$ to the normal, and rebound elastically with a speed of $10^3$ m/s, then the pressure on the wall is nearly:

JEE Main · 2018 · 08 Apr 2018 · Offline · Conservation of Momentum

The mass of a hydrogen molecule is

3.32 \times 1 0^{- 27}

kg. If

1 0^{23}

hydrogen molecules strike, per second, a fixed wall of area

2

^{2}

at an angle of

4 5^{\circ}

to the normal, and rebound elastically with a speed of

1 0^{3}

m/s, then the pressure on the wall is nearly:

Answer: (B)

Each molecule strikes at

4 5^{\circ}

to the normal and rebounds elastically, so only the normal component of its momentum reverses and the change per molecule is

Δ p = 2 m v cos 4 5^{\circ} = 2 m v

. Multiplying by the number arriving each second gives the force,

F = n Δ p = 1 0^{23} \times 2 \times 3.32 \times 1 0^{- 27} \times 1 0^{3}

N, and dividing by the area converts it to pressure,

P = \frac{F}{A} = \frac{1 0 ^{23} \times 3.32 \times 1 0 ^{- 27} \times 1 0 ^{3} \times 2}{2 \times 1 0 ^{- 4}} \approx 2.35 \times 1 0^{3}

N/m

^{2}

JEE Main · 2018 · 08 Apr 2018 · Offline · Single correct option