Question 200: Centre of Mass and Rotational Motion

Question

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

Accepted Answer

Considering one hydrogen molecule :
As collision is elastic so, e = 1
Initial momentum,
$\overrightarrow {{P_i}} $ = ${{mv} \over {\sqrt 2 }}$ $\widehat i$ $-$ ${{mv} \over {\sqrt 2 }}$ $\widehat j$
Final  momentum,
$\overrightarrow {{P_f}} $ = ${{mv} \over {\sqrt 2 }}\left( { - \widehat i} ight)$ $-$ ${{mv} \over {\sqrt 2 }}\widehat j$
$	herefore\,\,\,$ Change in momentum for single H molecule,
$\Delta $P = $\overrightarrow {{P_f}} $ $-$ $\overrightarrow {{P_i}} $
= ${{2mv} \over {\sqrt 2 }}\left( { - \widehat i} ight)$
$	herefore\,\,\,$ $\left| {\Delta P} ight|$ = ${{2mv} \over {\sqrt 2 }}$
Now for n hydrogen molecule total momentum changes per second,
= $\left( {{{2mv} \over {\sqrt 2 }}} ight)$ $ 	imes $ n
As we know,
Force (F) = ${{\Delta P} \over {\Delta t}}$
= ${{{2mv} \over {\sqrt 2 }}}$ $ 	imes $ n
$	herefore\,\,\,$ As direction of $\Delta $P is towards negative i so force on the molecule will also be towards negative i direction. From Newton's third law, the reaction force will be on the wall in positive i direction with same magnitude.
$	herefore\,\,\,$ Force on the wall = ${{{2mv} \over {\sqrt 2 }}}$ $ 	imes $ n
$	herefore\,\,\,$ Pressure on the wall,  P = ${F \over A}$
= ${{2mv\,n} \over {\sqrt 2 A}}$
= ${{2 	imes 3.32 	imes {{10}^{ - 27}} 	imes {{10}^3} 	imes {{10}^{23}}} \over {\sqrt 2  	imes2	imes {{10}^{ - 4}}}}$
= 2.35 $ 	imes $ 10
3
N m
$-$2

Answer

2.35 $	imes$ 10
3
N m
-2

Answer

4.70 $	imes$ 10
3
N m
-2

Answer

2.35 $	imes$ 10
2
N m
-2

Answer

4.70 $	imes$ 10
2
N m
-2

Centre of Mass and Rotational Motion

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 o to the normal, and rebound elastically with a speed of 10 3 m/s, then the pressure on the wall is nearly:

Choose the correct answer: