A sample of oxygen at NTP has volume V and a sample of hydrogen at NTP has the volume 4V Both the gases are mixed. If the speed of sound in hydrogen at NTP is 1270 m/s, that in mixture is

# A sample of oxygen at NTP has volume V and a sample of hydrogen at NTP has the volume 4V Both the gases are mixed. If the speed of sound in hydrogen at NTP is 1270 m/s, that in mixture is

1. A

2. B
635 m/s
3. C
830 m/s
4. D
950 m/s

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### Solution:

${\rho }_{mix}=\frac{{m}_{1}+{m}_{2}}{{v}_{1}+{v}_{2}}$

${\mathrm{\rho }}_{mix}=\frac{20{\mathrm{\rho }}_{\mathrm{H}}\mathrm{V}}{5\mathrm{V}}=4{\mathrm{\rho }}_{\mathrm{H}}$

$\mathrm{V}\propto \sqrt{\frac{1}{\mathrm{\rho }}}⇒\frac{{\mathrm{V}}_{\mathrm{mix}}}{{\mathrm{V}}_{\mathrm{H}}}=\sqrt{\frac{{\mathrm{\rho }}_{\mathrm{H}}}{4{\mathrm{\rho }}_{\mathrm{H}}}}$

${\mathrm{V}}_{\mathrm{mix}}=\frac{1270}{2}=635\mathrm{m}/\mathrm{s}$

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