A) \[\sqrt{3/2}\]
B) \[\sqrt{2}\]
C) \[\sqrt{2/3}\]
D) \[\sqrt{3}\]
Correct Answer: B
Solution :
From graph, \[{{T}^{2}}V\]= const. | .....(1) |
As we know that \[T{{V}^{\gamma -1}}=\] const. | |
\[\Rightarrow \,\,\,\,V{{T}^{\frac{1}{\gamma -1}}}=\] cons. | ....(2) |
On comparing (1) and (2), we get | |
\[\Rightarrow \,\,\,\gamma =3/2\] | |
Also \[{{\text{v}}_{rms}}=\sqrt{\frac{3P}{\rho }}\] and \[{{\text{v}}_{sound}}=\sqrt{\frac{P\gamma }{\rho }}\] | |
\[\Rightarrow \,\,\,\frac{{{\text{v}}_{rms}}}{{{\text{v}}_{sound}}}=\sqrt{\frac{3}{\gamma }}=\sqrt{2}\] |
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