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