Q146 / 150 · MHT CET 2024 (11 May Shift 2) · Physics
The ratio of the velocity of sound in hydrogen gas $\left(\gamma=\frac{7}{5}\right)$ to that in helium gas $\left(\gamma=\frac{5}{3}\right)$ at the same temperature is
- A$1: 1$
- B$7 ; 3$
- C$21: 25$
- Correct answerD$\sqrt{42}: 5$
Solution
Formula:
$\frac{v_H}{v_{H e}}=\sqrt{\frac{\gamma_H M_{H e}}{\gamma_{H e} M_H}} .$
Given: - $\gamma_H=\frac{7}{5}, \gamma_{H e}=\frac{5}{3}$, - $M_H=2, M_{H e}=4$.
Step 1: Substitute values: $\frac{v_H}{v_{H e}}=\sqrt{\frac{\frac{7}{5} \cdot 4}{\frac{5}{3} \cdot 2}}=\sqrt{\frac{28}{10} \cdot \frac{3}{5}}=\sqrt{\frac{84}{50}}=\frac{\sqrt{42}}{5} .$
Answer: $\frac{\sqrt{42}}{5}$, Option 4.
Given: - $\gamma_H=\frac{7}{5}, \gamma_{H e}=\frac{5}{3}$, - $M_H=2, M_{H e}=4$.
Step 1: Substitute values: $\frac{v_H}{v_{H e}}=\sqrt{\frac{\frac{7}{5} \cdot 4}{\frac{5}{3} \cdot 2}}=\sqrt{\frac{28}{10} \cdot \frac{3}{5}}=\sqrt{\frac{84}{50}}=\frac{\sqrt{42}}{5} .$
Answer: $\frac{\sqrt{42}}{5}$, Option 4.
Hence, the correct answer is option: 'D'.