Q126 / 180 · NEET 2025 · Physics

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$, respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas $A$ and $B$ are displaced by 16 cm and 9 cm , respectively. If the change in their internal energy is the same, then the ratio $\frac{r_A}{r_B}$ is equal to

  • A
    $\frac{4}{3}$
  • Correct answer
    B
    $\frac{3}{4}$
  • C
    $\frac{2}{\sqrt{3}}$
  • D
    $\frac{\sqrt{3}}{2}$

Solution

According to question Pressure is constant $P_A=P_B$ $\begin{aligned} & \mathrm{Q}_{\mathrm{A}}=\mathrm{Q}_{\mathrm{B}} \\ & \Delta \mathrm{U}_{\mathrm{A}}=\mathrm{U}_{\mathrm{B}} \end{aligned}$ So according to I law $\begin{aligned} & \mathrm{Q}=\Delta \mathrm{U}+\mathrm{w} \\ & \mathrm{w}_1=\mathrm{W}_2 \\ & \mathrm{P}_1 \Delta \mathrm{~V}_1=\mathrm{P}_2 \Delta \mathrm{~V}_2 \\ & \left(\pi \mathrm{r}_{\mathrm{A}}^2\right) \mathrm{x}_{\mathrm{B}}=\left(\pi \mathrm{r}_{\mathrm{B}}^2\right) \mathrm{x}_{\mathrm{A}} \\ & \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=\sqrt{\frac{\mathrm{x}_{\mathrm{B}}}{\mathrm{x}_{\mathrm{A}}}}=\sqrt{\frac{9}{16}}=\frac{3}{4} \end{aligned}$

Hence, the correct answer is option: 'B'.

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