Q 11-11-004NEETNEET 2025Top questionMedium
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 $r_A/r_B$ is equal to
Answer: (B) $\dfrac{3}{4}$
Concept. First law: equal $Q$ and equal $\Delta U$ mean equal work; at constant pressure $W = P\pi r^2x$.
Step 1. Equal work. $r_A^2 \times 16 = r_B^2 \times 9$.
Step 2. Ratio. $\dfrac{r_A}{r_B} = \dfrac34$.
Answer. $\dfrac34$ (Option B).
Solution by Sreeraj P, M.Sc Physics