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:
Same $Q$ and same $\Delta U\Rightarrow$ same $W = P\Delta V$. With equal $P$: $\pi r_A^2(16) = \pi r_B^2(9)\Rightarrow\dfrac{r_A}{r_B} = \sqrt{\dfrac{9}{16}} = \dfrac{3}{4}$.