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(C) The pressure exerted by an ideal gas is given by the formula $P = \frac{1}{3} \rho v_{rms}^2$,where $\rho$ is the density and $v_{rms}$ is the roo

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$4:1$

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(C) The pressure exerted by an ideal gas is given by the formula $P = \frac{1}{3} \rho v_{rms}^2$,where $\rho$ is the density and $v_{rms}$ is the root mean square velocity.Since the pressures $P_1$ and $P_2$ are equal,we have $P_1 = P_2$.Thus,$\frac{1}{3} \rho_1 v_{rms,1}^2 = \frac{1}{3} \rho_2 v_{rms,2}^2$.This simplifies to $\rho_1 v_{rms,1}^2 = \rho_2 v_{rms,2}^2$.Rearranging for the ratio of velocities,we get $\frac{v_{rms,1}^2}{v_{rms,2}^2} = \frac{\rho_2}{\rho_1}$.Given the ratio of densities $\rho_1 : \rho_2 = 1 : 16$,we have $\frac{\rho_2}{\rho_1} = \frac{16}{1} = 16$.Taking the square root on both sides,$\frac{v_{rms,1}}{v_{rms,2}} = \sqrt{16} = 4$.Therefore,the ratio of their r.m.s. velocities is $4:1$.

Equal volumes of two gases are kept in different containers having densities in the ratio $1:16$. They exert equal pressures on the walls of their respective containers. Then the ratio of their r.m.s. velocities is

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