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(B) The pressure exerted by an ideal gas is given by the formula $P = \frac{1}{3} \rho c^2$,where $\rho$ is the density and $c$ is the root mean squar

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$4: 1$

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(B) The pressure exerted by an ideal gas is given by the formula $P = \frac{1}{3} \rho c^2$,where $\rho$ is the density and $c$ is the root mean square (rms) speed.Since the pressures are equal,we have $P_1 = P_2$.Therefore,$\frac{1}{3} \rho_1 c_1^2 = \frac{1}{3} \rho_2 c_2^2$.This simplifies to $\frac{c_1^2}{c_2^2} = \frac{\rho_2}{\rho_1}$.Given the ratio of densities $\rho_1 : \rho_2 = 1 : 16$,we have $\frac{\rho_2}{\rho_1} = \frac{16}{1} = 16$.Substituting this into the equation,we get $\frac{c_1^2}{c_2^2} = 16$.Taking the square root on both sides,we find $\frac{c_1}{c_2} = \sqrt{16} = 4$.Thus,the ratio of their rms speeds $(c_1: c_2)$ is $4: 1$.

Equal volumes of two gases,having their densities in the ratio of $1: 16$,exert equal pressures on the walls of two containers. The ratio of their rms speeds $(c_1: c_2)$ is

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