Equal volumes of two gases, having their densities in the ratio of $1: 16$ exert equal pressures on the…

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 $\left(c_1: c_2\right)$ is
  1. 1 : 4
  2. 4 : 1
  3. 8 : 1
  4. 1 : 8

Solution

$\begin{aligned} & P=\frac{1}{3} \rho_1 c_1^2=\frac{1}{3} \rho_2 c_2^2 \\ & \therefore \frac{c_1^2}{c_2^2}=\frac{\rho_2}{\rho_1}=16 \\ & \therefore \frac{c_1}{c_2}=4\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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