Equal volumes of two gases are kept in different containers having densities in the ratio $1: 16$. They…

Equal volumes of two gases are kept in different containers having densities in the ratio $1: 16$. They exert equal pressures on the wall of their respective containers. Then the ratio of their r.m.s. velocities is
  1. 16:1
  2. 1:8
  3. 4:1
  4. 1:12

Solution

Pressure $P=\frac{1}{3} \rho c^2 \therefore c=\sqrt{\frac{3 p}{\rho}}$ $\therefore \frac{c_1}{c_2}=\sqrt{\frac{\rho_2}{\rho_1}}=\sqrt{\frac{16}{1}}=4$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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