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6. ⇒ (MHT CET 2021 21th September Evening Shift )

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

A. 16 : 1

B. 1 : 8

C. 4 : 1

D. 1 : 12

Correct Option is (C)

Pressure $P = \frac{1}{3} ρ c^{2} ∴ c = \sqrt{\frac{3 p}{ρ}}$

$∴ \frac{C_{1}}{C_{2}} = \sqrt{\frac{ρ_{2}}{ρ_{1}}} = \sqrt{\frac{16}{1}} = 4$

7. ⇒ (MHT CET 2021 20th September Evening Shift )

A perfect gas of volume 10 litre n compressed isothermally to a volume of 1 litre. The rms speed of the molecules will

A. decrease 5 times

B. remain unchanged

C. increase 5 times

D. increase 10 times

Correct Option is (B)

Since it is compressed isothermally, the temperature remains constant. The rms speed is given by,

$c = \sqrt{\frac{3 R T}{M}}$

Since temperature T remains constant, the rms speed remains unchanged.

⇒Kinetic Theory of Gases