The molecules of a given mass of a gas have rms velocity of `200 m//s at 27^(@)C and 1.0 xx 10^(5) N//m_(2)` pressure. When the temperature and pressure of the gas are respectively `127^(@)C and 0.05 xx 10^(5) Nm^(-2)`, the rms velocity of its molecules in `ms^(-1)` is

Options

A. `100sqrt(2)`
B. `(400)/(sqrt(3))`
C. `(100sqrt(2))/(3)`
D. `100/3`

Answer

B

Explanation

`v prop sqrt(T)implies (v)/(200)=sqrt((400)/(300)) implies v = (200xx2)/(sqrt(3)) m//s`
`implies v = 400/(sqrt(3)) m//s`.