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. `100 sqrt2`
B. `(400)/(sqrt3)`
C. `(100 sqrt2)/(3)`
D. `(100)/(3)`

Explanation

`(v_(2))/(v_(1)) = sqrt((T_(2))/(T_(1))) = sqrt((273 + 127)/(273 + 27)) = (2)/(sqrt3)`
`(v_(2))/(200) = (2)/(sqrt(3)) implies v_(2) = (400)/(sqrt(3)) m//s`