The ratio of the velocity of sound in Hydrogen gas `(gamma=7/5)` to that in Helium gas `(gamma=5/3)` at the same temperature is `sqrt(21/3)`.

Options

A. `sqrt((5)/(42))`
B. `sqrt((5)/(21))`
C. `sqrt(42)/(21)`
D. `sqrt(21)/(5)`

Answer

C

Explanation

Velocity of sound in gas , `v=sqrt((gammaP)/(d))`
`therefore (v_(H_2))/(v_(He))=sqrt((gamma_(H_(2))xxd_(He))/(d_(H_(2))xxgamma_(H_(2))))rArr(H_(2))/(He)=sqrt((7xx3xx2)/(5xx5))=[therefore(d_(He))/(d_(H_(2)))=2]`
`(v_(H_(2)))/(v_(He))=sqrt(42)/(5)`