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)/5`
D. `sqrt(21)/5`

Answer

C

Explanation

Velocity of sound in gas
`v=sqrt((gammaRT)/M)`
where the symbols have their usual meanings. At the same temperature,
`vpropsqrt(gamma/M)`
`therefore(v_(H_(2)))/(V_(He))=sqrt((gamma_(H_(2)))/(gamma_(He))xx(M_(He))/(M_(H_(2))))=sqrt(7/5xx3/5xx4/2)=(sqrt42)/5`