The ratio of the velocity of sound in hydrogen `(gamma= (7)/(5))` to that in helium `(gamma= (5)/(3))` at the same temperature is `(rho_1:rho_2=1:2)`

Options

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

Answer

C

Explanation

Velocity of sound in a gas
`V = sqrt((gammaP)/(density))` where `gamma = (C_(P))/(C_(V))`
`therefore` (Velocity in hydrogen `v_(1)`)/(Velocity in Helium `v_(2)`) = `sqrt((gamma_(1))/(d_(1)) xx (d_(2))/(gamma_(2))`
`therefore v_(1)/(v_(2)) = sqrt((7xx3xx2)/(5xx5))` as, `(d_(2))/(d_(1)) = 2` or `(v_(1))/(v_(2)) = sqrt(42)/(5)`