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According to Laplace's formula, the velo...

According to Laplace's formula, the velocity (V) of sound in a gas is given by `v=sqrt((gammaP)/(rho))`, where P is the pressure and `rho` is the density of the gas. What is the dimensional formula for `gamma` ?

A

`[L^(1)M^(1)T^(1)]`

B

`[L^(-1)M^(0)T^(-1)]`

C

`[L^(-1)M^(0)T^(1)]`

D

`[L^(0)M^(0)T^(0)]`

Text Solution

Verified by Experts

The correct Answer is:
c
`F=6pietarv`
`therefore eta=(F)/(6pirv) therefore [eta]=([F])/([r][v])=[(M^(1)L^(1)T^(-2))/(L^(1)L^(1)T^(-1))]`
`therefore [eta]=[M^(1)L^(-1)T^(-1)]`
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