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The dimensions of gamma in the relation ...

The dimensions of `gamma` in the relation `v = sqrt((gamma p)/(rho))` (where `v` is velocity, `p` is pressure , `rho` is density)

A

Dimensionless

B

`[LT^(-1)]`

C

`[ML^(-1) T^(-2)]`

D

`[ML^(-3)]`

Text Solution

Verified by Experts

The correct Answer is:
A
`V = sqrt((gamma p)/(rho))`
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Knowledge Check

  • 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)]`

  • 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)]`

  • If V = sqrt(gammap)/(rho) , then the dimensions of gamma will be (where p is pressure, rho is density and V is velocity) :

    A
    `M^(0)L^(0)T^(0)`
    B
    `M^(0)L^(0)T^(1)`
    C
    `M^(1) L^(0) T^(0)`
    D
    `M^(0) L^(1) T^(0)`

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