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If V = sqrt(gammap)/(rho), then the dime...

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)`

Text Solution

Verified by Experts

The correct Answer is:
A
`gamma = v^(2) (rho)/(p)`
`[gamma] = M^(0)L^(0)T^(0)`
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Knowledge Check

  • 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)]`

  • 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)]`

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