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If V=sqrt((gammaP)/(rho)),V =velocity, P...

If `V=sqrt((gammaP)/(rho)),V` =velocity, P= pressure `rho`= density, then dimension of `gamma` will be …….

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

`v=sqrt((gammaP)/(rho))`
`:.gamma=(v^(2)rho)/(P)`
`:.` Dimension of `gamma=((L^(1)T^(-1))^(2)xxM^(1)L^(-3)T^(0))/(M^(1)L^(-1)T^(-2))`
`=(M^(0)L^(2)T^(-2)xxM^(1)L^(-3)T^(0))/(M^(1)L^(-1)T^(-2))`
`=M^(0)L^(0)T^(0)`
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Knowledge Check

  • If energy (E), velocity (V) and force (F) are taken as fundamental quantity, then dimension of mass will be …..

    A
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    B
    `E^(1)v^(-2)F^(0)`
    C
    `E^(1)v^(-1)F^(1)`
    D
    `E^(1)v^(-2)F^(1)`

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