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If the velocity of light c, the constant...

If the velocity of light c, the constant of gravitation G and Plank's constant h be chosen as fundamental units, find the dimensions of mass, length and time in terms of c, G and h.

Text Solution

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`sqrt((hc)/(G)) , sqrt((Gh)/(e^3)) , sqrt((Gh)/(e^5))`
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Knowledge Check

  • If C the velocity of light, h planck's onstant and G Gravitational constant are taken as fundamental quantites, then the dimensional formula of mass is

    A
    `h^(-1//2)G^(1//2)C^0`
    B
    `h^(1//2)C^(1//2)G^(-1//2)`
    C
    `h^(-1//2)C^(1//2)G^(-1//2)`
    D
    `h^(-1//2)C^(-1//2)G^(-1//2)`

  • If C the velocity of light,h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is

    A
    `h^(-1//2)G^(1//2)C^(0)`
    B
    `h^(1//2)C^(1//2)G^(-1//2)`
    C
    `h^(-1//2)C^(1//2)G^(-1//2)`
    D
    `h^(-1//2)C^(-1//2)G^(-1//2)`

  • If C the velocity of light, h Planck's onstant and G Gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is

    A
    `h^(-1//2) G^(1//2) C^(0)`
    B
    `h^(1//2) C^(1//2) G^(-1//2)`
    C
    `h^(-1//2) C^(1//2) G^(-1//2)`
    D
    `h^(-1//2) C^(-1//2) G^(-1//2)`

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    If pressure P, velocity of light C and acceleration due to gravity g are chosen as fundamental units, then dimensional formula of mass is

    If pressure P, velocity of light C and acceleration due to gravity g are chosen as fundamental units, then dimensional formula of mass is

    If pressure P, velocity of light C and acceleration due to gravity g are chosen as fundamental units, then dimensional formula of mass is

    If force (F), Velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are

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