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if the velocity of light c, the constant of gravitation G and plank,s constant h be chosen os fundamentad units , find the dimensions of mass , length and time in terms of c , G and h.

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If the velocity of light c, the constant of gravitation G and Planck's constant h be chosen as fundamental units, find the value of a gram, a centimeter and a second in terms of new units of mass, length and time respectively. Given c = 3xx10^(10) cm s^(-1), G = 6.67xx10^(-8) dyne cm ^2 g^(-2), h = 6.6xx10^(-27) erg sec.

If the velocity of light c, the gravitational constant G and Planck constant h are chosen as the fundamental units, find the dimensions of length , mass, and time in the new system.

Knowledge Check

  • If the velocity of light (c) , gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is

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

  • If the velocity of light c, gravitational constant G and Planck's constant h be taken as fundamental units the dimension of mass in the new system will be-

    A
    `c^(1//2)h^(1//2)G^(1//2)`
    B
    `c^(1//2)h^(1//2)G^(-1//2)`
    C
    `c^(-3//2)h^(1//2)G^(1//2)`
    D
    `c^(-5//2)h^(1//2)G^(1//2)`

  • If velocity of light c, planck's constant h and gravitational constnat G are taken as fundamental quantities then the dimensions of the length will be

    A
    `sqrt((ch)/(G))`
    B
    `sqrt((hG)/(c^(5)))`
    C
    `sqrt((hG)/(c^(3)))`
    D
    `sqrt((hc^(3))/(G))`

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    If velocity of light c, Planck's constant G are taken as fundamental quantites, then express mass, length and time in terms of dimensions of these quantites.

    If the constant of gravitation (G) , Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimension of the radius of gyration is

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