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Planck's constant (h), gravitational con...

Planck's constant (h), gravitational constant (G) and the speed of light (c ) are taken as the fundamental quantities in a system. Find the dimensions of length and time in this system.

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To find the dimensions of length (L) and time (T) in a system where Planck's constant (h), gravitational constant (G), and the speed of light (c) are taken as fundamental quantities, we will use dimensional analysis. ### Step-by-Step Solution: 1. **Identify the Dimensions of Given Constants**: - Planck's constant (h): \( [h] = M L^2 T^{-1} \) - Gravitational constant (G): \( [G] = M^{-1} L^3 T^{-2} \) - Speed of light (c): \( [c] = L T^{-1} \) ...
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Knowledge Check

  • The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be:

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

  • The speed of light ( c), gravitational constant (G) and plank's constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be.

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

  • If force, acceleration and time are taken as fundamental quantities, then the dimensions of length will be:

    A
    `FT^(2)`
    B
    `F^(-1)A^(2)T^(-1)`
    C
    `FA^(2)T`
    D
    `AT^(2)`

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    The dimensions of gravitational constant G are :

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    If Planck's constant (h) and speed of light in vacuum (c ) are taken as two fundamental quantites, which on of the following can, in addition, be taken to express length, mass and time in terms of the three chosen fundamental quantities ?

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