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Planck units: length, time and mass from h, G and c

This type of question, asked 3 times: 1 Feb 2023, 30 Jan 2024, 5 Apr 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    1 Feb 2023

    100
    If the velocity of light cc, universal gravitational constant GG and Planck's constant hh are chosen as fundamental quantities. The dimensions of mass in the new system is:

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  2. Question 2

    30 Jan 2024

    104
    If mass is written as m=kcPG−1/2 h1/2m = kc^{P}G^{- 1/2}{\text{ }h}^{1/2} then the value of PP will be: (Constants have their usual meaning with kk a dimensionless constant)

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  3. Question 3

    5 Apr 2026 S2

    1
    Match List-I with List-II.
    List-IList-II
    (A) Meter (L)(I) hcG\sqrt{\frac{hc}{G}}
    (B) Second (S)(II) Ghc5\sqrt{\frac{Gh}{c^{5}}}
    (C) Kilogram (M)(III) K2L2c3Gh\sqrt{\frac{K^{2}L^{2}c^{3}}{Gh}}
    (D) Kelvin (K)(IV) Ghc3\sqrt{\frac{Gh}{c^{3}}}
    where hh (Planck's constant), GG (gravitational constant) and cc (speed of light in vacuum) are the fundamental units. Choose the correct answer from the options given below:

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