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JEE Main20231 Feb 2023Evening ShiftPhysicsUnits and DimensionsActual

If the velocity of light c , universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is:

Options

  1. Ah 1 2 c 1 2 G 1
  2. Bh 1 c 1 G - 1
  3. Ch - 1 2 c 1 2 G 1 2
  4. Dh 1 2 c 1 2 G - 1 2

Correct answer

D. h 1 2 c 1 2 G - 1 2

Step-by-step solution

If E is energy, then E = G m 1 m 2 r E r = G m 1 m 2 Since E = h c λ h c λ r = G m 1 m 2 ⇒ h c L L = G M 2 (both λ and r have dimensions of length) ∴ h c G = M

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