If the velocity of light c , universal gravitational constant G and planck's constant h are chosen as…

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:
  1. h12c12G1
  2. h1c1G-1
  3. h-12c12G12
  4. h12c12G-12

Solution

If E is energy, then

E=Gm1m2r

Er=Gm1m2

Since E=hcλ

hcλr=Gm1m2⇒hcLL=GM2

(both λ and r have dimensions of length)

∴hcG=M

Asked in: JEE Main 2023 (01 Feb Shift 2)

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