Planck's constant ( h ) , speed of light in a vacuum ( c ) and Newton's gravitational constant ( G ) are…

Planck's constant (h), speed of light in a vacuum ( c ) and Newton's gravitational constant ( G ) are three fundamental constants. Which of the following combinations of these has the dimension of length?
  1. hGc32
  2. hGc52
  3. hcG
  4. cG⁡ ⁡ h⁡ 3 2

Solution

L ∝hacbGc
L1=M1L2T-1aLT-1bM-1L3T-2c
Solving,
a=12, c=12, b=-32
⇒L=hGc32

Asked in: NEET 2016 (Phase 2)

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