Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of…

Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to:
  1. Ghc3
  2. hc5G
  3. Ghc5
  4. c3Gh

Solution

t=Gα. hβ cr

T=M-1L3T-2αML2T-1βLT-1γ

=M-α+βL3α+2β+γ T-2α-β-γ

- α+β=0

3α+2β+γ=0

-2α-β-γ=1

α=12;β=12;γ=-52

Asked in: JEE Main 2019 (09 Jan Shift 2)

Practice more Units and Dimensions questions on Aicharya