0 votes
99 views
in Physics by (98.9k points)
reopened by

Expression for time in terms of GG (universal gravitational constant), hh (Planck constant) and cc (speed of light) is proportional to :

A)\(\sqrt{\dfrac{Gh}{c^3}}\) 

B)\(\sqrt{\dfrac{ch}{G^3}}\) 

C) \(\sqrt{\dfrac{Gh}{c^5}}\) 

D)\(\sqrt{\dfrac{G^5h}{c}}\)

1 Answer

0 votes
by (98.9k points)
selected by
 
Best answer

The correct option is C) \(\sqrt{\dfrac{Gh}{c^5}}\)

Explaination::

\(F = \dfrac{GM^2}{R^2} \Rightarrow G = [M^{-1} L^3 T^{-2}]\) 

\(E = hv \Rightarrow h = [ML^2 T^{-1}]\) 

\(C = [LT^{-1}]\) 

\(t \propto G^x h^y C^z\) 

\([M^0 L^0T^1] = [M^{-x + y} L^{3x + 2y + z} T^{-2x - y - z}]\) 

on comparing the powers of M, L, T

\(-x + y = 0 \Rightarrow x = y\) 

\(3x + 2y + z = 0 \Rightarrow 5x + z = 0\) 

\(-2x - y - z = 1 \Rightarrow 3x+ z = -1\) 

on solving (i) and (ii) \(x = y = \dfrac{1}{2}, z = -\dfrac{5}{2}\) 

\(t \propto \sqrt{\dfrac{Gh}{C^5}}\)

Related questions

Doubtly is an online community for engineering students, offering:

  • Free viva questions PDFs
  • Previous year question papers (PYQs)
  • Academic doubt solutions
  • Expert-guided solutions

Get the pro version for free by logging in!

5.7k questions

5.1k answers

108 comments

554 users

...