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If G,c and h are fundemantal constants of physics then which of the following combination gives us dimensions and time
Asked by mvijithareddy67 | 13 Jan, 2024, 09:26: AM

units of planck's constant ,  h = J s = N m s = (kg m/ s2 ) m  s = kg m2 s-2

Dimension of h = M L2 T-1

units of speed of light  c = m/s

Dimension of c = L T-1

units of universal gravitational constant , G = N m2 kg-2 = kg m/s2 m2 kg-2 = kg-1 m3 s-2

Dimension of G = M-1 L3 T-2

Dimension of [ (hc)/(2G) ]1/2  = [  ( M L2 T-1 ) ( L T-1) / ( M-1L3T-2 ) ]1/2  = [ M ] 1/2  ≠  T

Dimension of  [ (hc) / G2 ]1/2  =  [  ( M L2 T-1 ) ( L T-1) / ( M-1L3T-2 )2 ]1/2  = [ M3 L-3 T2 ] 1/2  ≠  T

Dimension of  [ (h G) / c5 ]1/2 = [  ( M L2 T-1 )  ( M-1L3T-2 ) / ( L T-1)5 ]1/2  =  T

We get dimension of time in [ (h G) / c5 ]1/2

Answered by Thiyagarajan K | 13 Jan, 2024, 10:53: AM
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