Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) isproportional to:

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Accepted Answer

Correct answer: C. (c) Let t ∝G^xh^yC^z Dimensions of G= [M^-1L^3T^-2 ] h= [ ML^2T^-1 ] and C= [ LT^-1 ] [T ]= [M^-1L^3T^-2 ]^x [ ML^2T^-1 ]^y [ LT^-1 ]^z [M^0L^0T^1 ]= [M^-x+yL^3x+2y+zT^-2x-y-z ] By comparing the powers of M, L, T both the sides -x+y=0 ⇒x=y 3x+2y+z=0 ⇒5x+z=0 … .(i) -2x-y-z=1 ⇒3x+z=-1 … . . ( ii ) Solving eqns. (i ) and ( ii ) , x=y= 12 ,z=- 52 ∴t ∝ Ghc^5

$Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) isproportional to:$

Solution

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