An important milestone in the evolution of the universe just after the Big Bang is the Planck time tp, the value of which depends on three funda-mental constants-speed of light in vacuum c, Gravitational constant G and Planck’s constant h. Then, tp ∝

Question

An important milestone in the evolution of the universe just after the Big Bang is the Planck time tp, the value of which depends on three funda-mental constants-speed of light in vacuum c, Gravitational constant G and Planck’s constant h. Then, tp ∝ (A) Ghc5 (B) (c5/Gh) (C)  (Gh/c5) (D)  ((Gh/c5))1/2

Tardigrade Admin · Accepted Answer

[Gh] = [M-1L3T-2][ML2T-1] = [M0L5T-3] [c] = [LT-1] ∴ [(Gh/c5)]1/2 = [T] Hence, tp propto ((Gh/c5))1/2 (∵[tp ] = [T])

Q. An important milestone in the evolution of the universe just after the Big Bang is the Planck time $t_{p}$ , the value of which depends on three funda-mental constants-speed of light in vacuum c, Gravitational constant G and Planck’s constant h. Then, $t_{p} \propto$

$G h c^{5}$

$\frac{c ^{5}}{G h}$

$\frac{G h}{c ^{5}}$

$(\frac{G h}{c ^{5}})^{1/2}$

$[G h] = [M^{- 1} L^{3} T^{- 2}] [M L^{2} T^{- 1}] = [M^{0} L^{5} T^{- 3}]$
$[c] = [L T^{- 1}]$
$∴ [\frac{G h}{c ^{5}}]^{1/2} = [T]$
Hence, $t_{p} \propto (\frac{G h}{c ^{5}})^{1/2} (∵ [t_{p}] = [T])$

Q. An important milestone in the evolution of the universe just after the Big Bang is the Planck time tp​, the value of which depends on three funda-mental constants-speed of light in vacuum c, Gravitational constant G and Planck’s constant h. Then, tp​∝

Ghc5

Ghc5​

c5Gh​

(c5Gh​)1/2