Question

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, $t_p ∝$

• A. $Ghc^5$
• B. $\frac{c^{5}}{Gh}$
• C. $ \frac{Gh}{c^{5}}$
• D. $ \left(\frac{Gh}{c^{5}}\right)^{1/2}\quad$

Answer 1

Answer: (D)

$\left[Gh\right] = \left[M^{-1}L^{3}T^{-2}\right]\left[ML^{2}T^{-1}\right] = \left[M^{0}L^{5}T^{-3}\right]$
$\left[c\right] = \left[LT^{-1}\right]$
$\therefore \left[\frac{Gh}{c^{5}}\right]^{1/2} = \left[T\right]$
Hence, $t_{p} \propto \left(\frac{Gh}{c^{5}}\right)^{1/2}\quad\left(\because\left[t_{p} \right] = \left[T\right]\right)$