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 fundamental constants-speed $c$ of light in vacuum, gravitational constant $G$ and Planck’s constant $h$. Then, $t_{P} \propto$
A) $Ghc^{5}$
B) $\frac{c^{5}}{Gh}$
C) $\frac{Gh}{c^{5}}$
D) $\left( \frac{Gh}{c^{5}} \right)^{1/2}$
Explanation
Note carefully that every alterative has $Gh$ and $c^{5}$. $\lbrack Gh\rbrack = \left\lbrack M^{- 1}L^{3}T^{- 2} \right\rbrack\left\lbrack ML^{2}T^{- 1} \right\rbrack = \lbrack M^{0}L^{5}T^{3}\rbrack$ $\lbrack c\rbrack = \lbrack LT^{- 1}\rbrack$ $\therefore\ \ \ \ \ \left( \frac{Gh}{c^{5}} \right)^{1/2} = \lbrack T\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.