JEE PYQ: Units And Dimensions Question 19
Question 19 - 2019 (09 Jan Shift 2)
Expression for time in terms of $G$ (universal gravitational constant), $h$ (Planck constant) and $c$ (speed of light) is proportional to:
(1) $\sqrt{\frac{hc^5}{G}}$
(2) $\sqrt{\frac{c^3}{Gh}}$
(3) $\sqrt{\frac{Gh}{c^5}}$
(4) $\sqrt{\frac{Gh}{c^3}}$
Show Answer
Answer: (3)
Solution
Let $t \propto G^x h^y c^z$. Comparing dimensions: $x = y = \frac{1}{2}, z = -\frac{5}{2}$. So $t \propto \sqrt{\frac{Gh}{c^5}}$.
BETA
