JEE PYQ: Units And Dimensions Question 14
Question 14 - 2020 (09 Jan Shift 1)
A quantity $f$ is given by $f = \sqrt{\frac{hc^5}{G}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck’s constant. Dimension of $f$ is that of:
(1) area
(2) energy
(3) momentum
(4) volume
Show Answer
Answer: (2)
Solution
Dimension of $[h] = [ML^2T^{-1}]$, $[c] = [LT^{-1}]$, $[G] = [M^{-1}L^3T^{-2}]$. Hence $\sqrt{\frac{hc^5}{G}} = \sqrt{\frac{[ML^2T^{-1}][L^5T^{-5}]}{[M^{-1}L^3T^{-2}]}} = [ML^2T^{-2}]$ = energy.
BETA
