Q 11-01-195JEE MainJEE Main 2020 (9 Jan, Shift 1)Easy
A quantity $f$ is given by $f = \sqrt{\dfrac{hc^5}{G}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of:
Answer: (B) energy
$[h] = [\text{ML}^2\text{T}^{-1}]$, $[c] = [\text{LT}^{-1}]$, $[G] = [\text{M}^{-1}\text{L}^3\text{T}^{-2}]$.
$$\left[\frac{hc^5}{G}\right] = \frac{\text{ML}^2\text{T}^{-1}\cdot\text{L}^5\text{T}^{-5}}{\text{M}^{-1}\text{L}^3\text{T}^{-2}} = [\text{M}^2\text{L}^4\text{T}^{-4}]$$
$$[f] = [\text{ML}^2\text{T}^{-2}]$$
This is the dimension of energy.
Solution by Sreeraj P, M.Sc Physics