Question:
A quantity $f$ is given by $f=\sqrt{\frac{h c^{5}}{\mathrm{G}}}$ where $\mathrm{c}$ is speed of light
$\mathrm{G}$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of:
Correct Option: , 2
Solution:
(2) Dimension of $[h]=\left[M L^{2} T^{-1}\right]$
$[\mathrm{C}]=\left[L T^{-1}\right]$
$[G]=\left[M^{-1} L^{3} T^{-2}\right]$
Hence dimension of
$\left[\sqrt{\frac{h C^{5}}{G}}\right]=\frac{\left[M L^{2} T^{-1}\right] \cdot\left[L^{5} T^{-5}\right]}{\left[M^{-1} L^{3} T^{-2}\right]}$
$=\left[M L^{2} T^{-2}\right]=$ energy
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