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  4. A quantity f is given by f = √(hc5/G) where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :

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Q. 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 :

JEE MainJEE Main 2020Physical World, Units and Measurements

Solution:

$\left[h\right]=M^{1}L^{2}T^{-1}$
$\left[C\right]=L^{1}T^{-1}$
$\left[G\right]=M^{-1}L^{3}T^{-2}$
$\left[f\right]=\sqrt{\frac{M^{1}L^{2}T^{-1}\times L^{5}T^{-5}}{M^{-1}L^{3}T^{-2}}}=M^{1}L^{2}T^{-2}$