Units & Dimensions

JEE Main level, single correct, medium

118 of 149

Question 118 of 149

A quantity ff is given by f=hc5Gf=\sqrt{\dfrac{h{c}^{5}}{G}} where cc is speed of light, GG univasal gravitational constant and hh is the Planck’s constant. Dimension of ff is that of:

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Answer: (B) energy

[hc]=[MLT−23]\left[hc\right]=\left[MLT{}^{-2}3\right]
[c]=[LT−1]\left[c\right]=\left[L{T}^{-1}\right]
[G]=[M−1L3T−2]\left[G\right]=\left[{M}^{-1}{L}^{3}{T}^{-2}\right]
Substituting the dimensional formulas in the given formula,
[f]=[ML2T−2]\left[f\right]=\left[M{L}^{2}{T}^{-2}\right]

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