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  4. Energy (E) , angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant (h) is

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Q. Energy $\left(E\right)$ , angular momentum $\left(L\right)$ and universal gravitational constant $\left(G\right)$ are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant $\left(h\right)$ is

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

h = GxLyEz
[M1 L2T-1] = [M-1 L3T-2] x [M1 L2T-1]y [M1 L2T-2]z
Comparing the power, we get
1 = - x + y + z ... (i)
2 = 3x + 2y + 2z ... (ii)
-1 = - 2x - y - 2z ... (iii)
On solving Eq. (i), (ii) and (iii), we get x = 0