Question

The 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

• A. Zero
• B. $-1$
• C. $\frac{5}{3}$
• D. $1$

Answer 1

The correct option is A Zero

$h=G^x{L}^y{E}^z$
$\left[M^1{L}^2{T}^{-1}\right]={\left[M^{-1}{L}^3{T}^{-2}\right]}^x{\left[M^1{L}^2{T}^{-1}\right]}^y{\left[M^1{L}^2{T}^{-2}\right]}^z$
Comparing the power, we get
$1=-x+y+z$ ...(i)
$2=3x+2y+2z$ ...(ii)
$-1=-2x-y-2z$ ...(iii)
On solving equations (i), (ii) and (iii), we get
$x=0$