Question

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

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

Answer 1

Answer: (A)

h = G^xL^yE^z
[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