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Model Paper 10 — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETModel Paper 104 Marks
MCQ
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
    1
  • B
    0
  • C
    -1
  • D
    $\frac{5}{3}$
✓

Answer

B. 0
Explanation:
$\begin{array}{l}
h \propto G^x L^y E^z \\
{\left[M^1 L^2 T^{-1}\right]=\left[M^{-1} L^3 T^{-2}\right]^{x}\left[M^1 L^2 T^{-1}\right]^{y}\left[M^1 L^2 T^{-2}\right]^{z}} \\
{\left[M^1 L^2 T^{-1}\right]=k\left[M^{-1} L^3 T^{-2}\right]^{x}\left[M^1 L^2 T^{-1}\right]^{y}\left[M^1 L^2 T^{-2}\right]^{z}}
\end{array}$
Comparing the powers, we get;
$\begin{array}{l}
1=-x+y+z \ldots \text { (i) } \\
2=3 x+2 y+2 z \ldots \text { (ii) } \\
-1=-2 x-y-2 z \ldots \text { (iii) }
\end{array}$
On solving eqns. (i), (ii) and (iii), we get;
$x=0$

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