WBJEE · Physics · Units and Dimensions
If the dimensions of length are expressed as \(\mathrm{G}^{\times} \mathrm{C}^y \mathrm{~h}^{\mathrm{z}}\), where \(\mathrm{G}, \mathrm{C}\) and h are the universal gravitational constant, speed of light and Planck's constant respectively, then
- A \(\mathrm{x}=\frac{1}{2}, \mathrm{y}=\frac{1}{2}\)
- B \(x=\frac{1}{2}, z=\frac{1}{2}\)
- C \(y=\frac{1}{2}, z=\frac{3}{2}\)
- D \(y=-\frac{3}{2}, z=\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(y=-\frac{3}{2}, z=\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\begin{array}{ll}\text { } L=\left[M^{-1} L^3 T^{-2}\right]^x\left[L T^{-1}\right]^y\left[M L^2 T^{-1}\right]^z \\ M^0 L T^0=M^{-x+z} L^{3 x+y+2 z} T^{-2 x-y-2} & \\ -x+z=0 ; \quad 3 x+y+2 z=1 ; \qquad 2 x+y+z=0 \\ x=z ; \quad \qquad 2 z=1 \qquad \qquad \qquad 3x+y=0 \\ \qquad…
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