Question:medium
If the dimensions of length are expressed as \( G^x C^y h^z \), where \( G \), \( C \), and \( h \) are the universal gravitational constant, speed of light, and Planck's constant respectively, then:
If the dimensions of length are expressed as \( G^x C^y h^z \), where \( G \), \( C \), and \( h \) are the universal gravitational constant, speed of light, and Planck's constant respectively, then:
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In problems involving dimensional analysis, express each physical constant in terms of its fundamental dimensions (mass, length, time) and solve for the exponents that satisfy the dimensional consistency of the equation.
Updated On: Nov 28, 2025
- \( x = \frac{1}{2}, y = \frac{1}{2} \)
- \( x = \frac{1}{2}, z = \frac{1}{2} \)
- \( y = \frac{1}{2}, z = \frac{3}{2} \)