Question

Find the α, β, γ in the Y = \(C^\alpha h^\beta G^\gamma,\,\,\) 
\(\gamma\) = Young's Modulus
 \(c\) = speed of Light
 \(h\) = Plank's Constant
 \(G\) = gravitational Constant

• A. α=7, β=-1, γ=-2
• B. α=1, β=1, γ=2
• C. α=1, β=1, γ=-2
• D. α=-1, β=0, γ=2

Answer 1

The Correct Option is A

The correct option is (A)
\(Y=C^\alpha h^\beta G^\gamma\)
\(=[LT^{-1}]^\alpha[M^1L^2T^{-1}]^{\beta}[\frac{MLT^{-2}}{M^2}]^{\gamma}\)
\(=[LT^{-1}]^\alpha[M^1L^2T^{-1}]^{\beta}\,[M^{-1}L^3T^{-2}]^{-\gamma}\)
\(\beta-\gamma=1\,\,\,\,\,.....(1)\)
\(\alpha+2\beta+3\gamma=-1\,\,\,\,\,\,\,......(2)\)
\(\alpha+\beta+2\gamma=2\,\,\,\,\,\,\,......(3)\)
eq \((2)-(3)\)
\(\beta+\gamma=-3\)
\(\beta-\gamma=1\)
\(2\beta=-2\)
\(\beta=-1\)
\(\gamma=-2\)
\(\alpha=2-\beta-2\gamma\)
\(=2+1-2(-2)\)
\(=3+4=7\)