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
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
\(\gamma\) = Young's Modulus
\(c\) = speed of Light
\(h\) = Plank's Constant
\(G\) = gravitational Constant
Updated On: Sep 26, 2024
- α=7, β=-1, γ=-2
- α=1, β=1, γ=2
- α=1, β=1, γ=-2
- α=-1, β=0, γ=2
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The Correct Option is A
Solution and Explanation
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 \((2)-(3)\)
\(\beta+\gamma=-3\)
\(\beta-\gamma=1\)
\(2\beta=-2\)
\(\beta=-1\)
\(\gamma=-2\)
\(\alpha=2-\beta-2\gamma\)
\(=2+1-2(-2)\)
\(=3+4=7\)
\(Y=C^\alpha h^\beta G^\gamma\)
\(=[LT^{-1}]^\alpha[M^1L^2T^{-1}]^{\beta}[\frac{MLT^{-2}}{M^2}]^{\gamma}\)
\(=[LT^{-1}]^\alpha[M^1L^2T^{-1}]^{\beta}\,[M^{-1}L^3T^{-2}]^{-\gamma}\)
\(\beta-\gamma=1\,\,\,\,\,.....(1)\)
\(\alpha+2\beta+3\gamma=-1\,\,\,\,\,\,\,......(2)\)
\(\alpha+\beta+2\gamma=2\,\,\,\,\,\,\,......(3)\)
eq \((2)-(3)\)
\(\beta+\gamma=-3\)
\(\beta-\gamma=1\)
\(2\beta=-2\)
\(\beta=-1\)
\(\gamma=-2\)
\(\alpha=2-\beta-2\gamma\)
\(=2+1-2(-2)\)
\(=3+4=7\)
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Concepts Used:
Young’s Double Slit Experiment
- Considering two waves interfering at point P, having different distances. Consider a monochromatic light source ‘S’ kept at a relevant distance from two slits namely S1 and S2. S is at equal distance from S1 and S2. SO, we can assume that S1 and S2 are two coherent sources derived from S.
- The light passes through these slits and falls on the screen that is kept at the distance D from both the slits S1 and S2. It is considered that d is the separation between both the slits. The S1 is opened, S2 is closed and the screen opposite to the S1 is closed, but the screen opposite to S2 is illuminating.
- Thus, an interference pattern takes place when both the slits S1 and S2 are open. When the slit separation ‘d ‘and the screen distance D are kept unchanged, to reach point P the light waves from slits S1 and S2 must travel at different distances. It implies that there is a path difference in the Young double-slit experiment between the two slits S1 and S2.
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