The Young's modulus of elasticity Y can be expressed as a function of the gravitational constant G, Planck's constant h, and the speed of light c, in the form Y = cᵅhᵝGᵞ. Which of the following values for α, β, and γ are accurate?

α = 7, β = −1, γ = −2
α = −7, β = −1, γ = −2
α = 7, β = −1, γ = 2
α = −7, β = 1, γ = −2

Correct answer: α = 7, β = −1, γ = −2

Solution

Dimensional analysis is used to express Young's modulus in terms of G, h, and c. By equating the dimensions of both sides, the correct exponents are determined as α = 7, β = −1, and γ = −2.

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