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Q.

Young’s modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G, Planck’s constant h and the speed of light c, $Y = c^{α} h^{β} G^{γ}$ . Which of the following is the correct option?

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a

$α = - 7, β = - 1, γ = - 2$

b

$α = 7, β = - 1, γ = - 2$

c

$α = - 7, β = 1, γ = - 2$

d

$α = 7, β = - 1, γ = 2$

answer is A.

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Detailed Solution

Y has dimension of strong i.e ${ML}^{- 1} T^{- 2}$
$\begin{array}{l} {ML}^{- 1} T^{- 2} = C^{α} h^{β} G^{γ} = {({LT}^{- 1})}^{α} {({ML}^{2} T^{- 1})}^{β} {({ML}^{3} T^{- 2})}^{γ} \\ {ML}^{- 1} T^{- 2} = M^{β - γ} L^{α + 2 β + 3 γ} T^{- α - β - 2 γ} \\ β - γ = 1, α + 2 β + 3 γ = - 1 and - α - β - 2 γ = - 2 \end{array}$
Solving the above we will set $α = 7, β = - 1, and γ = - 2$

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Young’s modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G, Planck’s constant h and the speed of light c, Y=cαhβGγ . Which of the following is the correct option?