Young's modulus of elasticity is expressed in terms of three derived quantities, namely, the gravitational constant , Planck's constant and the speed of light , as Which of the following is the correct option? [2023]

Question

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 $c$ , as $Y = c^{α} h^{β} G^{γ} .$ Which of the following is the correct option? [2023]

Smart Achievers · Accepted Answer

(1)

$Given, Y = c^{α} h^{β} G^{γ}$

$M L^{- 1} T^{- 2} = {(L T^{- 1})}^{α} {(M L^{2} T^{- 1})}^{β} {(M^{- 1} L^{3} T^{- 2})}^{γ}$

Equating powers

$1 = β - γ ...(i)$

$- 1 = α + 2 β + 3 γ ...(ii)$

$- 2 = - α - β - 2 γ ...(iii)$

$- 3 = β + γ ...(iv)$

$(By adding eq. (ii) & (iii))$

$Now by adding eq. (i) & (iv) we get,$

$- 2 = 2 β$

$∴$ $β = - 1, γ = - 2$

$- 1 = α - 2 - 6$ $∴$ $α = 7$

Solution

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 $c$ , as $Y = c^{α} h^{β} G^{γ} .$ Which of the following is the correct option [2023]

1 $α = 7, β = - 1, γ = - 2$

2 $α = - 7, β = - 1, γ = - 2$

3 $α = 7, β = - 1, γ = 2$

4 $α = - 7, β = 1, γ = - 2$

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Solution

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, as Y=cαhβGγ. Which of the following is the correct option [2023]

1 α=7, β=-1, γ=-2

2 α=-7, β=-1, γ=-2

3 α=7, β=-1, γ=2

4 α=-7, β=1, γ=-2