JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Units & Measurement

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 ?

Answer: (A)

Solution

Young's modulus has dimensions

[Y] = M L^{- 1} T^{- 2}

.

The dimensions are:

[c] = L T^{- 1}

[h] = M L^{2} T^{- 1}

[G] = M^{- 1} L^{3} T^{- 2}

.

Substituting:

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

Comparing powers:

From the first and third equations:

β - γ = 1

and

α + β + 2 γ = 2

.
Adding these:

α + 2 β + γ = 3

.

Combining with the second equation:

2 β = - 2

, so

β = - 1

.
Then

γ = - 2

and

α = 7

JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Single correct option