JEE Advanced2023PhysicsUnits and DimensionsActual
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?
Options
- Aα = 7 ,   β = - 1 ,   γ = – 2
- Bα = – 7 ,   β = – 1 ,   γ = – 2
- Cα = 7 ,   β = – 1 ,   γ = 2
- Dα = – 7 ,   β = 1 ,   γ = – 2
Correct answer
A. α = 7 ,   β = - 1 ,   γ = – 2
Step-by-step solution
Dimensions of Young's modulus: M 1 L – 1 T   – 2 Dimensions of velocity of light: M 0 L 1 T – 1 Dimensions of Planck's constant:   M 1 L 2   T – 1 Dimensions of Gravitational constant: M – 1 L 3 T – 2 Now, as given in the question Y = c α h β G γ ⇒ M 1 L – 1 T   – 2 = M 0 L 1 T – 1 α   M 1 L 2   T – 1 β M – 1 L 3 T – 2 γ Comparing exponent of the M, L & T both sides, we g