1Which of these has the same dimensions as Young's modulus?
Young's modulus and strain energy density both have the dimensions [M L⁻¹ T⁻²].
Properties of matterClass 11, Mechanical Properties of Solids
Dimensional formula of Young's modulus
[M L-1 T-2]
Stress divided by strain. Strain has no dimension, so the modulus has the dimension of stress.
How to get the dimensional formula of Young's modulus
- Start from the definition: Young's modulus = stress / strain.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- area = length × length, so area is [L] × [L] = [L2].
- stress = force / area, so stress is [M L T-2] / [L2] = [M L-1 T-2].
- strain = length / length, so strain is [L] / [L] = [M0 L0 T0].
- Put in the dimension of each part: [M L-1 T-2] / [M0 L0 T0].
- Add the powers of each base quantity: [M L-1 T-2].
Quantities with the dimensions [M L⁻¹ T⁻²]
Equal dimensions do not make them the same quantity. Compare Young's modulus with the others in the full grid.
Three questions on Young's modulus
2What is the SI unit of Young's modulus?
The SI unit of Young's modulus is the pascal (Pa).
3Which one has different dimensions from the others?
Reynolds number is [M⁰ L⁰ T⁰]. The other three are all [M L⁻¹ T⁻²].
An equation that uses Young's modulus
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
v = sqrt(Y / ρ)v[L T-1]=sqrt(Y/rho)[L T-1]Dimensionally consistentEvery term is [L T-1]
v = velocityY = Young's modulus
Young's modulus: quick answers
What is the dimensional formula of Young's modulus?
The dimensional formula of Young's modulus is [M L⁻¹ T⁻²]. It comes from Young's modulus = stress / strain.
What is the SI unit of Young's modulus?
The SI unit of Young's modulus is the pascal (Pa).
Which quantities have the same dimensions as Young's modulus?
Young's modulus shares [M L⁻¹ T⁻²] with energy density, pressure, stress, strain energy density, bulk modulus, shear modulus. Equal dimensions do not make them the same quantity.