1Which of these has the same dimensions as shear modulus?
Shear 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 Shear modulus
[M L-1 T-2]
Shearing stress divided by shearing strain, also called the modulus of rigidity.
How to get the dimensional formula of shear modulus
- Start from the definition: shear 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 shear modulus with the others in the full grid.
Three questions on shear modulus
2What is the SI unit of shear modulus?
The SI unit of shear modulus is the pascal (Pa).
3Which one has different dimensions from the others?
Velocity gradient is [T⁻¹]. The other three are all [M L⁻¹ T⁻²].
Shear modulus: quick answers
What is the dimensional formula of shear modulus?
The dimensional formula of shear modulus is [M L⁻¹ T⁻²]. It comes from shear modulus = stress / strain.
What is the SI unit of shear modulus?
The SI unit of shear modulus is the pascal (Pa).
Which quantities have the same dimensions as shear modulus?
Shear modulus shares [M L⁻¹ T⁻²] with energy density, pressure, stress, strain energy density, Young's modulus, bulk modulus. Equal dimensions do not make them the same quantity.