1Which of these has the same dimensions as bulk modulus?
Bulk 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 Bulk modulus
[M L-1 T-2]
Pressure change divided by the fractional change in volume. It is the inverse of compressibility.
How to get the dimensional formula of bulk modulus
- Start from the definition: bulk modulus = pressure / 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].
- pressure = force / area, so pressure 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 bulk modulus with the others in the full grid.
Three questions on bulk modulus
2What is the SI unit of bulk modulus?
The SI unit of bulk modulus is the pascal (Pa).
3Which one has different dimensions from the others?
Kinematic viscosity is [L² T⁻¹]. The other three are all [M L⁻¹ T⁻²].
Bulk modulus: quick answers
What is the dimensional formula of bulk modulus?
The dimensional formula of bulk modulus is [M L⁻¹ T⁻²]. It comes from bulk modulus = pressure / strain.
What is the SI unit of bulk modulus?
The SI unit of bulk modulus is the pascal (Pa).
Which quantities have the same dimensions as bulk modulus?
Bulk modulus shares [M L⁻¹ T⁻²] with energy density, pressure, stress, strain energy density, Young's modulus, shear modulus. Equal dimensions do not make them the same quantity.