Physics · Mechanical Properties Of Solids · NEET
When you increase pressure p on a body, its volume decreases, so ΔV is negative. Without the minus sign, B would come out negative. The minus sign is added so that bulk modulus is always a positive number. So the sign just corrects for the fact that volume shrinks under pressure - it does not change the size of B.
Young's modulus (Y) deals with a change in LENGTH under a stretching force along one direction: Y = FL/(A·ΔL). Bulk modulus (B) deals with a change in VOLUME under uniform pressure from all sides: B = -p/(ΔV/V). Young's modulus needs a wire or rod being pulled; bulk modulus needs a body squeezed by a fluid or gas on every side. Both have the SI unit N/m² (pascal).
Volume strain (ΔV/V) has no unit, so bulk modulus has the same unit as pressure. SI unit = N/m² = pascal (Pa). Its dimensional formula is [M L⁻¹ T⁻²], the same as stress, Young's modulus and shear modulus. NEET often tests that all three moduli share this same dimension.
Yes - bulk modulus is the ONLY modulus of elasticity defined for all three states. Solids, liquids and gases can all be compressed in volume, so all three have a bulk modulus. Young's modulus and shear modulus apply only to solids because liquids and gases cannot resist a change of shape or length. NCERT states this directly.
Solids have the highest bulk modulus because their atoms are tightly bound, so they are hardest to compress. Gases have the lowest bulk modulus - NCERT notes gases are about a million times more compressible than solids. So order of bulk modulus: solids > liquids > gases.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
B = -p / (ΔV/V), where p is the applied uniform (hydraulic) pressure, ΔV is the change in volume and V is the original volume. The minus sign keeps B positive because volume decreases under pressure.
The SI unit is N/m² or pascal (Pa), the same as pressure and Young's modulus. Its dimensional formula is [M L⁻¹ T⁻²].
Gas molecules are far apart and weakly bound, so a small pressure causes a large fractional volume change. A large ΔV/V for a given p means a small B. That is why gases are about a million times more compressible than solids.
Bulk modulus is a scalar quantity. It is a ratio of hydraulic stress to volume strain, and pressure acts equally in all directions, so there is no single direction associated with it.
The reciprocal of bulk modulus (1/B) is called compressibility. A material with high compressibility has a low bulk modulus and is easy to squeeze. This is explored in the next concept, compressibility and its relation to bulk modulus.
