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What is bulk modulus? Derive an expression for bulk modulus.

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Definition:

Bulk modulus is defined as the ratio of volume stress to volume strain.

It is denoted by ‘K’.

Unit: N/m2 or Pa in SI system

Dimensions: [L-1M1T-2]

Expression for bulk modulus:

(i) If a sphere made from rubber is completely immersed in a liquid, it will be uniformly compressed from all sides.

Let, F = Compressive force,

dP = Change in pressure,

dV = Change in volume,

V = Original volume.

(ii) Volume stress = \(\frac{|\overrightarrow{F}|}{A}\) = dP

(iii) The negative sign indicates that there is a decrease in volume.

The magnitude of the volume strain is \(\frac{dV}{V}\)

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