value of bulk modulus. In other words, bulk modulus measures the resistance of solids to change in their volume. For an example, we know that gases can be easily compressed than solids. This means that gases have small value of bulk modulus compared to solids.
Compressibility The reciprocal of the bulk modulus is called compressibility. It is defined as the fractional change in volume per unit increase in pressure. From equation ( . ), we can say that the compressibility C= K n =− =− ∆ ∆ ε σ ( .
) Since gases have small value of bulk modulus than solids, their values of compressibility is very high. Within the elastic limit, stress is proportional to strain (obey Hooke’s law). Therefore, it shows a straight line behaviour. So, Young modulus can be computed by taking slope of these straight lines.
Hence, calculating the slope for the straight line, we get Slope of A > Slope of B > Slope of C Which implies, Young modulus of C < Young modulus of B < Young modulus of A Notice that larger the slope, lesser the strain (fractional change in length). So, the material is much stiffer. Hence, the elasticity of wire A is greater than wire B which is greater than C. From this example, we have understood that Young’s modulus measures the resistance of solid to a change in its length.
EXAMPLE . A wire m long has a cross-sectional area . × – m . It is subjected to a load of kg.
If Young’s modulus of the material is × N m – , calculate the elongation produced in the wire. Take g = ms – . Solution We know that F Y × ∆ ∆= F Y = Bulk modulus: The bulk modulus is defined as the ratio of the volume stress to the volume strain. Bulk modulus, K = Normal(Perpendicular)stressorPressure Volumestrain After pumping the air in the cycle tyre, usually we press the