Question

A spherical sample of a new kind of enamel is subject to an increase in pressure of 120 MPa which results in a reduction in radius of 2.0%. That is, the radius of the sample has reduced from r0 to 0.98r0.

What is the bulk modulus of this enamel? (to 2 s.f and in GPa)

[note: the volume of a sphere is given by V equals 4 over 3 pi r cubed and the change in volume is given by capital delta V equals V minus V subscript 0]

Answer 1

$$K=-\frac{\Delta P}{\frac{\Delta V}{V}}=\frac{\Delta P}{1-\frac{r^3}{r^3_0}}$$

$$K=\frac{0.12}{1-0.98^3}=2.0\ GPa$$