Question

A rubber ball is taken to depth 1km inside water so that its volume reduces by 0.05% .What is the bulk modulus of rubber?

Answer 1

Answer:

The bulk modulus of rubber is $2\times10^{10}\ N/m^2$.

Explanation:

Given that,

Depth h = 1 km = 1000 m

Let us consider the initial volume is V and its volume reduces by 0.05%.

Then the final volume is

$\Delta V = V\times\dfrac{0.05}{100}$

The bulk modulus is defined as

$B = \dfrac{\dfrac{F}{A}}{-\dfrac{\Delta V}{V}}$

We know that,

Pressure is the force upon area.

$B = \dfrac{P}{-\dfrac{\Delta V}{V}}$.....(I)

Where,P = pressure

V = volume

$\Delta V$ = change volume

We know that,

The pressure is defined as:

$P = \rho g h$

Where, g = acceleration due to gravity

h = depth

$\rho$ = density of water

Put the value into the formula

$P = 1000\times9.8\times1000$

$P = 9.8\times 10^{6}$

Put the value of P  in equation (I)

$B = \dfrac{9.8\times10^{6}}{\dfrac{V\times\dfrac{0.05}{100}}{V}}$

$B = \dfrac{9.8\times10^{6}\times100}{0.05}$

$B = 1.96\times10^{10}\ N/m^2$

$B = 2\times10^{10}\ N/m^2$

Hence, The bulk modulus of rubber is $2\times10^{10}\ N/m^2$.