Question

a ball falling in a lake of depth 200m shows 0.1 percent decrease in its volume at the bottom. what is the bulk modulus of the material of the ball.

Answer 1

Answer:

The bulk modulus of the material of the ball is $B = 19.6\times10^{8}\ N/m^2$.

Explanation:

Given that,

Depth = 200 m

$\dfrac{\Delta v}{v} = 0.1\%$

We know that ,

The bulk modulus is

$B = \dfrac{-\Delta p}{\dfrac{\Delta v}{v}}$

Where, p = Pressure

V = Volume

The pressure is

$\Delta P = \rho g h$....(I)

Where, $\rho$ = density of water

g = acceleration due to gravity

h = depth

We substitute the value in equation (I)

$\Delta P=1000\times9.8\times200$

$\Delta P=19.6\times10^{5}\ N/m^2$

Put the value of $\Delta P$ and $\dfrac{\Delta v}{v}$ into the formula of bulk modulus

$B=\dfrac{19.6\times10^{5}}{\dfrac{0.1}{100}}$

$B = 19.6\times10^{8}\ N/m^2$

Hence, The bulk modulus of the material of the ball is $B = 19.6\times10^{8}\ N/m^2$.