Question

If a rubber ball is taken down to a 100m deep Laker, it's volume decreases by 0.1%. if g is 10 m/s^2, then the bulk modulus of elasticity for rubber in N/m^2 is
(Answer is 10^9)

Answer 1

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Answer 2

Answer:

The bulk modulus of elasticity for rubber is $2\times10^{9}\ N/m^2$.

Explanation:

Given that,

Height h = 100 m

$g = 10 m/s^2$

Change in volume $\dfrac{\Delta V}{V}=\dfrac{0.1}{100}$

The bulk modulus is defined as:

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

Here, $\Delta V$ = Change in volume

$\Delta P$= change in pressure

Put the value of change in pressure and change in volume in equation (I)

$B=\dfrac{h\rho g}{\dfrac{\Delta V}{V}}$

$B=\dfrac{200\times1\times10^3\times10}{\dfrac{0.1}{100}}$

$B=\dfrac{200\times1\times10^3\times10\times100}{0.1}$

$B=2\times10^{9}\ N/m^2$

Hence, The bulk modulus of elasticity for rubber is $2\times10^{9}\ N/m^2$.