First slide

Elastic Modulie

Question

The bulk modulus of water if its volume changes from 100 litre to 99.5 litre under a pressure of 100 atm is (Take 1 atm = $10^{5} N m^{- 2})$

Moderate

A

$2 \times 10^{7} {Nm}^{- 2}$
B

$2 \times 10^{8} {Nm}^{- 2}$
C

2 $\times 10^{9} {Nm}^{- 2}$
D

$2 \times 10^{10} {Nm}^{- 2}$

Solution

According to definition of bulk modulus,
B = $\frac{P}{\frac{∆ V}{V}}$
Here, P = 100 atm = $100 \times 10^{5} {Nm}^{- 2} = 10^{7} {Nm}^{- 2}$
$∆ V = (99.5 - 100) litre = - 0.5 litre$
V = 100 litre
B = $\frac{10^{7} {Nm}^{- 2}}{(- 0.5 litre / 100)} = 2 \times 10^{9} {Nm}^{- 2}$

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