First slide

Elastic Modulie

Question

The compressibility of water is $6 \times 10^{- 10} N^{- 1} m^{2}$ . If one litre is subjected to a pressure of 4 x $10^{7}$ N $m^{- 2}$ , the decrease in its volume is

Moderate

A

10 cc
B

24 cc
C

15 cc
D

12 cc

Solution

$Bulk modulus, B = - \frac{P}{(\frac{∆ V}{V})}$
-ve sign shows that with a increase in pressure, a decrease in volume occurs.
Compressibility, K = $\frac{1}{2} = - \frac{∆ V}{PV}$
Decrease in volume, $∆ V = PVK$
= 4 $\times 10^{7} \times 1 \times 6 \times 10^{- 10}$
= 24 $\times 10^{- 3} litre$
= 24 $\times 10^{- 3} 10^{3} {cm}^{3} = 24 cc$

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