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Question

The initial volume of water is 2000 cm3. Determine the change in volume of the water when external pressure is changed from 105 Nm2 to 106 Nm2.
[Take compressibility of water as 60×1011 m2/N]

A
2.08×105 m3
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B
1.08×106 m3
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C
2.08×106 m3
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D
1.08×105 m3
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Solution

The correct option is B 1.08×106 m3
From the data given in the question,
Change in pressure (ΔP)=106 Nm2105 Nm2=9×105 Nm2
Initial volume V=2×103 m3
We know that,
Compressibility =1|Bulk modulus|
From the definition of Bulk modulus of elasticity,
Bulk modulus (B)=V×ΔPΔV
Compressibility =(ΔVV)ΔP
60×1011=ΔV2×103×9×105
ΔV=60×1011×2×103×9×105
ΔV=1.08×106 m3
Hence, option (b) is the correct answer.

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