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Question: The fractional change in the volume of a glass slab when subjected to hydraulic pressure of 14 atm I...

The fractional change in the volume of a glass slab when subjected to hydraulic pressure of 14 atm Is

A

1.44 x 10−5^{-5}

B

3.5 x 10−5^{-5}

C

2.74 x 10−5^{-5}

D

3.14×10−5^{-5}

Answer

3.5 x 10−5^{-5}

Explanation

Solution

The fractional change in volume is given by ΔVV=PB\frac{\Delta V}{V} = \frac{P}{B}. Given P=14P = 14 atm and B=40×109B = 40 \times 10^9 Nm−2^{-2}. We convert pressure to Nm−2^{-2}: P=14×105P = 14 \times 10^5 Nm−2^{-2}. Then, ΔVV=14×10540×109=1440×10−4=0.35×10−4=3.5×10−5\frac{\Delta V}{V} = \frac{14 \times 10^5}{40 \times 10^9} = \frac{14}{40} \times 10^{-4} = 0.35 \times 10^{-4} = 3.5 \times 10^{-5}.