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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Some Mechanical Properties of Matter

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Some Mechanical Properties of Matter

Determine the increase in pressure needed to reduce the volume of a...

Determine the increase in pressure needed to reduce the volume of a water sample by

0.01\%

. The bulk modulus of water is

2.1 \times 10^9 \text{ N/m}^2

.

Options

A $2.1 \times 10^5 \text{ N/m}^2$
B $2.1 \times 10^4 \text{ N/m}^2$
C $2.1 \times 10^6 \text{ N/m}^2$
D $2.1 \times 10^7 \text{ N/m}^2$

Correct answer

A. $2.1 \times 10^5 \text{ N/m}^2$

Step-by-step solution

The bulk modulus

B

is defined as:

B = \dfrac{\Delta P}{\dfrac{\Delta V}{V}}

Given the percentage reduction in volume is

0.01\%

, the fractional change in volume is:

\dfrac{\Delta V}{V} = \dfrac{0.01}{100} = 10^{-4}

The bulk modulus of water is

B = 2.1 \times 10^9 \text{ N/m}^2

.

The required increase in pressure

\Delta P

is:

\Delta P = B \times \dfrac{\Delta V}{V}

\Delta P = (2.1 \times 10^9) \times 10^{-4}

\Delta P = 2.1 \times 10^5 \text{ N/m}^2

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