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# MCQs on Compressibility and Bulk Modulus

Which one of the following is the correct relation between compressibility β and Bulk Modulus k

a) β = k

b) β = 1/k

c) β = 2k

d) β = k/2

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b

Explanation: Compressibility β of a liquid is deβned as the ratio of volumetric strain to the compressive stress while Bulk Modulus is the ratio of compressive stress to volumetric strain. Hence, β = 1/k is the correct relation.

Which one of the following is true about Bulk Modulus of elasticity?

a) it is the ratio of compressive stress to volumetric strain

b) it is the ratio of compressive stress to linear strain

c) it is the ratio of tensile stress to volumetric strain

d) it is the ratio of tensile stress to linear strain

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a

Explanation: Bulk Modulus k is related to the compression of a liquid and the decrease in volume per unit volume. It is the ratio of compressive stress to the volumetric strain.

The value of the Bulk Modulus of elasticity for an incompressible fluid is

a) zero

b) unity

c) infinity

d) very low

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c

Explanation: k = 1/β, where k= Bulk Modulus of elasticity and β= compressibility. For an incompressible fluid, β=0, thus the value of k will tend to infinity.

adve

Three fluids 1, 2 and 3 have Bulk Moduli of k1, k2 and k3 respectively. If k1 > k2 > k3, which liquid will have the highest compressibility?

a) liquid 1

b) liquid 2

c) liquid 3

d) they’ll have equal compressibilities

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c

Explanation: k = 1=β, where k= Bulk Modulus of elasticity and β= compressibility. If k1 > k2 > k3, then β1 < β2 < β3. Thus, liquid 3 will have the highest compressibility.

Bulk Modulus, Pressure, Force, Stress – Which one of these won’t have the same unit as the others?

a) Bulk Modulus

b) Pressure

c) Force

d) Stress

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c

Explanation: The SI unit of Bulk Modulus, Pressure and Stress is N/m2 but the unit of Force is N.

Which of the following is the dimension of Bulk Modulus?

a) [M1L-1T-1].

b) [M1L-1T-2].

c) [M1L1T-2].

d) [M1L1T-1].

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b

Explanation:

Which one of the following is the unit of compressibility?

a) m=N

b) m2=N

c) m3=N

d) it is unitless

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b

Explanation: k = 1/β, where k= Bulk Modulus of elasticity and β= compressibility.

Thus the unit of Bulk modulus is N/m2 and the unit of compressibility becomes m2/N.

Which of the following is the dimension of compressibility?

a) [M1L1T-2].

b) [M1L1T-1].

c) [M-1L1T-2].

d) [M-1L1T2].

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d

Explanation: k = 1/β, where k = Bulk Modulus of elasticity and β= compressibility.

and [β] = [1/k] = [M-1L1T2].