Question:
Statement (A): For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero.
Statement (B): The volume contraction of a metal cube of bulk modulus \(140\,\text{GPa}\), \(10\,\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7\times 10^6\,\text{Pa}\), is \(-0.05\,\text{m}^3\).
Statement (C): A spiral spring is stretched by a weight attached to it. The strain is tensile.
Statement (A): For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero.
Statement (B): The volume contraction of a metal cube of bulk modulus \(140\,\text{GPa}\), \(10\,\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7\times 10^6\,\text{Pa}\), is \(-0.05\,\text{m}^3\).
Statement (C): A spiral spring is stretched by a weight attached to it. The strain is tensile.
Statement (B): The volume contraction of a metal cube of bulk modulus \(140\,\text{GPa}\), \(10\,\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7\times 10^6\,\text{Pa}\), is \(-0.05\,\text{m}^3\).
Statement (C): A spiral spring is stretched by a weight attached to it. The strain is tensile.
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For bulk modulus questions, use \(\Delta V=-\frac{PV}{K}\). Also, ideal liquids are incompressible and cannot resist shear stress.
Updated On: Jun 26, 2026
- A, B and C are true
- A, B are true, C is false
- A, C are true, B is false
- B and C are true, A is false
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The Correct Option is C
Solution and Explanation
Step 1: Check Statement (A).
An ideal liquid is incompressible.
So, its volume does not change under pressure.
Hence, its bulk modulus is infinite.
Also, a liquid cannot sustain shear stress, so its shear modulus is zero.
Therefore, Statement (A) is true.
Step 2: Check Statement (B).
Bulk modulus is given by \[ K=-\frac{P V}{\Delta V} \] So, \[ \Delta V=-\frac{PV}{K} \] Given, \[ P=7\times 10^6\,\text{Pa} \] \[ K=140\,\text{GPa}=140\times 10^9\,\text{Pa} \] Edge of cube: \[ 10\,\text{cm}=0.1\,\text{m} \] Volume: \[ V=(0.1)^3=10^{-3}\,\text{m}^3 \] Thus, \[ \Delta V=-\frac{(7\times 10^6)(10^{-3})}{140\times 10^9} \] \[ \Delta V=-5\times 10^{-8}\,\text{m}^3 \] This is not equal to \[ -0.05\,\text{m}^3 \] Therefore, Statement (B) is false.
Step 3: Check Statement (C).
When a spiral spring is stretched by attaching a weight, its length increases.
Increase in length corresponds to tensile strain.
Therefore, Statement (C) is true.
Step 4: Final conclusion.
Hence, \[ \boxed{\text{A, C are true, B is false}} \]
An ideal liquid is incompressible.
So, its volume does not change under pressure.
Hence, its bulk modulus is infinite.
Also, a liquid cannot sustain shear stress, so its shear modulus is zero.
Therefore, Statement (A) is true.
Step 2: Check Statement (B).
Bulk modulus is given by \[ K=-\frac{P V}{\Delta V} \] So, \[ \Delta V=-\frac{PV}{K} \] Given, \[ P=7\times 10^6\,\text{Pa} \] \[ K=140\,\text{GPa}=140\times 10^9\,\text{Pa} \] Edge of cube: \[ 10\,\text{cm}=0.1\,\text{m} \] Volume: \[ V=(0.1)^3=10^{-3}\,\text{m}^3 \] Thus, \[ \Delta V=-\frac{(7\times 10^6)(10^{-3})}{140\times 10^9} \] \[ \Delta V=-5\times 10^{-8}\,\text{m}^3 \] This is not equal to \[ -0.05\,\text{m}^3 \] Therefore, Statement (B) is false.
Step 3: Check Statement (C).
When a spiral spring is stretched by attaching a weight, its length increases.
Increase in length corresponds to tensile strain.
Therefore, Statement (C) is true.
Step 4: Final conclusion.
Hence, \[ \boxed{\text{A, C are true, B is false}} \]
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