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A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric stress of 0.5 MPa. If bulk modulus of the bail material is 16 GPa, the change in volume of the ball would be approximately equal to
  • a)
    0.0156 mm3
  • b)
    1.56 x 10-4mm3
  • c)
    0.156 mm3
  • d)
    0.00156 mm3
Correct answer is option 'A'. Can you explain this answer?
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A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric ...
Bulk modulus
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A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric ...
**Given:**
- Volume of the ball = 0.5 x 103 mm3
- Volumetric stress = 0.5 MPa
- Bulk modulus of the ball material = 16 GPa

**To find:**
Change in volume of the ball

**Solution:**
In this problem, we need to use the concept of bulk modulus to calculate the change in volume of the ball.

**Bulk modulus (K)** is a measure of a material's resistance to change in volume under pressure. It is defined as the ratio of volumetric stress (σ) to volumetric strain (ε).

Mathematically, bulk modulus is given by:
K = σ/ε

Rearranging the equation, we can find the volumetric strain:
ε = σ/K

To find the change in volume (ΔV) of the ball, we need to calculate the volumetric strain and multiply it by the initial volume of the ball.

**Calculations:**

Given:
Volume of the ball (V) = 0.5 x 103 mm3 = 0.5 x 10-3 cm3
Volumetric stress (σ) = 0.5 MPa = 0.5 N/cm2
Bulk modulus (K) = 16 GPa = 16 x 109 N/cm2

Using the formula for volumetric strain:
ε = σ/K

Substituting the given values:
ε = 0.5 N/cm2 / 16 x 109 N/cm2

Calculating the volumetric strain:
ε = 3.125 x 10-11

To find the change in volume (ΔV):
ΔV = ε x V

Substituting the values of ε and V:
ΔV = 3.125 x 10-11 x 0.5 x 10-3 cm3

Simplifying the expression:
ΔV = 1.5625 x 10-14 cm3

Converting the answer to mm3:
ΔV = 1.5625 x 10-14 x 103 mm3

Therefore, the change in volume of the ball is approximately 0.0156 mm3.

Hence, the correct answer is option A) 0.0156 mm3.
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A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric stress of 0.5 MPa. If bulk modulus of the bail material is 16 GPa, the change in volume of the ball would be approximately equal toa)0.0156 mm3b)1.56 x 10-4mm3c)0.156 mm3d)0.00156 mm3Correct answer is option 'A'. Can you explain this answer?
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A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric stress of 0.5 MPa. If bulk modulus of the bail material is 16 GPa, the change in volume of the ball would be approximately equal toa)0.0156 mm3b)1.56 x 10-4mm3c)0.156 mm3d)0.00156 mm3Correct answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric stress of 0.5 MPa. If bulk modulus of the bail material is 16 GPa, the change in volume of the ball would be approximately equal toa)0.0156 mm3b)1.56 x 10-4mm3c)0.156 mm3d)0.00156 mm3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical ball of 0.5 x 103 mm3 volume is subjected to a volumetric stress of 0.5 MPa. If bulk modulus of the bail material is 16 GPa, the change in volume of the ball would be approximately equal toa)0.0156 mm3b)1.56 x 10-4mm3c)0.156 mm3d)0.00156 mm3Correct answer is option 'A'. Can you explain this answer?.
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