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A spherical ball of a material of a diameter of 160mm goes down to a depth of 600 m in sea water. If the specific weight of sea water is 10.2kN/m3 and the bulk modulus of the material of the ball is 160kN/mm2, determine the change in volume of ball. 
  • a)
    80
  • b)
    82
  • c)
    75
  • d)
    62
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A spherical ball of a material of a diameter of 160mm goes down to a d...


Given data:
- Diameter of the ball = 160 mm
- Depth in sea water = 600 m
- Specific weight of sea water = 10.2 kN/m^3
- Bulk modulus of the material = 160 kN/mm^2

Calculating initial volume of the ball:
- Radius of the ball (r) = Diameter/2 = 160/2 = 80 mm = 0.08 m
- Initial volume of the ball (V) = 4/3 * π * r^3 = 4/3 * π * (0.08)^3 = 2.144 x 10^-3 m^3

Calculating change in pressure:
- Change in pressure (ΔP) = Specific weight * depth = 10.2 * 600 = 6120 N/m^2 = 6.12 kN/m^2

Calculating change in volume:
- Change in volume (ΔV) = -ΔP * V / Bulk modulus = -6120 * 2.144 x 10^-3 / 160 = -0.08208 m^3 = 82 mm^3

Therefore, the change in volume of the ball is 82 mm^3, which corresponds to option 'B'.
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A spherical ball of a material of a diameter of 160mm goes down to a d...
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A spherical ball of a material of a diameter of 160mm goes down to a depth of 600 m in sea water. If the specific weight of sea water is 10.2kN/m3 and the bulk modulus of the material of the ball is 160kN/mm2, determine the change in volume of ball.a)80b)82c)75d)62Correct answer is option 'B'. Can you explain this answer?
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