A solid sphere of brass (bulk modulus of 14.0 ✕ 1010 N/m2) with a diameter of 2.20 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sinks to a depth of 2.40 km? (Take the density of ocean water to be 1,030 kg/m3.)
1 answer:
Answer:
Diameter decreases by the diameter of 0.0312 m.
Explanation:
Given that,
Bulk modulus = 14.0 × 10¹⁰ N/m²
Diameter d = 2.20 m
Depth = 2.40 km
Pressure = ρ g h = 1030 × 9.81 × 2.4 × 1000
= 24.25 × 10⁶ N/m²
Volume =
Bulk modulus is equal to
now
Δ r = -0.0156 m
change in diameter
Δ d = -2 × 0.0156
Δ d = -0.0312 m
Diameter decreases by the diameter of 0.0312 m.
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