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Physics For Scientists & Engineers
Found in: Page 439

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Short Answer

Review. A solid sphere of brass (bulk modulus of 14.0×1010Nm2) with a diameter of 3.00 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sinks to a depth of 1 km?

The decrease in diameter is ΔD=2.66×103 m.

See the step by step solution

Step by Step Solution

Given Data:

The magnetic field, B=14.0×1010Nm2

The depth of ocean, h=1 km=1000 m

The diameter of sphere, D=3.0  m

The radius is,

r=D2=3.0 m2=1.5  m

A concept:

The pressure P in a fluid is the force per unit area exerted by the fluid on a surface:


In the SI system, pressure has units of Newton’s per square meter Nm2, and 1 Nm2=1 Pascal (Pa).

Bulk modulus is given by,

role="math" localid="1663696968659" B=Pvv

Find the decrease in diameter:

Applying the formula of Bulk modulus here, you get


While pressure is,


Combining both, you get



Δr=2.4×1043=0.062 m

Also diameter, D=2r

Therefore decrease in diameter is,

ΔD=2Δr=2×0.062 m=0.124 m

Hence, the decrease in diameter is ΔD=0.124 m.

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