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Question

# A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, (drr), is?

A
mg3Ka
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B
mgKa
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C
Kamg
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D
Ka3mg
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Solution

## The correct option is C mg3KaVolume of sphere V=4π3r3Decrease in volume of sphere −dV=4π33r2drBulk modulus K=PV−dV⟹ −dV=PVK ........(1)Pressure P=ForceArea=mga ......(2)Using (2) in (1), we get 4π33r2dr=mga.4π3r3.1K⟹ drr=mg3Ka

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