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Question

# A solid sphere of radius R made of a material of bulk modulus B is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. Find the fractional decrease in the radius of the sphere (ΔRR), when a mass M is placed on the piston to compress the liquid.

A
MgAB
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B
Mg4AB
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C
Mg3AB
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D
Mg2AB
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Solution

## The correct option is C Mg3ABPressure increased due to weight M P=ForceArea=MgA.... (1) And we know, −ΔVV=PB ⇒−ΔVV=MgAB...... (2) [∵P=MgA] where −ΔVV= Fractional decrease in the volume P= Increased Pressure B= Bulk modulus Volume of a sphere is V=43πR3 (where R is radius) ⇒ΔVV=3ΔRR Now, using (2), we have −ΔRR=Mg3AB (-ve sign indicates decrease in radius) ∴ Fractional decrease in radius is Mg3AB

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