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Q.

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 change in the radius of the sphere (dRR) , when a mass M is placed on the piston to compress the liquid.

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a

Mg2AB

b

Mg3AB

c

2MgAB

d

3MgAB

answer is B.

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Detailed Solution

As fro a spherical body V=43πR3,ΔVV=3ΔRR Now by definition of bulk modulusB=−VΔPΔVi.e|ΔVV|=ΔPB=MgAB[as  ΔP=MgA] dRR=13ΔVV⇒dRR=Mg3AB
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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 change in the radius of the sphere (dRR) , when a mass M is placed on the piston to compress the liquid.