A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, `deltaR//R`, is .............A. `(Mg)/(AK)`B. `(Mg)/(3AK)`C. `(3Mg)/(AK)`D. `(Mg)/(2AK)`

A solid sphere of radius R made of a material of bulk modulus K is sur

1.	A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, `deltaR//R`, is .............A. `(Mg)/(AK)`B. `(Mg)/(3AK)`C. `(3Mg)/(AK)`D. `(Mg)/(2AK)`
Answer» Correct Answer - B Change in pressure due to placing of mass of prism is `/_p=(Mg)/A` From bulk modulus definition `K=(-dp)/(dV//V)` `\|(dV)/V\|=(/_P)/K=(Mg)/(AK)` From `V=4/3pir^(3)` `(dV)/V=(3dR)/Rimplies(dR)/R=1/3(dV)/V=(Mg)/(3AK)`

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