A solid sphere of radius \( R \), made up of a material of bulk modulus \( K \) is surrounded by...

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A solid sphere of radius \( R \), made up of a 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. When a mass \( M \) is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is
(1) \( \frac{M g}{A K} \)
(2) \( \frac{M g}{3 A K} \)
(3) \( \frac{3 M g}{A K} \)
(4) \( \frac{M g}{2 A K} \)
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