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. 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, δ R/R, is ………

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Navjyot Kalra · Answer

K = -∆P / ∆V / V where∆P = Mg / A &there4;∆V / V = Mg / AK &rArr; - (Vf - Vi) / Vi = Mg / AK &rArr; V&shy;i &ndash; Vf / Vi = Mg / AK &rArr; 4/3 &pi;R3 &ndash; 4/3 &pi; (R - &delta;R)3 / 4/3 &pi;R3 = Mg / AK &rArr; R3 &ndash; [R3 &ndash; 3R3&delta; R] / R3 Mg / AK &rArr; &delta;R / R = Mg / 3AK

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