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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 ………

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 ………

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
K = -∆P / ∆V / V
where∆P = Mg / A ∴∆V / V = Mg / AK
⇒ - (Vf - Vi) / Vi = Mg / AK ⇒ V­i – Vf / Vi = Mg / AK
⇒ 4/3 πR3 – 4/3 π (R - δR)3 / 4/3 πR3 = Mg / AK
⇒ R3 – [R3 – 3R3δ R] / R3 Mg / AK
⇒ δR / R = Mg / 3AK

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