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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 liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, d R/R, is…..

  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 liquid. When a mass M is placed on the piston to compress the liquid the fractional change in the radius of the sphere, d R/R, is…..

Grade:12th pass

2 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago

Ans. K = -?P/?V/V

Where ?P = Mg/A ?-?V/V =Mg/AK

? -(Vf-Vi)/Vi = Mg/AK ? Vi-Vf/Vi = Mg/AK

?4/3pR3– 4/3p(R-dR)3/4/3pR3= Mg/AK

?R3- [R3 – 3R2?r]/R3 = Mg/AK

??R/R = Mg/3AK

Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

When mass M is placed on the piston, the excess pressure ,
P = Mg/A.
As this pressure is equally applicable from all the direction on the sphere , hence there will be become in volume due to decrease in radius of sphere.
Volume of the sphere, V = 4/3 πR³
Differentiating it, we get
Δt = 4/3 π(3 R²)ΔR = 4πR² ΔR
∴ ΔV/V = 4/3R² ΔR/4/3 πR³ = 3ΔR/ R
We know that, B = P/dV/V = Mg/A/3ΔR/R
or, ΔR/R = Mg/3BA

Thanks and Regards

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