A solid sphere of radius R made of a material of bulk modules B is surrounded by a liquid in a cylindrical container. A massless area A floats on the surface of the liquid . When a mas M is placed on the piston to compress the liquid, find fractional change in the radius of the sphere

Answers (1)
A Avinash Dongre


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 decrease  in volume due to decrease in radius of sphere. 

Volume of the sphere, V = \frac{4}{3}*\pi*R^3

Differentiating it , we get  
                   \Delta V = \frac{4}{3}*\pi*3*R^2\Delta R= = 4*\pi*R^2 \Delta R 
∴                   ΔV/V =  3ΔR/ R 

   We know that,B = \frac{P}{\frac{\Delta V}{V}}

or,                     ΔR/R = Mg/3BA