Question

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 ?

Answer 1

Hi

Here is your answer,

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



Hope it helps you !

Answer 2

Answer:

Explanation:

I.