A solid sphere of radius R made of a material of bulk modulus B, is surrounded by a liquid in acylindrical container. A massless piston of area A (the area of container is also A) floats on thesurface of the liquid. When a mass M is placed on the piston to compress the liquid, fractionalchange in radius of the sphere is . The value of n is3𝑀𝑔𝑛𝐴𝐵
Question
A solid sphere of radius R made of a material of bulk modulus B, is surrounded by a liquid in acylindrical container. A massless piston of area A (the area of container is also A) floats on thesurface of the liquid. When a mass M is placed on the piston to compress the liquid, fractionalchange in radius of the sphere is . The value of n is3𝑀𝑔𝑛𝐴𝐵
Solution
The problem is asking for the fractional change in the radius of the sphere when a mass M is placed on the piston. The fractional change in radius is given by the formula:
ΔR/R = 3Mg/(nAB)
Where:
- ΔR is the change in radius
- R is the original radius
- M is the mass placed on the piston
- g is the acceleration due to gravity
- A is the area of the piston
- B is the bulk modulus of the material
- n is the value we are trying to find
Rearranging the formula to solve for n gives:
n = 3Mg/(ΔR/R * AB)
So, the value of n is the ratio of the force applied by the mass (3Mg) to the product of the fractional change in radius (ΔR/R), the area of the piston (A), and the bulk modulus of the material (B).
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