Properties of Matter 1 Question 18

18. 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 piston 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, δR/R, is ………. .

(1988,2M)

Show Answer

Answer:

Correct Answer: 18. Mg3AK

Solution:

  1. Δp=MgA⇒|ΔVV|=Δpk=MgAk

Now as,

V=43πR3 or V∝R3

∴ΔVV=3(ΔRR)

 or ΔRR=13(ΔVV)⋯(i)

∴ From Eq. (i)

ΔRR=Mg3Ak

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