A solid sphere of radius R made up 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 is

Question

A solid sphere of radius R made up 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 is, M g A K, M g 3 A K, 3 M g A K, M g 2 A K

MARKS App · Accepted Answer

Change in pressure due to placing of mass on piston is, ∆ p = M g A From Bulk modulus definition K = − Δ p Δ V ⇒ ∆ V V = ∆ p K = M g A K F r o m V = 4 3 π r 3 ∆ V V = 3 ∆ R R ⇒ ∆ R R = 1 3 ∆ V V = M g 3 A K

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