A solid sphere of radius r made of a soft 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, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere d r r , is:

Question

A solid sphere of radius r made of a soft 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, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere d r r , is:, m g K a, K a m g, K a 3 m g, m g 3 K a

MARKS App · Accepted Answer

For sphere, ∨ = 4 3 π r 3 ⇒ ∆ ∨ ∨ = 3 ∆ r r ⇒ P = K Δ V V ⇒ P = 3 K Δ R R ⇒ m g 3 K a = Δ R R .

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