NTA Abhyas JEE Main2020PhysicsMechanical Properties of SolidsPractice
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
Options
- AM g A K
- BM g 3 A K
- C3 M g A K
- DM g 2 A K
Correct answer
B. M g 3 A K
Step-by-step solution
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