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

Question

Quantrex Academy · Accepted Answer

Correct answer: B. (Mg)/(3AK)

Change in pressure due to placing of mass on piston is,

∆p = \dfrac{Mg}{A}

From Bulk modulus definition

K = \dfrac{- \Deltap}{\Delta V}

⇒ \left|\dfrac{∆V}{V}\right| = \dfrac{∆ p}{K} = \dfrac{Mg}{AK}

FromV = \dfrac{4}{3}\pir^{3}

\dfrac{∆V}{V} = \dfrac{3∆R}{R}

⇒ \dfrac{∆R}{R} = \dfrac{1}{3}\dfrac{∆V}{V}

= \dfrac{Mg}{3AK}

A solid sphere of radius R made up of a material of bulk modulus K...

Options

Correct answer

Step-by-step solution

More from Mechanical Properties of Solids