Q 11-08-105JEE MainJEE Main 2018 (8 Apr)Easy
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 $\left(\dfrac{dr}{r}\right)$, is:
Answer: (D) $\dfrac{mg}{3Ka}$
The extra pressure transmitted through the liquid is $P = \dfrac{mg}{a}$, so
$$\frac{dV}{V} = \frac PK = \frac{mg}{aK}$$
For a sphere $V\propto r^3$, so $\dfrac{dV}{V} = 3\dfrac{dr}{r}$:
$$\frac{dr}{r} = \frac{mg}{3Ka}$$
Solution by Sreeraj P, M.Sc Physics