### JEE Main On 08 April 2018 Question 3

##### 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, $ ( \frac{dr}{r} ), $ is: [JEE Main Online 08-04-2018]

#### Options:

A) $ \frac{mg}{3Ka} $

B) $ \frac{mg}{Ka} $

C) $ \frac{Ka}{mg} $

D) $ \frac{Ka}{3mg} $

## Show Answer

#### Answer:

Correct Answer: A

#### Solution:

- $ K=\frac{mg/a}{\frac{\Delta V}{V}} $ and $ V=\frac{4}{3}\pi r^{3} $

$ \therefore \frac{\Delta V}{V}=3\frac{dr}{r} $ So, $ K=\frac{mg/a}{3\frac{dr}{r}}\Rightarrow \frac{dr}{r}=\frac{mg}{3Ka} $