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} $
