JEE Mains · Physics · STD 11- 8. mechanical properties of solids
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 crosssection 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, \(\left( {\frac{{dr}}{r}} \right)\) is
- A \(\frac{{Ka}}{{3mg}}\)
- B \(\frac{{mg}}{{3Ka}}\)
- C \(\frac{{mg}}{{ka}}\)
- D \(\frac{{Ka}}{{mg}}\)
Answer & Solution
Correct Answer
(B) \(\frac{{mg}}{{3Ka}}\)
Step-by-step Solution
Detailed explanation
\(\Delta P = \frac{{mg}}{a}\) \(k = - \frac{{\frac{{mg}}{A}}}{{\frac{{4\pi {r^2}dr}}{{\frac{4}{3}\pi {r^3}}}}}\) \(\frac{{dr}}{r} = - \frac{{mg}}{{3KA}}\)
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