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 the entire cross-section of the 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:
1. \(\dfrac{Ka}{mg}\)

2. \(\dfrac{Ka}{3mg}\)

3. \(\dfrac{mg}{3Ka}\)

4. \(\dfrac{mg}{Ka}\)

A cube of metal is subjected to a hydrostatic pressure of \(4~\text{GPa}\). The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, \(B=8 \times 10^{10} ~\text{Pa}\))
1. \(5\)
2. \(20\)
3. \(0.6\)
4. \(1.67\)

The normal density of a material is \(\rho\) and its bulk modulus of elasticity is \(K\). The magnitude of the increase in the density of material when a pressure \(P\) is applied uniformly on all sides, will be: