The volume contraction of a solid copper cube, \(10~\text{cm}\) on an edge, when subjected to a hydraulic pressure of \(7.0\times10^6~\text{Pa}\) is:
(Bulk modulus of copper is \(140 \times10^{9}~\text{Pa}.\))
1. \( 3.1 \times 10^{-2} ~\text{m}^3 \)
2. \(9.1 \times 10^{-3} ~\text{cm}^3 \)
3. \(5.0 \times 10^{-2} ~\text{cm}^3 \)
4. \(7.9 \times 10^{-2} ~\text{cm}^3 \)$$

The average depth of the Indian Ocean is about \(3000~\text m.\) The fractional compression \(\frac{\Delta V}{V},\) of water at the bottom of the ocean is? 
(Given that the bulk modulus of water is \(2.2\times10^{9}~\text{Nm}^{-2}\) and \(g=10~\text{ms}^{-2}\))
1. \(1.36\times10^{-3}\)
2. \(2.36\times10^{-3}\)
3. \(1.36\times10^{-2}\)
4. \(2.36\times10^{-2}\)

The edge of an aluminum cube is \(10~\text{cm}\) long. One face of the cube is firmly fixed to a vertical wall. A mass of \(100~\text{kg}\) is then attached to the opposite face of the cube. The shear modulus of aluminum is \(25~\text{GPa}.\) What is the vertical deflection of this face?
1. \(4.86 \times10^{-6}~\text m\)
2. \(3.92 \times 10^{-7}~\text m\)
3. \(3.01 \times10^{-6}~\text m\) 
4. \(6.36 \times10^{-7}~\text m\)

How much should the pressure on a litre of water be changed to compress it by \(0.10 \%?\)
(Given Bulk modulus of water, \(\beta=2.2\times 10^9~\text{N-m}^2\))
1. \(4.8 \times 10^6~\text{N/m}^2\) 
2. \(2.2 \times 10^6~\text{N/m}^2\) 
3. \(5.1 \times 10^6~\text{N/m}^2\) 
4. \(3.3 \times 10^6~\text{N/m}^2\)