The bulk modulus of water is \(2\times 10^{9}~\text{N/m}^2.\)${\mathrm{}}^{}$ The increase in pressure required to decrease the volume of the water sample by \(0.1\%\) is:
1. \(4 \times 10^{6}~\text{N/m}^2\)
2. \(2 \times 10^{6}~\text{N/m}^2\)
3. \(2 \times 10^{8}~\text{N/m}^2\)
4. \(8 \times 10^{6}~\text{N/m}^2\)

A ball falling into a lake of depth \(200~\text{m}\) shows a \(0.1\%\) decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?
1. \(19.6\times 10^{8}~\text{N/m}^2\)
2. \(19.6\times 10^{-10}~\text{N/m}^2\)
3. \(19.6\times 10^{10}~\text{N/m}^2\)
4. \(19.6\times 10^{-8}~\text{N/m}^2\)

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 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. \(4.86\times 10^{-6}~\text{m}\)
2. \(3.92\times 10^{-7}~\text{m}\)
3. \(3.01\times 10^{-7}~\text{m}\)
4. \(6.36\times 10^{-7}~\text{m}\)

A uniform cube is subjected to volume compression. If each side is decreased by \(1\%\), then bulk strain is:

A square lead slab of side \(50~\text{cm}\) and thickness \(10~\text{cm}\) is subject to a shearing force (on its narrow face) of \(9.0\times 10^{4}~\text{N}.\)$\mathrm{}$ The lower edge is riveted to the floor as shown in the figure below. How much will the upper edge be displaced? (Shear modulus of lead \(= 5.6\times 10^{9}~\text{Nm}^{-2}\))