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

A vessel of \(1\times 10^{-3}\) m³ volume contains oil. When a pressure of \(1.2 \times10^5\) N/m² is applied on it, then volume decreases by \(0.3 \times 10^{-6}\) m³. The bulk modulus of oil is:

A ball falling into a lake of depth 200 m shows a 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

1. $19.6\times {10}^{8}N/m^2$               

2. $19.6\times {10}^{-10}N/m^2$

3. $19.6\times {10}^{10}N/m^2$               

4. $19.6\times {10}^{-8}N/m^2$

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

The modulus of rigidity of the ideal liquid is:

The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 GPa. What is the vertical deflection of this face?

$\mathrm{}$
1. 4.86×10^-6m

2. 3.92×10^-7m

3. 3.01×10^-7m

4. 6.36×10^-7m

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

1.   0.16 mm

2.   1.8 mm

3.   18 mm

4.   16 mm