The bulk modulus of water is \(2\times 10^{9}~\text{N/m}^2\). The increase in pressure required to decrease the volume of 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. \(8 \times 10^{6}~\text{N/m}^2\)
1. | \(1 \times 10^6~\text{N/m}^2\) | 2. | \(2 \times 10^7~\text{N/m}^2\) |
3. | \(4 \times 10^8~\text{N/m}^2\) | 4. | \(6 \times 10^{10}~\text{N/m}^2\) |
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, \(10\) cm on an edge, when subjected to a hydraulic pressure of \(7.0\times10^6\) 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 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?
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:
1. | \(0.01\) | 2. | \(0.06\) |
3. | \(0.02\) | 4. | \(0.03\) |
A square lead slab of side \(50\) cm and thickness \(10\) cm is subject to a shearing force (on its narrow face) of \(9.0\times 10^{4}~\text{N}\). 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 \(= 5.6\times 10^{9}~\text{Nm}^{-2}\))
1. | \(0.16\) mm | 2. | \(1.8\) mm |
3. | \(18\) mm | 4. | \(16\) mm |