Q. No.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. \(6.36\times 10^{-7}~\text{m}\)
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. \(6.36\times 10^{-7}~\text{m}\)
Four identical hollow cylindrical columns of mild steel support a big structure of a mass of \(50,000\) kg. The inner and outer radii of each column are \(30\) cm and \(60\) cm respectively. Assuming the load distribution to be uniform, the compressional strain of each column is:
(Given, Young's modulus of steel, \(Y = 2\times 10^{11}~\text{Pa}\))
| 1. | \(3.03\times 10^{-7}\) | 2. | \(2.8\times 10^{-6}\) |
| 3. | \(7.22\times 10^{-7}\) | 4. | \(4.34\times 10^{-7}\) |
1. \(7.06\times 10^{4}~\text{N}\)
2. \(5.03\times 10^{4}~\text{N}\)
3. \(1.09\times 10^{4}~\text{N}\)
4. \(17\times 10^{4}~\text{N}\)
A \(14.5\) kg mass, fastened to the end of a steel wire of unstretched length \(1.0\) m, is whirled in a vertical circle with an angular velocity of \(2\) rev/s at the bottom of the circle. The cross-sectional area of the wire is \(0.065~\text{cm}^2\). The elongation of the wire when the mass is at the lowest point of its path is:
(Young's modulus = \(2×10^{11}~\text{N/m}^2\))
| 1. | \(7 . 01 \times 10^{-3}~\text{m}\) | 2. | \(2 . 35 \times 10^{-3}~\text{m}\) |
| 3. | \( 1 . 87 \times 10^{-3}~\text{m}\) | 4. | \(3 . 31 \times 10^{-3}~\text{m}\) |
What is the density of water at a depth where pressure is \(80.0\) atm, given that its density at the surface is \(1.03\times10^{3}~\text{kg m}^{-3}\)?
| 1. | \(0 . 021 \times 10^{3}~\text{kg m}^{-3}\) | 2. | \(4.022 \times10^{3}~\text{kg m}^{-3}\) |
| 3. | \(3.034 \times 10^{3}~\text{kg m}^{-3}\) | 4. | \(1.034 \times 10^{3}~\text{kg m}^{-3}\) |
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. \(7.9 \times 10^{-2} ~\text{cm}^3 \)
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. \(3.3 \times 10^6~\text{N/m}^2\)
Anvils made of single crystals of diamond, with the shape as shown in the figure, are used to investigate the behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of \(0.50\) mm, and the wide ends are subjected to a compressional force of \(50,000\) N. What is the pressure at the tip of the anvil?
1. \(2.5\times10^{11}\) Pa
2. \(3.7\times10^{11}\) Pa
3. \(2.1\times10^{11}\) Pa
4. \(1.9\times10^{11}\) Pa
| 1. | \(0.7\) m from wire \(A\) |
| 2. | \(0.07\) m from wire \(A\) |
| 3. | \(7.0\) m from wire \(A\) |
| 4. | \(0.007\) m from wire \(A\) |
Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 6.9× Pa? (Assume that each rivet is to carry one-quarter of the load.)
1. 7850 N
2. 6000 N
3. 7070.73 N
4. 7799.76 N
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