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 \(1.03\times10^{3}~\text{kg m}^{-3}\)?

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
${\mathrm{}}^{}$

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×${10}^7$ 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

The Marina trench is located in the Pacific Ocean, and at one place it is nearly \(11 \) km beneath the surface of the water. The water pressure at the bottom of the trench is about \(1.1 \times10^8\) Pa. A steel ball of initial volume \(0.32\) m³ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches the bottom? (Given: \(B_{\mathrm{steel}}=1.6 \times10^{11}\) N/m²)${}^{}$

Select the correct alternative(s).

1. Elastic forces are not always conservative

2. Elastic forces are always conservative

3. Elastic forces are conservative only when Hooke's law is obeyed

4. Elastic forces are not conservative

Which of the following affects the elasticity of a substance?

1. Change in temperature

2. Impurity in substance

3. Hammering

4. All of these