One end of a uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in the roof and a weight \(W_1\) is suspended from its lower end. If \(A\) is the area of the cross-section of the wire, the stress in the wire at a height \(\frac{3L}{4}\) from its lower end is:
1. \(\frac{W+W_1}{A}\)
2. \(\frac{4W+W_1}{3A}\)
3. \(\frac{3W+W_1}{4A}\)
4. \(\frac{\frac{3}{4}W+W_1}{A}\)

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. \(8 \times 10^{6}~\text{N/m}^2\)

To break a wire, a force of \(10^6~\text{N/m}^{2}\) is required. If the density of the material is \(3\times 10^{3}~\text{kg/m}^3,\) then the length of the wire which will break by its own weight will be:
1. \(34~\text m\) 
2. \(30~\text m\) 
3. \(300~\text m\) 
4. \(3~\text m\) 

The length of elastic string, obeying Hooke's law is \(l_1\) metres when the tension is \(4~\text{N}\), and \(l_2\) metres when the tension is \(5~\text{N}\). The length in metres when the tension is \(0~\text{N}\) will be:
1. \(5l_1-4l_2\)
2. \(5l_2-4l_1\)
3. \(9l_1-8l_2\)
4. \(9l_2-8l_1\)

Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area \(A\) and the second wire has a cross-sectional area \(3A\). If the length of the first wire is increased by \(\Delta l\) on applying a force \(F\), how much force is needed to stretch the second wire by the same amount?

Overall changes in volume and radius of a uniform cylindrical steel wire are \(0.2\%\) and \(0.002\%\) respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is: \(\left(2.0\times 10^{11}~\text{Nm}^{-2}\right)\)
1. \(3.2\times 10^{11}~\text{Nm}^{-2}\)
2. \(3.2\times 10^{7}~\text{Nm}^{-2}\)
3. \(3.6\times 10^{9}~\text{Nm}^{-2}\)
4. \(3.9\times 10^{8}~\text{Nm}^{-2}\)

A 1000 kg lift is tied with metallic wires of maximum safe stress of 1.4 $\times$ 10⁸ N m^-2. If the maximum acceleration of the lift is 1.2 m s^-2, then the minimum diameter of the wire is:
1. 1 m 

2. 0.1 m

3. 0.01 m 

4. 0.001 m

A wire can sustain a weight of 10 kg before breaking. If the wire is cut into two equal parts, then each part can sustain a weight of:

A uniform cylinder rod of length \(L\), cross-sectional area \(A\) and Young's modulus \(Y\) is acted upon by the forces, as shown in the figure. The elongation of the rod is:

           
1. \(\frac{3FL}{5AY}\)

2. \(\frac{2FL}{5AY}\)

3. \(\frac{2FL}{8AY}\)

4. \(\frac{8FL}{3AY}\)