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. \(3~\text m\) 

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:

If the ratio of lengths, radii, and Young's modulus of steel and brass wires in the figure are \(a,\) \(b\) and \(c\) respectively, then the corresponding ratio of increase in their lengths will be:

                                    
1. \(\dfrac{2 a^{2} c}{b}\)

2. \(\dfrac{3 a}{2 b^{2} c}\)

3. \(\dfrac{2 a c}{b^{2}}\)

4. \(\dfrac{3 c}{2 a b^{2}}\)

A material has Poisson's ratio of \(0.5\). If a uniform rod made of it suffers a longitudinal strain of \(2\times 10^{-3}\), what is the percentage increase in volume?
1. \(2\%\)
2. \(4\%\)
3. \(0\%\)
4. \(5\%\)

lf \(\rho\) is the density of the material of a wire and \(\sigma\) is the breaking stress, the greatest length of the wire that can hang freely without breaking is:
1. \(\dfrac{2}{\rho g}\)

2. \(\dfrac{\rho}{\sigma g}\)

3. \(\dfrac{\rho g}{2 \sigma}\)

4. \(\dfrac{\sigma}{\rho g}\)

The work done per unit volume to stretch the length of a wire by \(1\%\) with a constant cross-sectional area will be:
\((Y = 9\times10^{11}~\text{N/m}^2)\)
1. \(9\times 10^{11}~\text{J}\)
2. \(4.5\times 10^{7}~\text{J}\)
3. \(9\times 10^{7}~\text{J}\)
4. \(4.5\times 10^{11}~\text{J}\)

A wire of length \(L\) and cross-sectional area \(A\) is made of a material of Young's modulus \(Y.\) It is stretched by an amount \(x.\) The work done is:

1. \(\dfrac{Y x A}{2 L}\)

2. \(\dfrac{Y x^{2} A}{L}\)

3. \(\dfrac{Y x^{2} A}{2 L}\)

4. \(\dfrac{2 Y x^{2} A}{L}\)