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:

Copper of fixed volume \(V\) is drawn into a wire of length \(l.\) When this wire is subjected to a constant force \(F,\) the extension produced in the wire is \(\Delta l.\) Which of the following graphs is a straight line?
1. \(\Delta l ~\text{vs}~\frac{1}{l}\)
2. \(\Delta l ~\text{vs}~l^2\)
3. \(\Delta l ~\text{vs}~\frac{1}{l^2}\)
4. \(\Delta l ~\text{vs}~l\)

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?

A light rod of length \(2~\text{m}\) is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight \(W\) is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area \(A_1 = 0.1~\text{cm}^2\) and brass wire of cross-sectional area\(A_2 = 0.2~\text{cm}^2\). To have equal stress in both wires, \(\frac{T_1}{T_2}?\)${\mathrm{}}_{}$

The stress versus strain graphs for wires of two materials \(A\) and \(B\) are as shown in the figure. If \(Y_A\) $\mathrm{and}$ \(Y_B\) are the Young's moduli of the materials, then:

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 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. \(\frac{\frac{3}{4}W+W_1}{A}\)