Steel and copper wires of the same length and area are stretched by the same weight one after the other. Young's modulus of steel and copper are \(2\times10^{11} ~\text{N/m}^2\) and  \(1.2\times10^{11}~\text{N/m}^2.\) The ratio of increase in length is: 

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. \(\dfrac{3 c}{2 a b^{2}}\)

The Young's modulus of a wire is numerically equal to the stress at a point when:

A metallic rope of diameter \(1~ \text{mm}\) breaks at \(10 ~\text{N}\) force. If the wire of the same material has a diameter of \(2~\text{mm},\) then the breaking force is:

In the CGS system, Young's modulus of a steel wire is \(2\times 10^{12}~\text{dyne/cm}^2.\) To double the length of a wire of unit cross-section area, the force required is:
1. \(4\times 10^{6}~\text{dynes}\)
2. \(2\times 10^{12}~\text{dynes}\)
3. \(2\times 10^{12}~\text{newtons}\)
4. \(2\times 10^{8}~\text{dynes}\)

 The area of cross-section of a wire of length \(1.1\) m is \(1\) mm². It is loaded with mass of \(1\) kg. If Young's modulus of copper is \(1.1\times10^{11}\) N/m², then the increase in length will be: (If \(g = 10~\text{m/s}^2)\)