A wire of cross-section \(A_{1}\) and length \(l_1\) breaks when it is under tension \(T_{1};\) a second wire made of the same material but of cross-section \(A_{2}\) and length \(l_2\) breaks under tension \(T_{2}.\) A third wire of the same material having cross-section \(A,\) length \(l\) breaks under tension \(\frac{T_1+T_2}{2}\). Then,

A steel wire of length \(4.7\) m and cross-sectional area \(3.0 \times 10^{-5}\) m² is stretched by the same amount as a copper wire of length \(3.5\) m and cross-sectional area of \(4.0 \times 10^{-5}\) m² under a given load. The ratio of Young’s modulus of steel to that of copper is:
1. \(1.79:1\)
2. \(1:1.79\)
3. \(1:1\)
4. \(1.97:1\)

Two wires of diameter \(0.25\) cm, one made of steel and the other made of brass are loaded, as shown in the figure. The unloaded length of the steel wire is \(1.5\) m and that of the brass wire is \(1.0\) m. The elongation of the steel wire will be:
(Given that Young's modulus of the steel, \(Y_S=2 \times 10^{11}\) Pa$\mathrm{}$ and Young's modulus of brass, \(Y_B=1 \times 10^{11}\) Pa)

A rope \(1\) cm in diameter breaks if the tension in it exceeds \(500\) N. The maximum tension that may be given to a similar rope of diameter \(2\) cm is:
1. \(500\) N
2. \(250\) N
3. \(1000\) N
4. \(2000\) N

The length of a metal wire is \(l_1\) when the tension in it is \(T_1\) and is \(l_2\) when the tension is \(T_2.\) The natural length of the wire is:
1. \(\frac{l_{1}+l_{2}}{2}\)

2. \(\sqrt{l_{1} l_{2}}\)

3. \(\frac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)

4. \(\frac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)