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 $\dfrac{T_1+T_2}{2}.$ Then:

A steel wire of length $4.7~\text m$ and cross-sectional area $3.0 \times 10^{-5}~\text{m}^2$ is stretched by the same amount as a copper wire of length $3.5~\text m$ and cross-sectional area of $4.0 \times 10^{-5}~\text m^2$ 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 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: