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.	\(\dfrac{l_{1}+l_{2}}{2}\)	2.	\(\sqrt{l_{1} l_{2}}\)
3.	\(\dfrac{l_{1} T_{2}-l_{2} T_{1}}{T_{2}-T_{1}}\)	4.	\(\dfrac{l_{1} T_{2}+l_{2} T_{1}}{T_{2}+T_{1}}\)

A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

When a metal wire elongates by hanging a load on it, the gravitational potential energy decreases.

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 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