A wire of length \(L,\) area of cross section \(A\) is hanging from a fixed support. The length of the wire changes to \({L}_1\) when mass \(M\) is suspended from its free end. The expression for Young's modulus is:
| 1. | \(\dfrac{{Mg(L}_1-{L)}}{{AL}}\) | 2. | \(\dfrac{{MgL}}{{AL}_1}\) |
| 3. | \(\dfrac{{MgL}}{{A(L}_1-{L})}\) | 4. | \(\dfrac{{MgL}_1}{{AL}}\) |
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?
| 1. | \(9F\) | 2. | \(6F\) |
| 3. | \(4F\) | 4. | \(F\) |