- 1(current)
Q. No.A wire has a length \(l_1\) when it is under tension \(T_1,\) and length \(l_2\) when it is under tension \(T_2.\) When it is under a tension \(T_1 + T_2,\) its length is:
1. \(l_1+l_2\)
2. \(\dfrac{l_1T_1+l_2T_2}{T_1+T_2}\)
3. \(\dfrac{l_1T_1-l_2T_2}{T_1-T_2}\)
4. \(\dfrac{l_1T_2+l_2T_1}{T_1+T_2}\)
Two wires of identical dimensions but of different materials having Young's moduli \(Y_1, Y_2\) are joined end to end. When the first wire is under a tension \(T,\) it elongates by \(x_1\) while the second wire elongates by \(x_2\) under the same tension \(T.\) The elongation of the composite wire when it is under tension \(T\) is:
| 1. | \(x_1+x_2\) | 2. | \(\dfrac{Y_1x_1+Y_2x_2}{Y_1+Y_2}\) |
| 3. | \(\dfrac{x_1+x_2}{2}\) | 4. | \(\dfrac{Y_1x_2+Y_2x_1}{Y_1+Y_2}\) |
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:
| 1. | \(A=\dfrac{A_1+A_2}{2},~l=\dfrac{l_1+l_2}{2}\) |
| 2. | \(l=\dfrac{l_1+l_2}{2}\) |
| 3. | \(A=\dfrac{A_1+A_2}{2}\) |
| 4. | \(A=\dfrac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\dfrac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
- 1(current)
Q. No.
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