Q. No.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. | \(A=\dfrac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\dfrac{l_1T_1+l_2T_2}{2(T_1+T_2)}\) |
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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. | \(\dfrac{Y_1x_2+Y_2x_1}{Y_1+Y_2}\) |
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Two wires \((A, B)\) of identical lengths have breaking stresses in the ratio \(1:2,\) while their cross-sectional areas are the same. When a block of mass \(M\) is placed on the horizontal light rod, it is observed that wire \(A\) breaks if \(M\) is placed slightly to the left, while \(B\) breaks if \(M\) is placed slightly to right.
| 1. | \(\dfrac12\) | 2. | \(\dfrac14\) |
| 3. | \(\dfrac21\) | 4. | \(\dfrac41\) |
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| 1. | tensile, \(\dfrac{F}{3A}\) |
| 2. | compressive, \(\dfrac{F}{3A}\) |
| 3. | tensile, \(\dfrac{2F}{3A}\) |
| 4. | compressive, \(\dfrac{2F}{3A}\) |
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| 1. | \(\dfrac{3 M g l}{A Y}\) | 2. | \(\dfrac{2 M g l}{A Y}\) |
| 3. | \(\dfrac{3 M g l}{2 A Y}\) | 4. | \(\dfrac{M g l}{A Y}\) |
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1. tensile2. compressive
3. shear
4. zero
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| 1. | no stress. | 2. | compressive stress. |
| 3. | tensile stress. | 4. | shear stress. |
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| 1. |  |
2. |  |
| 3. |  |
4. |  |
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| 1. | \(1\) | 2. | \(2\) |
| 3. | \(\sqrt 2\) | 4. | \(\dfrac12\) |
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1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
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