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Q. No.Consider two wires \(X\) and \(Y.\) The radius of the wire \(X\) is \(3\) times the radius of \(Y.\) If they are stretched by the same load, then the stress on \(Y\) is:
| 1. | equal to that on \(X\) | 2. | thrice that on \(X\) |
| 3. | nine times that on \(X\) | 4. | half that on \(X\) |
Subtopic: Stress - Strain |
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The breaking stress of a wire depends on:
| 1. | material of the wire |
| 2. | length of the wire |
| 3. | radius of the wire |
| 4. | shape of the cross-section |
Subtopic: Stress - Strain |
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Level 1: 80%+
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The area of cross-section of the rope used to lift a load by a crane is \(2.5\times10^{-4}~\text{m}^2.\) The maximum lifting capacity of the crane is \(10~\text{metric tons}.\) To increase the lifting capacity of the crane to \(25~\text{metric tons},\) the required area of the cross-section of the rope should be: (Take \(g=10~\text{ms}^{-2}\) )
1. \(6.25\times10^{-4}~\text{m}^2\)
2. \(10\times10^{-4}~\text{m}^2\)
3. \(1\times10^{-4}~\text{m}^2\)
4. \(1.67\times10^{-4}~\text{m}^2\)
1. \(6.25\times10^{-4}~\text{m}^2\)
2. \(10\times10^{-4}~\text{m}^2\)
3. \(1\times10^{-4}~\text{m}^2\)
4. \(1.67\times10^{-4}~\text{m}^2\)
Subtopic: Stress - Strain |
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Level 2: 60%+
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The breaking stress in two wires of different materials \(A,B\) are in the ratio: \(\dfrac{S_A}{S_B}=\dfrac12,\) while their radii are in the ratio: \(\dfrac{r_A}{r_B}=\dfrac12.\) The tensions under which they break are \(T_A\) and \(T_B.\) Then \(\dfrac{T_A}{T_B}=\)?
| 1. | \(2\) | 2. | \(\dfrac14\) |
| 3. | \(\dfrac18\) | 4. | \(\dfrac1{2\sqrt2}\) |
Subtopic: Stress - Strain |
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Level 2: 60%+
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A metal wire of length \(0.5\) m and cross-sectional area \(10^{-4}\) m2 has breaking stress \(5\times10^{8}\) Nm–2. A block of \(10\) kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of the block will be:
1. \(15\) m/s
2. \(50\) m/s
3. \(25\) m/s
4. \(40\) m/s
1. \(15\) m/s
2. \(50\) m/s
3. \(25\) m/s
4. \(40\) m/s
Subtopic: Stress - Strain |
78%
Level 2: 60%+
JEE
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Consider two wires \(A\) and \(B\) which are made of same material. The diameter of \(A\) is four times larger than \(B.\) If they are stretched by same load, then the stress on \(B\) is:
1. equal to that on \(A\)
2. sixteen times that on \(A\)
3. twice that on \(A\)
4. half that on \(A\)
1. equal to that on \(A\)
2. sixteen times that on \(A\)
3. twice that on \(A\)
4. half that on \(A\)
Subtopic: Stress - Strain |
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Level 1: 80%+
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Let a wire be suspended from the ceiling (rigid support) and stretched by a weight \(W\) attached at its free end. The longitudinal stress at any point of the cross-sectional area \(A\) of the wire is:
| 1. | zero | 2. | \(\frac{2W}{A}\) |
| 3. | \(\frac{W}{A}\) | 4. | \(\frac{W}{2A}\) |
Subtopic: Stress - Strain |
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Level 2: 60%+
NEET - 2023
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A steel cable with a radius of \(1.5~\text{cm}\) supports a chairlift at a ski area. If the maximum stress is not to exceed \(10^{8}~\text{N/m}^2,\) what is the maximum load that the cable can support?
1. \(7.06\times 10^{4}~\text{N}\)
2. \(5.03\times 10^{4}~\text{N}\)
3. \(1.09\times 10^{4}~\text{N}\)
4. \(17\times 10^{4}~\text{N}\)
1. \(7.06\times 10^{4}~\text{N}\)
2. \(5.03\times 10^{4}~\text{N}\)
3. \(1.09\times 10^{4}~\text{N}\)
4. \(17\times 10^{4}~\text{N}\)
Subtopic: Stress - Strain |
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A spring is stretched by applying a load to its free end. The strain produced in the spring is:
1. volumetric2. shear
3. longitudinal and shear
4. longitudinal
Subtopic: Stress - Strain |
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Level 2: 60%+
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A rod of length \(1.05\) m having negligible mass is supported at its ends by two wires of steel (wire \(A\)) and aluminium (wire \(B\)) of equal lengths as shown in the figure. The cross-sectional areas of wires \(A\) and \(B\) are \(1.0~\text{mm}^2\) and \(2.0~\text{mm}^2\) respectively. At what point along the rod should a mass m be suspended in order to produce equal stresses in both steel and aluminium wires?
| 1. | \(0.7\) m from wire \(A\) |
| 2. | \(0.07\) m from wire \(A\) |
| 3. | \(7.0\) m from wire \(A\) |
| 4. | \(0.007\) m from wire \(A\) |
Subtopic: Stress - Strain |
63%
Level 2: 60%+
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