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Q. No.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. \(1.67\times10^{-4}~\text{m}^2\)
Subtopic: Stress - Strain |
79%
From NCERT
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A square aluminium (shear modulus is \(25\times10^{9}~\text{Nm}^{-2}\)) slab of side \(60~\text{cm}\) and thickness of \(15~\text{cm}\) is subjected to a shearing force (on its narrow face) of \(18.0\times10^{4}~\text {N}.\) The lower edge is riveted to the floor. The displacement of the upper edge is:
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
1. \(30~\mu \text m\)
2. \(48~\mu \text m\)
3. \(16~\mu \text m\)
4. \(64~\mu \text m\)
Subtopic: Shear and bulk modulus |
59%
From NCERT
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The force required to stretch a wire of cross-section \(1\) cm2 to double its length will be:
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
(Given Young’s modulus of the wire \(=2\times10^{11}\) N/m2)
1. \(1\times10^{7}\) N
2. \(1.5\times10^{7}\) N
3. \(2\times10^{7}\) N
4. \(2.5\times10^{7}\) N
Subtopic: Young's modulus |
81%
From NCERT
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A wire of length \(\mathrm{L}\) is hanging from a fixed support. The length changes to \(\mathrm{L}_{1}\) and \(\mathrm{L}_{2}\) when masses \(1\) kg and \(2\) kg are suspended respectively from its free end. The value of \(\mathrm{L}\) is equal to:
1. \(\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}} \)
2. \(\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2} \)
3. \(2 \mathrm{~L}_{1}-\mathrm{L}_{2} \)
4. \(3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}\)
1. \(\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}} \)
2. \(\frac{\mathrm{L}_{1}+\mathrm{L}_{2}}{2} \)
3. \(2 \mathrm{~L}_{1}-\mathrm{L}_{2} \)
4. \(3 \mathrm{~L}_{1}-2 \mathrm{~L}_{2}\)
Subtopic: Young's modulus |
78%
From NCERT
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The bulk modulus of a liquid is \(3\times10^{10}\) Nm–2. The pressure required to reduce the volume of liquid by \(2\text{%}\) is:
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
1. \(3\times10^{8}\) Nm–2
2. \(9\times10^{8}\) Nm–2
3. \(6\times10^{8}\) Nm–2
4. \(12\times10^{8}\) Nm–2
Subtopic: Shear and bulk modulus |
90%
From NCERT
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A vertical wire \(5~\text m\) long and \(8\times 10^{-3}~\text{cm}^2\) cross-sectional area has Young's modulus \(=200~\text {GPa}\) (as shown in the figure). What will be the extension in its length, when a \(2~\text{kg}\) object is fastened to its free end?
1. \(0.625~\text{mm}\)
2. \(0.65~\text{mm}\)
3. \(0.672~\text{mm}\)
4. \(0.72~\text{mm}\)
1. \(0.625~\text{mm}\)
2. \(0.65~\text{mm}\)
3. \(0.672~\text{mm}\)
4. \(0.72~\text{mm}\)
Subtopic: Young's modulus |
87%
From NCERT
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A material like rubber which can be stretched to cause large strain is called:
1. highly elastic
2. ductile
3. plastic
4. elastomers
1. highly elastic
2. ductile
3. plastic
4. elastomers
Subtopic: Stress - Strain Curve |
63%
From NCERT
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A wire can sustain a weight of \(20~\text{kg}\) before breaking. If the wire is cut into two equal pieces, each part can support a weight of:
| 1. | \(10~\text{kg}\) | 2. | \(20~\text{kg}\) |
| 3. | \(40~\text{kg}\) | 4. | \(80~\text{kg}\) |
Subtopic: Stress - Strain |
77%
From NCERT
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The elastic behaviour of a material for linear stress and linear strain is captured in the graph below. The energy density, for a linear strain of \(5 \times 10^{-4} \) is:
\((\)assume that the material is elastic up to the linear strain of \(5 \times 10^{-4})\)
\((\)assume that the material is elastic up to the linear strain of \(5 \times 10^{-4})\)
| 1. | \(15\) kJ/m3 | 2. | \(20\) kJ/m3 |
| 3. | \(25\) kJ/m3 | 4. | \(30\) kJ/m3 |
Subtopic: Stress - Strain Curve |
76%
From NCERT
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Poisson's ratio of a material is \(0.5.\) If the force is applied to a wire of this material, decrement in cross-sectional area of the wire is \(4\text{%}.\) The percentage increase in its length is:
1. \(1\text{%}\)
2. \(2\text{%}\)
3. \(2.5\text{%}\)
4. \(4\text{%}\)
1. \(1\text{%}\)
2. \(2\text{%}\)
3. \(2.5\text{%}\)
4. \(4\text{%}\)
Subtopic: Poisson's Ratio |
61%
From NCERT
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