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Q. No.If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are \(p,\) \(q\) and \(s\) respectively, then the corresponding ratio of increase in their lengths would be:
1.
\(\dfrac{5 q}{\left(7 {sp}^2\right)} \)
2.
\(\dfrac{7 q}{\left(5 sp^2\right)} \)
3.
\(\dfrac{2 q}{(5 s p)} \)
4.
\(\dfrac{7 q}{(5 s p)}\)
Subtopic: Young's modulus |
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Level 2: 60%+
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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 |
69%
Level 2: 60%+
NEET - 2023
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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 |
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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%
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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%
Level 2: 60%+
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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 |
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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 |
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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%
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A wire of natural length \(L\) is suspended vertically from a fixed point. The length changes to \(L_1\) and \(L_2\) when masses \(1\) kg and \(2\) kg are suspended, respectively, from its free end. The value of \(L\) is:
| 1. | \(\sqrt{L_1L_2} \) | 2. | \(\dfrac{L_1+L_2}{2}\) |
| 3. | \(2L_1-L_2 \) | 4. | \(3L_1-2L_2\) |
Subtopic: Young's modulus |
75%
Level 2: 60%+
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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%
Level 1: 80%+
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