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Q. No.A uniform rod of mass \(10~\text{kg}\) and length \(6~\text m\) is hanged from the ceiling as shown in the figure. Given the area of the cross-section of rod \(3~\text{mm}^2\) and Young’s modulus is \(2\times10^{11}~\text{N/m}^2.\) The extension in the rod’s length is:
(Take \(g=10~\text{m/s}^2\))
1. \(1~\text{mm}\)
2. \(0.5~\text{mm}\)
3. \(0.25~\text{mm}\)
4. \(1.2~\text{mm}\)
Subtopic: Elasticity |
From NCERT
JEE
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Choose the option showing the correct relation between Poisson’s ratio(\(\sigma\)), Bulk modulus(\(B\)), and Modulus of rigidity(\(G\)).
1. \(\mathit{\sigma}{=}\frac{{3}{B}{-}{2}{G}}{{2}{G}{+}{6}{B}}\)
2. \(\mathit{\sigma}{=}\frac{{6}{B}{+}{2}{G}}{{3}{B}{-}{2}{G}}\)
3. \(\mathit{\sigma}{=}\frac{9BG}{{3}{B}{+}{G}}\)
4. \({B}{=}\frac{{3}\mathit{\sigma}{-}{3}{G}}{{6}\mathit{\sigma}{+}{2}{G}}\)
1. \(\mathit{\sigma}{=}\frac{{3}{B}{-}{2}{G}}{{2}{G}{+}{6}{B}}\)
2. \(\mathit{\sigma}{=}\frac{{6}{B}{+}{2}{G}}{{3}{B}{-}{2}{G}}\)
3. \(\mathit{\sigma}{=}\frac{9BG}{{3}{B}{+}{G}}\)
4. \({B}{=}\frac{{3}\mathit{\sigma}{-}{3}{G}}{{6}\mathit{\sigma}{+}{2}{G}}\)
Subtopic: Elasticity |
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JEE
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Subtopic: Elasticity |
From NCERT
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Elastic forces are:
| 1. | always conservative |
| 2. | not always conservative |
| 3. | never conservative |
| 4. | none of the above |
Subtopic: Hooke's Law |
From NCERT
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Select the incorrect definition:
| 1. | Deforming Force: A force that changes the configuration of a body. |
| 2. | Elasticity: The property of regaining the original configuration. |
| 3. | Plastic body: A body that can be easily melted. |
| 4. | Elastic limit: The point beyond which a material begins to flow. |
Subtopic: Elasticity |
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Two equal and opposite forces, each of magnitude \(F,\) are applied along a rod of transverse sectional area \(A.\) The normal stress on a section \(PQ\) inclined at an angle \(\theta\) to the transverse section is given by:
| 1. | \(\dfrac{F}{A} \mathrm{sin \theta}\) | 2. | \(\dfrac{F}{A} \mathrm{cos \theta}\) |
| 3. | \(\dfrac{F}{2A} \mathrm{sin2 \theta}\) | 4. | \(\dfrac{F}{A} \mathrm{cos^2 \theta}\) |
Subtopic: Stress - Strain |
From NCERT
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One end of uniform wire of length \(L\) and of weight \(W\) is attached rigidly to a point in a roof and a weight \(W_1\) is suspended from the lower end. If \(A\) is area of cross-section of the wire, the stress in the wire at a height \(3L \over 4\) from its lower end is:
1. \(W_1 \over A\)
2. \(\frac{\left(W_1+\frac{W}{4}\right)}{A} \)
3. \(\left(W_1+ {3W \over 4}\right) \over A\)
4. \(W_1 + W \over A\)
1. \(W_1 \over A\)
2. \(\frac{\left(W_1+\frac{W}{4}\right)}{A} \)
3. \(\left(W_1+ {3W \over 4}\right) \over A\)
4. \(W_1 + W \over A\)
Subtopic: Stress - Strain |
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From NCERT
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Consider a uniform beam \(\text{AB},\) which is being pulled by a horizontal force \(F\) applied at the end \(\text A,\) so that it is accelerated uniformly. The cross-section of the beam is \(A.\) Let the stress at the ends \(\text A,\text B\) be \(S_\text A,S_\text B\) and that at the centre \(\text C\) be \(S_\text C.\) Then:
| 1. | \(S_\text A=\text{zero},S_\text B=\text{maximum,}\) \(S_\text C=\text{intermediate}\) |
| 2. | \(S_\text A=\text{maximum, }S_\text B=0,\) \(S_\text C=\text{intermediate}\) |
| 3. | \(S_\text A=S_\text B=\text{maximum},\) \(S_\text C=\text{zero}\) |
| 4. | \(S_\text A=S_\text B=S_\text C=\text{constant throughout}\) |
Subtopic: Stress - Strain |
From NCERT
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An ideal gas has an isothermal bulk modulus of \(B_1.\) Its volume is doubled, isothermally. The bulk modulus is now:
| 1. | \(B_1\) | 2. | \(2B_1\) |
| 3. | \( \dfrac {B_1}{2}\) | 4. | \(\dfrac {B_1}{\sqrt 2}\) |
Subtopic: Shear and bulk modulus |
From NCERT
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A uniform rod \(AB\) is rotated at a constant angular speed about its end \(A,\) the rotation axis being perpendicular to \(AB.\) During rotation, stresses are set up in the rod. Let the stress at \(A\) be \(\sigma_A\) and that at the centre \(C\) be \(\sigma_C.\) Then:
1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
Subtopic: Stress - Strain |
From NCERT
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