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Q. No.Subtopic: Elasticity |
85%
Level 1: 80%+
Hints
The dimensions of the ratio of pressure to the elastic modulus is:
| 1. | \([ML^{-2}]\) | 2. | \([LT^{-2}]\) |
| 3. | \([L^2]\) | 4. | \([M^0L^0T^0]\) (dimensionless) |
Subtopic: Shear and bulk modulus |
89%
Level 1: 80%+
Hints
The equivalent of spring constant \(k\) for a wire of length \(L\), cross-sectional area, and Young's modulus \(Y\)is:
1. \(\dfrac{Y L}{A} \)
2. \(\dfrac{YA}{L}\)
3. \(\dfrac{A L}{Y}\)
4. \( YAL \)
1. \(\dfrac{Y L}{A} \)
2. \(\dfrac{YA}{L}\)
3. \(\dfrac{A L}{Y}\)
4. \( YAL \)
Subtopic: Young's modulus |
88%
Level 1: 80%+
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The energy density in a wire which is under stress is given by:
| 1. | \({\Large\frac12}\text{(stress)}^2 \) | 2. | \({\Large\frac12}\text{(strain)}^2\) |
| 3. | \({\Large\frac12}\text{(stress)}\times\text{(strain)}\) | 4. | \({\Large\frac{1}{2}\frac{\text{(stress)}^2}{\text{strain}}}\) |
Subtopic: Potential energy of wire |
87%
Level 1: 80%+
Hints
A block of mass \(M\) is attached to a prop on a smooth horizontal surface of a truck by means of a wire of length \(L,\) cross-section \(\alpha.\) Young's modulus of elasticity of the material of the wire is \(Y.\) The truck accelerates forward with an acceleration \(a=\dfrac{g}{2}.\) The change in length of the wire is:
| 1. | \({\dfrac{MgL}{\alpha Y}}\) | 2. | \({ \dfrac{MgL}{2\alpha Y}}\) |
| 3. | \({\dfrac{2MgL}{\alpha Y}}\) | 4. | \({ \dfrac{MgL}{4\alpha Y}}\) |
Subtopic: Stress - Strain |
86%
Level 1: 80%+
Hints
Given below are two statements:
| Statement I: | Stress is proportional to the strain, within elastic limit (Hooke's law limit). |
| Statement II: | The energy stored locally in an elastic body, when it is under stress (within Hooke's law limit), is proportional to the product of the stress and the strain. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Hooke's Law |
77%
Level 2: 60%+
Hints
The dimensions of stress, strain, and Young's modulus of elasticity are, respectively:
| 1. | \(\left[MT^{-2}\right], ~[L]~,~\left[ML^{-1}T^{-2}\right]\) |
| 2. | \(\left[ML^{-1}T^{-2}\right],~\left[M^0L^{0}T^{0}\right],~\left[ML^{-1}T^{-2}\right]\) |
| 3. | \(\left[M^0L^0T^0\right],~[L]~,~\left[ML^{-1}T^{-2}\right]\) |
| 4. | \(\left[MLT^{-2}\right]~,\left[ML^2T^{-2}\right],~\left[MT^{-2}\right]\) |
Subtopic: Young's modulus |
90%
Level 1: 80%+
Hints
The SI unit of Bulk modulus is same as:
| 1. | Young's modulus |
| 2. | Stress |
| 3. | Poisson's ratio |
| 4. | Both (1) and (2) |
Subtopic: Shear and bulk modulus | Young's modulus |
83%
Level 1: 80%+
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A steel plate of face area \(1~\text{cm}^2\) and thickness \(4~\text{cm}\) is rigidly fixed at the lower surface. The tangential force \(F=10~\text{kN}\) is applied on the upper surface, as shown in the figure. The lateral displacement \(x\) of the upper surface with respect to the lower surface is:
(given, the modulus of rigidly for steel is \(8 \times 10^{11}~\text{N/m}^2)\)
1. \(5.0 \times 10^{-5}~\text{m} \)
2. \(5.0 \times 10^{-6}~\text{m} \)
3. \(2.5 \times 10^{-3}~\text{m} \)
4. \(2.5 \times 10^{-4}~\text{m} \)
Subtopic: Young's modulus |
79%
Level 2: 60%+
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Work done by the restoring force in a wire within its elastic limit is \(-10~\text{J}\). The maximum amount of heat produced in the wire is:
1. \(10~\text{J}\)
2. \(20~\text{J}\)
3. \(5~\text{J}\)
4. \(15~\text{J}\)
1. \(10~\text{J}\)
2. \(20~\text{J}\)
3. \(5~\text{J}\)
4. \(15~\text{J}\)
Subtopic: Potential energy of wire |
79%
Level 2: 60%+
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