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Q. No.The dimensional formula of modulus of rigidity is:
1. \(\left [\mathrm{ML}^{-1} \mathrm{~T}^{-2} \right] \)
2. \(\left [ \mathrm{ML}^{-2} \mathrm{~T}^{2} \right ] \)
3. \(\left [ \mathrm{MLT}^{-1} \right ] \)
4. \(\left [ \mathrm{ML}^{} \mathrm{~T}^{-2} \right ] \)
Subtopic: Dimensions |
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Level 2: 60%+
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The dimensions of the Planck constant are equal to that of:
1. energy
2. momentum
3. angular momentum
4. power
1. energy
2. momentum
3. angular momentum
4. power
Subtopic: Dimensions |
79%
Level 2: 60%+
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If momentum \([P],\) area \([A]\) and time \([T]\) are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is:
1. \([PA^{-1}T^0]\)
2. \([PAT^{-1}]\)
3. \([PA^{-1}T]\)
4. \([PA^{-1}T^{-1}]\)
1. \([PA^{-1}T^0]\)
2. \([PAT^{-1}]\)
3. \([PA^{-1}T]\)
4. \([PA^{-1}T^{-1}]\)
Subtopic: Dimensions |
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Level 2: 60%+
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In a Vernier Calipers. \(10\) divisions of the Vernier scale is equal to the \(9\) divisions of the main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and \(4\)th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\) mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6\)th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:
1. \(3.02~\text{cm}\)
2. \(3.06~\text{cm}\)
3. \(3.10~\text{cm}\)
4. \(3.20~\text{cm}\)
1. \(3.02~\text{cm}\)
2. \(3.06~\text{cm}\)
3. \(3.10~\text{cm}\)
4. \(3.20~\text{cm}\)
Subtopic: Measurement & Measuring Devices |
52%
Level 3: 35%-60%
Hints
Which, among the pairs of quantities has the same dimensions?
| 1. | \({\large\frac{\text{force}}{\text{volume}}},\text{ surface tension}\) |
| 2. | \(\text{torque},\text{ pressure}\times\text{volume}\) |
| 3. | \(\text{specific heat}\times\text{mass},\text{ energy}\) |
| 4. | \({\large\frac{\text{pressure}}{\text{acceleration}}},\text{ density}\) |
Subtopic: Dimensions |
72%
Level 2: 60%+
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The force \(F\) acting on a body as a function of position \((x)\) and time \((t)\) is expressed as \(F=A \sin \left(k_1 x\right)+B \cos \left(k_2 t\right).\) From the given information, match Column-I with Column-II.
Codes:
| Column-I | Column-II | ||
| \((\mathrm A)\) | Dimensions of \(A\) | \((\mathrm P)\) | \([M^0L^0T^{-1}]\) |
| \((\mathrm B)\) | Dimensions of \(k_{1}\) | \((\mathrm Q)\) | \([M^0L^{-1}T^{-1}]\) |
| \((\mathrm C)\) | Dimensions of \(k_{2}\) | \((\mathrm R)\) | \([MLT^{-2}]\) |
| \((\mathrm D)\) | Dimensions of \(k_{1}k_{2}\) | \((\mathrm S)\) | \([M^0L^{-1}T^{0}]\) |
| 1. | \(\mathrm {A \rightarrow R, B \rightarrow S, C \rightarrow P, D \rightarrow Q }\) |
| 2. | \(\mathrm {A \rightarrow P, B \rightarrow Q, C \rightarrow R, D \rightarrow S }\) |
| 3. | \(\mathrm {A \rightarrow R, B \rightarrow P, C \rightarrow Q, D \rightarrow S }\) |
| 4. | \(\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R}\) |
Subtopic: Dimensions |
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Level 2: 60%+
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Given below are two statements:
| Statement A: | In a number less than \(1\), all zeros on the right of decimal point are significant. |
| Statement B: | Zeros between two non-zero numbers are not significant. |
| 1. | Statement A is correct. |
| 2. | Statement B is correct. |
| 3. | Both Statements A and Statement B are correct. |
| 4. | Both Statements A and Statement B are incorrect. |
Subtopic: Significant Figures |
59%
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | When we change the unit of measurement of a quantity, its numerical value changes. |
| Reason (R): | The smaller the unit of measurement, the smaller is its numerical value. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Dimensions |
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For a real gas the equation of gas is given by; \(\left({P+{{an^{2}}\over{V^{2}}}}\right)\left({V-bn}\right)=nRT\). If symbols have their usual meaning, then the dimensions of \({{V^{2}}\over{an^{2}}}\) is same as that of:
1. compressibility
2. bulk modulus
3. viscosity
4. energy density
1. compressibility
2. bulk modulus
3. viscosity
4. energy density
Subtopic: Dimensions |
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Level 2: 60%+
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The mass of a box measured by the grocer’s balance is \(2.300~\text{kg}\). Two gold pieces of masses \(20.15~\text{g}\) and \(20.17~\text{g}\) are added to the box. The total mass of the box and the difference in the masses of the gold piece, recorded to correct significant figures, will be, respectively:
| 1. | \(2340.32~\text{g}\), \(0.002~\text{g}\) |
| 2. | \(2.340~\text{kg}\), \(0.02~\text{g}\) |
| 3. | \(2.3~\text{kg}\), \(0~\text{g}\) |
| 4. | \(2.334032~\text{kg}\), \(0.02~\text{g}\) |
Subtopic: Significant Figures |
65%
Level 2: 60%+
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