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Q. No.Four students measure the height of a tower. Each student uses a different method and each measures the height many times. The data for each are plotted below. The measurement with the highest precision is:
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| (I) | (II) |
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| (III) | (IV) |
1. I
2. II
3. III
4. IV
Subtopic: Errors |
59%
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In the expressions below: \(g\) = gravitational acceleration; \(h\) = height; \(m\) = mass; \(R\) = electrical resistance; \(t\) = time; \(v\) = velocity; \(V\) = voltage. Which of the following expressions have units of power?
(a) \(\frac{mv^2}{2t}\)
(b) \(\frac{V^2}{R}\)
(c) \(\frac{mgh}{t}\)
(a) \(\frac{mv^2}{2t}\)
(b) \(\frac{V^2}{R}\)
(c) \(\frac{mgh}{t}\)
| 1. | (a) and (b) only |
| 2. | (a) only |
| 3. | (b) and c) only |
| 4. | (a), (b) and (c) |
Subtopic: Dimensions |
72%
From NCERT
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Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I | List-II | ||
| (a) | Gravitational constant (\(G\)) | (i) | \([{L}^2 {~T}^{-2}] \) |
| (b) | Gravitational potential energy | (ii) | \([{M}^{-1} {~L}^3 {~T}^{-2}] \) |
| (c) | Gravitational potential | (iii) | \([{LT}^{-2}] \) |
| (d) | Gravitational intensity | (iv) | \([{ML}^2 {~T}^{-2}]\) |
Choose the correct answer from the options given below:
| (a) | (b) | (c) | (d) | |
| 1. | (iv) | (ii) | (i) | (iii) |
| 2. | (ii) | (i) | (iv) | (iii) |
| 3. | (ii) | (iv) | (i) | (iii) |
| 4. | (ii) | (iv) | (iii) | (i) |
Subtopic: Dimensions |
71%
From NCERT
NEET - 2022
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Which of the following equations is dimensionally correct?
\((I)~~ v=\sqrt{\dfrac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\dfrac{mgl}{I}}~~~~~~(III)~~v=\dfrac{Pr^2}{2\eta l}\)
(where \(v=\) speed, \(P=\) pressure; \(r,\) \(l\) are lengths; \(\rho=\) density, \(m=\) mass, \(g=\) acceleration due to gravity, \(I=\) moment of inertia, and \(\eta=\) coefficient of viscosity)
| 1. | \(I~ \text{and}~II\) |
| 2. | \(I~ \text{and}~III\) |
| 3. | \(II~ \text{and}~III\) |
| 4. | \(I,~II~\text{and}~III\) |
Subtopic: Dimensions |
68%
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Match the units mentioned in List-I with the units in List-II.
| List-I | List-II |
| (a) H/s | (i) s2 |
| (b) H×A | (ii) Wb |
| (c) H×F | (iii) s |
| (d) \(\Omega\)×F | (iv) \(\Omega\) |
| 1. | (a) – (ii), (b) – (iv), (c) – (i), (d) – (iii) |
| 2. | (a) – (iv), (b) – (ii), (c) – (i), (d) – (iii) |
| 3. | (a) – (iv), (b) – (ii), (c) – (iii), (d) – (i) |
| 4. | (a) – (ii), (b) – (iii), (c) – (iv), (d) – (i) |
Subtopic: Dimensions |
65%
From NCERT
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Match the following quantities in List-I with their dimensions in List-II.
| List-I | List-II | ||
| (a) | acceleration | (i) | \([M^0L^0T^0 ]\) |
| (b) | torque | (ii) | \([ML^{-1}T^{-2} ]\) |
| (c) | absorptive power | (iii) | \([LT^{-2} ]\) |
| (d) | pressure | (iv) | \([ML^2T^{-2} ]\) |
| 1. | (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) |
| 2. | (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv) |
| 3. | (a)-(iii), (b)-(i), (c)-(ii), (d)-(iv) |
| 4. | (a)-(ii), (b)-(iv), (c)-(iii), (d)-(i) |
Subtopic: Dimensions |
86%
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Match the units of some physical quantities in List I with their corresponding dimensions in List II.
| List I | List II | ||
| (a) | Ohm | (i) | \([ML^2T^{-2}A^{-1}]\) |
| (b) | Farad | (ii) | \([ML^2T^{-2}A^{-2}]\) |
| (c) | Henry | (iii) | \([M^{-1}L^{-2}T^4A^2]\) |
| (d) | Weber | (iv) | \([ML^2T^{-3}A^{-2}]\) |
| 1. | (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) |
| 2. | (a)-(iv), (b)-(iii), (c)-(i), (d)-(ii) |
| 3. | (a)-(ii), (b)-(iii), (c)-(i), (d)-(iv) |
| 4. | (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) |
Subtopic: Dimensions |
65%
From NCERT
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Which two of the following five physical parameters have the same dimensions?
| (1) | Energy density |
| (2) | Refractive index |
| (3) | Dielectric constant |
| (4) | Young's modulus |
| (5) | Magnetic field |
Choose the correct option:
| 1. | (2) and (4) |
| 2. | (3) and (5) |
| 3. | (1) and (4) |
| 4. | (1) and (5) |
Subtopic: Dimensions |
72%
From NCERT
AIPMT - 2008
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Match List-I with List-II:
| List-I | List-II | ||
| (a) | \(h\) (Planck's constant) | (i) | \(\left[ MLT^{-1} \right]\) |
| (b) | \(E\) (kinetic energy) | (ii) | \(\left[ ML^{2}T^{-1} \right]\) |
| (c) | \(V\) (electric potential) | (iii) | \(\left[ ML^{2}T^{-2} \right]\) |
| (d) | \(p\) (linear momentum) | (iv) | \(\left[ ML^{2}A^{-1}T^{-3} \right]\) |
| 1. | (a) → (iii), (b) → (iv), (c) → (ii), (d) → (i) |
| 2. | (a) → (ii), (b) → (iii), (c) → (iv), (d) → (i) |
| 3. | (a) → (i), (b) → (ii), (c) → (iv), (d) → (iii) |
| 4. | (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) |
Subtopic: Dimensions |
90%
From NCERT
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Which of the following quantities have the same dimension?
(A) \(\frac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) (B) \(\text{Torque}\times\text{time}\)
(C) \(\text{Momentum}\times\text{length}\) (D) \(\frac{\text{Power}}{\text{time}}\)
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
(A) \(\frac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) (B) \(\text{Torque}\times\text{time}\)
(C) \(\text{Momentum}\times\text{length}\) (D) \(\frac{\text{Power}}{\text{time}}\)
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
Subtopic: Dimensions |
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