Q. No.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?
Choose the correct option from the options given below:
Which of the following expressions have units of power?
| (A) | \(\dfrac{mv^2}{2t}\) |
| (B) | \(\dfrac{V^2}{R}\) |
| (C) | \(\dfrac{mgh}{t}\) |
| 1. | (A) and (B) only |
| 2. | (A) only |
| 3. | (B) and (C) only |
| 4. | (A), (B), and (C) |
Subtopic: Dimensions |
73%
Level 2: 60%+
Hints
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 |
63%
Level 2: 60%+
Hints
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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 |
62%
Level 2: 60%+
Hints
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%
Level 1: 80%+
Hints
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 |
63%
Level 2: 60%+
Hints
Which two of the following five physical parameters have the same dimensions?
| (A) | Energy density |
| (B) | Refractive index |
| (C) | Dielectric constant |
| (D) | Young's modulus |
| (E) | Magnetic field |
Choose the correct option from the given ones:
| 1. | (B) and (D) |
| 2. | (C) and (E) |
| 3. | (A) and (D) |
| 4. | (A) and (E) |
Subtopic: Dimensions |
73%
Level 2: 60%+
AIPMT - 2008
Hints
Match List-I with List-II.
Choose the correct option from the given ones:
| List-I | List-II | ||
| (a) | \({h} \) (Planck's constant) | (i) | \([MLT^{-1}]\) |
| (b) | \({E} \) (kinetic energy) | (ii) | \([ML^2T^{-1}]\) |
| (c) | \(V\) (electric potential) | (iii) | \([ML^2T^{-2}]\) |
| (d) | \(p\) (linear momentum) | (iv) | \([ML^2A^{-1}T^{-3}]\) |
Choose the correct option from the given ones:
| 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 |
89%
Level 1: 80%+
Hints
Links
Which of the following quantities have the same dimension?
1. B, C
2. A, B, C
3. B, D
4. A, B, C, D
| (A) | \(\dfrac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}\) | (B) | \(\text{Torque}\times\text{time}\) |
| (C) | \(\text{Momentum}\times\text{length}\) | (D) | \(\dfrac{\text{Power}}{\text{time}}\) |
2. A, B, C
3. B, D
4. A, B, C, D
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
Which of the quantities below have the same dimensions?
1. A, B
2. B, C
3. A, C
4. A, B, C
| (A) | \(\dfrac{\text{electric field }\times\text{ magnetic field}}{\mu_0}\) |
| (B) | \(\dfrac{\varepsilon_0\times\text{(electric potential)}^2\times\text{ velocity}}{\text{area}}\) |
| (C) | \(\dfrac{\text{power}}{\text{area}}\) |
2. B, C
3. A, C
4. A, B, C
Subtopic: Dimensions |
Level 3: 35%-60%
Hints
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
| (a) | \(y = a\sin \left(2\pi t / T\right)\) |
| (b) | \(y = a\sin(vt)\) |
| (c) | \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\) |
| (d) | \(y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)\) |
(Symbols have their usual meanings.)
Choose the correct option:
| 1. | (a), (c) |
| 2. | (a), (b) |
| 3. | (b), (c) |
| 4. | (a), (d) |
Subtopic: Dimensions |
61%
Level 2: 60%+
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