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Q. No.If force, time, and velocity are taken as fundamental quantities, what will be the dimensional formula of energy?
1. \([{FTV}]\)
2. \([{FT}^2{V}]\)
3. \([{FT}{V}^2]\)
4. \([{FT}^2{V}^2]\)
Subtopic: Dimensions |
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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 |
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The velocity \(v\) of a particle at a time \(t\) is given by \(v=a t+\dfrac{b}{t+c}.\) The dimensions of \(a,\) \(b\) and \(c\) are respectively:
1. \(\left [ LT^{-2} \right ],\) \(\left [ L\right ],\) \(\left [ T\right ]\)
2. \(\left [ L^{2}\right ],\) \(\left [ T\right ],\) \(\left [ LT^{2} \right ]\)
3. \(\left [ LT^{2} \right ],\) \(\left [ LT \right ],\) \(\left [ L\right ]\)
4. \(\left [ L\right ],\) \(\left [ LT \right ],\) \(\left [ T^{2}\right ]\)
1. \(\left [ LT^{-2} \right ],\) \(\left [ L\right ],\) \(\left [ T\right ]\)
2. \(\left [ L^{2}\right ],\) \(\left [ T\right ],\) \(\left [ LT^{2} \right ]\)
3. \(\left [ LT^{2} \right ],\) \(\left [ LT \right ],\) \(\left [ L\right ]\)
4. \(\left [ L\right ],\) \(\left [ LT \right ],\) \(\left [ T^{2}\right ]\)
Subtopic: Dimensions |
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Which, of the following quantities, is a fundamental quantity?
| 1. | Electric charge | 2. | Magnetic field |
| 3. | Temperature | 4. | Thermal energy |
Subtopic: Dimensions |
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Two different quantities having the same dimension are:
| 1. | \(\text{momentum, power}\) | 2. | \(\text{power, pressure}\) |
| 3. | \(\text{work, torque}\) | 4. | \(\text{pressure, torque}\) |
Subtopic: Dimensions |
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Match List-I with List-II.
Choose the correct answer from the options given below:
| List-I | List-II |
| A. Torque | I. N-m s-1 |
| B. Stress | II. J-kg-1 |
| C. Latent Heat | III. N-m |
| D. Power | IV. N-m-2 |
Choose the correct answer from the options given below:
| 1. | A-III, B-II, C-I, D-IV |
| 2. | A-III, B-IV, C-II, D-I |
| 3. | A-IV, B-I, C-III, D-II |
| 4. | A-II, B-III, C-I, D-IV |
Subtopic: Dimensions |
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The equation of a circle is given by:
\( (x-At)^2+\left(y-\dfrac{t}{B}\right)^2=R^2, \)
where \(R\) is the radius of the circle, and the dimension of \(t\) is \([T].\)
The dimensions of \(A\) and \(B\) are respectively:
\( (x-At)^2+\left(y-\dfrac{t}{B}\right)^2=R^2, \)
where \(R\) is the radius of the circle, and the dimension of \(t\) is \([T].\)
The dimensions of \(A\) and \(B\) are respectively:
| 1. | \(A=\left[{L}^{-1} {T}^{-1}\right], B=\left[{L}^{-1} {T}\right] \) |
| 2. | \(A=\left[{LT}\right], B=\left[{LT}^{-1}\right] \) |
| 3. | \(A=\left[{LT}^{-1}\right], B=\left[{L}^{-1} {T}\right] \) |
| 4. | \(A=\left[{L}^{-1}{T}\right], B=\left[{L}^{-1} {T}^{-1}\right] \) |
Subtopic: Dimensions |
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Match the physical quantities given in Column-I with their corresponding dimensions in Column-II and units in Column-III.
Codes:
| Column-I (Physical Quantities) |
Column-II (Dimensions) |
Column-III (Units) |
|||
| \(\mathrm{(A)}\) | Stefan's constant \(\sigma\) | \(\mathrm{(P)}\) | \([M^1L^1T^{-2}A^{-2}]\) | \(\mathrm{(i)}\) | \(\text{W/m}^2\) |
| \(\mathrm{(B)}\) | Wien's constant \(\beta\) | \(\mathrm{(Q)}\) | \([M^{1}L^0T^{-3}K^{-4}]\) | \(\mathrm{(ii)}\) | \(\text{K.m}\) |
| \(\mathrm{(C)}\) | Coefficient of viscosity \(\eta\) | \(\mathrm{(R)}\) | \([M^1L^0T^{-3}]\) | \(\mathrm{(iii)}\) | \(\text{tesla .m/A}\) |
| \(\mathrm{(D)}\) | Emissive power of radiation | \(\mathrm{(S)}\) | \([M^0L^1T^0K^1]\) | \(\mathrm{(iv)}\) | \(\text{W/m}^2.\text K^4\) |
| \(\mathrm{(T)}\) | \([M^1L^2T^{-2}A^{-2}]\) | \(\mathrm{(v)}\) | \(\text{poise}\) | ||
| \(\mathrm{(U)}\) | \([M^1L^{-1}T^{-1}]\) | \(\mathrm{(vi)}\) | \(\text{henry}\) | ||
| \(\mathrm{A}\) | \(\mathrm{B}\) | \(\mathrm{C}\) | \(\mathrm{D}\) | |
| 1. | \(\mathrm{Q, iii}\) | \(\mathrm{S, i}\) | \(\mathrm{P, ii}\) | \(\mathrm{R, iv}\) |
| 2. | \(\mathrm{P, i}\) | \(\mathrm{Q, iii}\) | \(\mathrm{S, ii}\) | \(\mathrm{R, v}\) |
| 3. | \(\mathrm{Q, iv}\) | \(\mathrm{S, ii}\) | \(\mathrm{U, v}\) | \(\mathrm{R, i}\) |
| 4. | \(\mathrm{Q, ii}\) | \(\mathrm{S, iv}\) | \(\mathrm{P, i}\) | \(\mathrm{R, iii}\) |
Subtopic: Dimensions |
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Column-I lists a few physical quantities and Column-II lists their dimensions. Choose the correct option matching two lists correctly.
| Column-I | Column-II | ||
| (P) | pressure gradient | (A) | \(\left[M^1 L^2 T^{-2}\right]\) |
| (Q) | energy density | (B) | \(\left[M^1 L^1 T^{-1}\right]\) |
| (R) | torque | (C) | \(\left[M^1 L^{-2} T^{-2}\right]\) |
| (S) | impulse | (D) | \(\left[M^1 L^{-1} T^{-2}\right]\) |
| 1. | (P) − (C), (Q) − (A), (R) − (B), (S) − (D) |
| 2. | (P) − (C), (Q) − (D), (R) − (A), (S) − (B) |
| 3. | (P) − (A), (Q)− (D), (R) − (B), (S) − (C) |
| 4. | (P) − (A), (Q) − (C), (R) − (B), (S) − (D) |
Subtopic: Dimensions |
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