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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 | ||
| \(\mathrm{(a)}\) | \({h} \) (Planck's constant) | \(\mathrm{(i)}\) | \([MLT^{-1}]\) |
| \(\mathrm{(b)}\) | \({E} \) (kinetic energy) | \(\mathrm{(ii)}\) | \([ML^2T^{-1}]\) |
| \(\mathrm{(c)}\) | \(V\) (electric potential) | \(\mathrm{(iii)}\) | \([ML^2T^{-2}]\) |
| \(\mathrm{(d)}\) | \(p\) (linear momentum) | \(\mathrm{(iv)}\) | \([ML^2A^{-1}T^{-3}]\) |
Choose the correct option from the given ones:
| 1. | \(\mathrm{(a) → (iii), (b) → (iv), (c) → (ii), (d) → (i)}\) |
| 2. | \(\mathrm{(a) → (ii), (b) → (iii), (c) → (iv), (d) → (i)}\) |
| 3. | \(\mathrm{(a) → (i), (b) → (ii), (c) → (iv), (d) → (iii)}\) |
| 4. | \(\mathrm{(a) → (iii), (b) → (ii), (c) → (iv), (d) → (i)}\) |
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
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 | ||
| \(\mathrm{(A)}\) | Torque | \(\mathrm{(I)}\) | N-m s-1 |
| \(\mathrm{(B)}\) | Stress | \(\mathrm{(II)}\) | J-kg-1 |
| \(\mathrm{(C)}\) | Latent Heat | \(\mathrm{(III)}\) | N-m |
| \(\mathrm{(D)}\) | Power | \(\mathrm{(IV)}\) | N-m-2 |
Choose the correct answer from the options given below:
| 1. | \(\mathrm{A-III, B-II, C-I, D-IV}\) |
| 2. | \(\mathrm{A-III, B-IV, C-II, D-I}\) |
| 3. | \(\mathrm{A-IV, B-I, C-III, D-II}\) |
| 4. | \(\mathrm{A-II, B-III, C-I, D-IV}\) |
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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The distance \(x\) travelled by a particle as a function of time \(t\) is given by the equation:
\(x = ct^2 + bt^3.\)
What are the dimensions of \(c\) & \(b \text{?}\)
\(x = ct^2 + bt^3.\)
What are the dimensions of \(c\) & \(b \text{?}\)
| 1. | \([T^{-2}], [T^{-3}]\) | 2. | \([LT^{-2}], [LT^{-3}]\) |
| 3. | \([T^{2}], [T^{3}]\) | 4. | \([LT^{2}], [LT^{3}]\) |
Subtopic: Dimensions |
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If the dimensions of a physical quantity are given by \([M^aL^bT^c],\) then the physical quantity will be:
| 1. | pressure if \(a=1,\) \(b=-1,\) \(c=-2\) |
| 2. | velocity if \(a=1,\) \(b=0,\) \(c=-1\) |
| 3. | acceleration if \(a=1,\) \(b=1,\) \(c=-2\) |
| 4. | force if \(a=0,\) \(b=-1,\) \(c=-2\) |
Subtopic: Dimensions |
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AIPMT - 2009
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