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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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Level 1: 80%+
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Match List-I with List-II.
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. \(\left [ L\right ],\) \(\left [ LT \right ],\) \(\left [ T^{2}\right ]\)
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.
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:
 
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.
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 \(\mathrm{(S)}\) \([M^0L^1T^0K^1]\) \(\mathrm{(iv)}\) \(\text{W/m}^2.\text K^4\)
\(\mathrm{(T)}\) \([M^1L^2T^{-2}A^{-2}]\) \(\mathrm{(v)}\) \(\text{poise}\)
\(\mathrm{(U)}\) \([M^1L^{-1}T^{-1}]\) \(\mathrm{(vi)}\) \(\text{henry}\)
Codes:
\(\mathrm{A}\) \(\mathrm{B}\) \(\mathrm{C}\) \(\mathrm{D}\)
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 \(c\) & \(b \text{?}\) 
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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