The quantities which have the same dimensions as those of solid angle are:
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle
Subtopic:  Dimensions |
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A force defined by; \(F = \alpha t^2 + \beta t\) acts on a particle at a given time \(t.\) The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is: 
1. \(\alpha t / \beta \) 2. \(\alpha \beta t \)
3. \(\alpha \beta / t \) 4. \(\beta t / \alpha\)
Subtopic:  Dimensions |
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The potential energy of a particle moving along the \(x\text-\)direction varies as \(\mathrm{V}=\frac{\mathrm{A}x^{2}}{\sqrt{x}+\mathrm{B}}.\)The dimensions of \(\frac{\mathrm{A}^2}{\mathrm{B}}\) are:
1. \([{M}^{3/2}{L}^{1/2}{T}^{-3}]\)
2. \([M^{1/2}LT^{-3}]\)
3. \([{M}^2{L}^{1/2}{T}^{-4}]\)
4. \([ML^{2}T^{-4}]\)
Subtopic:  Dimensions |
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The mechanical quantity, which has dimensions of reciprocal of mass \((M^{-1}),\) is:
1. angular momentum
2. coefficient of thermal conductivity 
3. torque 
4. gravitational constant 
Subtopic:  Dimensions |
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Plane angle and solid angle have:
1. both units and dimensions
2. units but no dimensions
3. dimensions but no units
4. no units and no dimensions
Subtopic:  Dimensions |
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The dimensions \([MLT^{-2}A^{-2}]\) belong to the:
1. electric permittivity
2. magnetic flux
3. self-inductance
4. magnetic permeability
Subtopic:  Dimensions |
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Match List-I with List-II.
 
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 |
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The physical quantity that has the same dimensional formula as pressure is:
1. Force
2. Momentum
3. Young's modulus of elasticity
4. Coefficient of viscosity
Subtopic:  Dimensions |
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If force \([F]\), acceleration \([A]\) and time \([T]\) are chosen as the fundamental physical quantities, then find the dimensions of energy:
1. \(\left[FAT^{-1}\right]\)
2. \(\left[FA^{-1}T\right]\)
3. \(\left[FAT\right]\)
4. \(\left[FAT^{2}\right]\)

Subtopic:  Dimensions |
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If \(E\) and \(G\), respectively, denote energy and gravitational constant, then \(\dfrac{E}{G}\) has the dimensions of:

1. \([ML^0T^0]\) 2. \([M^2L^{-2}T^{-1}]\)
3. \([M^2L^{-1}T^{0}]\) 4. \([ML^{-1}T^{-1}]\)
Subtopic:  Dimensions |
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