Q. No.A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A.\) It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R.\) When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to \(0\) (zero) in time \(T.\) If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^\alpha A^\beta \rho^\gamma R^\delta\) then:
| 1. | \(a=-\dfrac{1}{2},~ \alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 2. | \(a=\dfrac{1}{2},~\alpha=\dfrac{1}{2},~ \beta=-\dfrac{1}{2}, ~\gamma=\dfrac{1}{2},~ \delta=\dfrac{7}{2}\) |
| 3. | \(a=\dfrac{1}{2}, ~\alpha=\dfrac{1}{2}, ~\beta=-1, ~\gamma=+1, ~\delta=\dfrac{3}{2}\) |
| 4. | \(a=-\dfrac{1}{2}, ~\alpha=-\dfrac{1}{2}, ~\beta=-1, ~\gamma=-\dfrac{1}{2}, ~\delta=\dfrac{5}{2}\) |
Subtopic: Dimensions |
From NCERT
NEET - 2025
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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
1. stress and angle
2. strain and arc
3. angular speed and stress
4. strain and angle
Subtopic: Dimensions |
63%
From NCERT
NEET - 2024
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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 |
65%
From NCERT
NEET - 2024
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The potential energy of a particle moving along the \(x\text-\)direction varies as \({V}=\dfrac{{A}x^{2}}{\sqrt{x}+{B}}.\) The dimensions of \(\dfrac{A^2}{B}\) 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 |
74%
From NCERT
NEET - 2024
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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 |
60%
From NCERT
NEET - 2023
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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 |
77%
From NCERT
NEET - 2022
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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
1. electric permittivity
2. magnetic flux
3. self-inductance
4. magnetic permeability
Subtopic: Dimensions |
From NCERT
NEET - 2022
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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
1. Force
2. Momentum
3. Young's modulus of elasticity
4. Coefficient of viscosity
Subtopic: Dimensions |
81%
From NCERT
NEET - 2022
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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 |
67%
From NCERT
NEET - 2021
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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. \([ML^{-1}T^{-1}]\)
1. \([ML^0T^0]\)
2. \([M^2L^{-2}T^{-1}]\)
3. \([M^2L^{-1}T^{0}]\)
4. \([ML^{-1}T^{-1}]\)
Subtopic: Dimensions |
78%
From NCERT
NEET - 2021
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