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 |
53%
Level 3: 35%-60%
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 |
64%
Level 2: 60%+
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 |
66%
Level 2: 60%+
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%
Level 2: 60%+
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 |
61%
Level 2: 60%+
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%
Level 2: 60%+
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 |
Level 3: 35%-60%
NEET - 2022
Hints
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 |
82%
Level 1: 80%+
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 |
68%
Level 2: 60%+
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 |
79%
Level 2: 60%+
NEET - 2021
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