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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 |
55%
Level 3: 35%-60%
NEET - 2025
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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 |
75%
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 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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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
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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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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%
Level 2: 60%+
NEET - 2021
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The energy required to break one bond in DNA is \(10^{-20}~\text{J}\). This value in eV is nearly:
1. \(0.6\)
2. \(0.06\)
3. \(0.006\)
4. \(6\)
Subtopic: Dimensions |
72%
Level 2: 60%+
NEET - 2020
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A physical quantity of the dimensions of length that can be formed out of \(c, G,~\text{and}~\dfrac{e^2}{4\pi\varepsilon_0}\)is:
(\(c\) is the velocity of light, \(G\) is the universal constant of gravitation and \(e\) is charge)
| 1. | \(c^2\left[G \dfrac{e^2}{4 \pi \varepsilon_0}\right]^{\dfrac{1}{2}}\) | 2. | \(\dfrac{1}{c^2}\left[\dfrac{e^2}{4 G \pi \varepsilon_0}\right]^{\dfrac{1}{2}}\) |
| 3. | \(\dfrac{1}{c} G \dfrac{e^2}{4 \pi \varepsilon_0}\) | 4. | \(\dfrac{1}{c^2}\left[G \dfrac{e^2}{4 \pi \varepsilon_0}\right]^{\dfrac{1}{2}}\) |
Subtopic: Dimensions |
56%
Level 3: 35%-60%
NEET - 2017
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If energy \((E),\) velocity \((v)\) and time \((T)\) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
1. \([Ev^{-2}T^{-1}]\)
2. \([Ev^{-1}T^{-2}]\)
3. \([Ev^{-2}T^{-2}]\)
4. \([E^{-2}v^{-1}T^{-3}]\)
1. \([Ev^{-2}T^{-1}]\)
2. \([Ev^{-1}T^{-2}]\)
3. \([Ev^{-2}T^{-2}]\)
4. \([E^{-2}v^{-1}T^{-3}]\)
Subtopic: Dimensions |
72%
Level 2: 60%+
NEET - 2015
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