A physical quantity of the dimensions of length that can be formed out of \(c, G,~\text{and}~\frac{e^2}{4\pi\varepsilon_0}\)is [\(c\) is the velocity of light, \(G\) is the universal constant of gravitation and \(e\) is charge]:
\(1. ~c^2\left[G \frac{e^2}{4 \pi \varepsilon_0}\right]^{\frac{1}{2}}\\ 2.~ \frac{1}{c^2}\left[\frac{e^2}{4 G \pi \varepsilon_0}\right]^{\frac{1}{2}}\\ 3. ~\frac{1}{c} G \frac{e^2}{4 \pi \varepsilon_0}\\ 4. ~\frac{1}{c^2}\left[G \frac{e^2}{4 \pi \varepsilon_0}\right]^{\frac{1}{2}}\)

Subtopic:  Dimensions |
 54%
From NCERT
NEET - 2017
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A student measured the diameter of a small steel ball using a screw gauge of least count \(0.001\) cm. The main scale reading is \(5\) mm and zero of circular scale division coincides with \(25\) divisions above the reference level. If the screw gauge has a zero error of \(-0.004\) cm, the correct diameter of the ball is:
1. \(0.521\) cm
2. \(0.525\) cm
3. \(0.053\) cm
4. \(0.529\) cm

Subtopic:  Measurement & Measuring Devices |
 63%
From NCERT
NEET - 2018
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If dimensions of critical velocity \({v_c}\) of a liquid flowing through a tube are expressed as \(\eta^{x}\rho^yr^{z}\), where \(\eta, \rho~\text{and}~r\) are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of \({x},\) \({y},\) and \({z},\) respectively, will be:
1. \(1,-1,-1\)
2. \(-1,-1,1\)
3. \(-1,-1,-1\)
4. \(1,1,1\)

Subtopic:  Dimensions |
 68%
From NCERT
NEET - 2015
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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. \([E^{-2}v^{-1}T^{-3}]\)

Subtopic:  Dimensions |
 69%
From NCERT
NEET - 2015
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If force (\(F\)), velocity (\(\mathrm{v}\)), and time (\(T\)) are taken as fundamental units, the dimensions of mass will be:
1. \( {\left[\mathrm{FvT}^{-1}\right]} \)
2. \({\left[\mathrm{FvT}^{-2}\right]} \)
3. \( {\left[\mathrm{Fv}^{-1} \mathrm{~T}^{-1}\right]} \)
4. \( {\left[\mathrm{Fv}^{-1} \mathrm{~T}\right]}\)

Subtopic:  Dimensions |
 71%
From NCERT
AIPMT - 2014
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In an experiment, four quantities \(a,\) \(b,\) \(c\) and \(d\) are measured with percentage error \(1\)%, \(2\)%, \(3\)% and \(4\)% respectively. Quantity \(P\) is calculated as follows: 
\(P=\frac{a^3b^2}{cd}\)
Percentage error in \(P\) is:
1. \(10\%\)
2. \(7\%\)
3. \(4\%\)
4. \(14\%\)
Subtopic:  Errors |
 89%
From NCERT
AIPMT - 2013
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The dimensions of μ0ε0-1/2 are:

1.  L-1 T

2.  LT-1

3.  L-1/2 T1/2

4.  L-1/2 T-1/2

Subtopic:  Dimensions |
 85%
From NCERT
AIPMT - 2011
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The dimensions of 12ε0E2 where ε0 is the permittivity of free space and E is the electric field, are:

1. [ML2T-2]

2. [ML-1T-2]

3.  [ML2T-1]

4.  [MLT-1]

Subtopic:  Dimensions |
 71%
From NCERT
AIPMT - 2010
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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 |
 87%
From NCERT
AIPMT - 2009
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Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T, and current I, would be:

1. [ML2T-3I-1]

2. [ML2T-2]

3. [ML2T-1I-1]

4. [ML2T-3I-2]

Subtopic:  Dimensions |
 67%
From NCERT
AIPMT - 2007
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