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 |
 70%
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When the circular scale of a screw gauge completes \(2\) rotations, it covers \(1\) mm over the pitch scale. The total number of circular scale divisions is \(50\). The least count of the screw gauge in metres is:
1. \(10^{-4}\)
2. \(10^{-5}\)
3. \(10^{-2}\)
4. \(10^{-3}\)

Subtopic:  Measurement & Measuring Devices |
 54%
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The determination of the value of acceleration due to gravity \((g)\) by simple pendulum method employs the formula,
 \(g=4\pi^2\frac{L}{T^2}\)
The expression for the relative error in the value of \(g\) is:
1.  \(\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)\)
2.  \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]\)
3.  \(\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]\)
4.  \(\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)\)

Subtopic:  Errors |
 76%
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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 |
 80%
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The percentage error in the measurement of \(g\) is:
[Given,  \(g=\frac{4\pi^2L}{T^2},L=(10\pm0.1)~\text{cm, }T=(100\pm1)~\text s\)]
1. \(2\%\)
2. \(5\%\)
3. \(3\%\)
4. \(7\%\)
Subtopic:  Errors |
 73%
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The area of a rectangular field (in \(\mathrm{m^2}\)) of length \(55.3\) m and breadth \(25\) m after rounding off the value, for correct significant digits is:
1. \(14\times10^{2}\)
2. \(138\times10^{1}\)
3. \(1382\)
4. \(1382.5\)
Subtopic:  Significant Figures |
 58%
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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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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 |
 78%
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A metal wire has mass \((0.4\pm 0.002)~\mathrm{g}\), radius \((0.3\pm 0.001)~\mathrm{mm}\) and length \((5\pm 0.02)~\mathrm{cm}\). The maximum possible percentage error in the measurement of density will nearly be:
1. \(1.4 \%\)
2. \(1.2 \%\)
3. \(1.3 \%\)
4. \(1.6 \%\)
Subtopic:  Errors |
From NCERT
NEET - 2023
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The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
1. Random errors
2. Instrumental errors
3. Personal errors
4. Least count errors
Subtopic:  Errors |
 67%
From NCERT
NEET - 2023
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