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 |
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The unit of length, parsec is used for the measurement of:
 
1.  wavelength of light
2.  size of an atom
3.  astronomical distance
4. height of a building
Subtopic:  Measurement & Measuring Devices |
 81%
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The area of a rectangular field (in \(\text{m}^2\)) 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 |
 59%
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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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Darcy's law describes the volume flow rate \((Q)\) of a viscous fluid (viscosity : \(\mu\)) through a porous medium, under the action of a pressure difference.    \(\frac{Q}{A}=\frac{k}{\mu}\left(\frac{{\large p}_{1}-{\large p}_{2}}{L}\right) \)
Here, \(k\) is the permeability of the medium. The unit of \(k\) is (SI units)
             
1. m
2. m2
3. m2/s
4. m/s2
Subtopic:  Dimensions |
 52%
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The acceleration due to gravity on the surface of the earth is \(g=10\) m/s2. The value in km/(minute)2 is:
1. \(36\)
2. \(0.6\)
3. \(\frac{10}{6}\)
4. \(3.6\)

Subtopic:  Dimensions |
 62%
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Which of the following equations is dimensionally correct?
\((I)~~ v=\sqrt{\frac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\frac{mgl}{I}}~~~~~~(III)~~v=\frac{Pr^2}{2\eta l}\)
(where  \(v=\) speed, \(P=\) pressure; \(r,\) \(l\) are lengths; \(\rho=\)  density, \(m=\) mass, \(g=\) acceleration due to gravity, \(I=\) moment of inertia, and \(\eta=\) coefficient of viscosity)

1. \(I~ and~II\)
2. \(I~ and~III\)
3. \(II~ and~III\)
4. \(I,~II~and~III\)
Subtopic:  Dimensions |
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The radius of a circle is stated as \(2.12\) cm. Its area should be written as:

1. \(14\mathrm{~cm^2}\) 2. \(14.1\mathrm{~cm^2}\)
3. \(14.11\mathrm{~cm^2}\) 4. \(14.1124\mathrm{~cm^2}\)
Subtopic:  Significant Figures |
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The dimensions of \(\left [ML^{-1} T^{-2} \right ]\) may correspond to:

a. work done by a force
b. linear momentum
c. pressure
d. energy per unit volume


Choose the correct option:

1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. none of the above

Subtopic:  Dimensions |
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\(\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]\)
The value of \(\mathrm{n}\) is:
1. \(0\)
2. \(-1\)
3. \(1\)
4. none of these

Subtopic:  Dimensions |
 52%
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