Q. No.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
| 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) |
1. \(14\times10^{2}\)
2. \(138\times10^{1}\)
3. \(1382\)
4. \(1382.5\)
| 1. | both units and dimensions |
| 2. | units but no dimensions |
| 3. | dimensions but no units |
| 4. | no units and no dimensions |
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
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. \(3.6\)
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. | \(I,~II~and~III\) |
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. \(14.1124\mathrm{~cm^2}\)
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 |
\(\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]\)
The value of \(\mathrm{n}\) is:
1. \(0\)
2. \(-1\)
3. \(1\)
4. none of these
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