Q. No.Which two of the following five physical parameters have the same dimensions?
| (1) | Energy density |
| (2) | Refractive index |
| (3) | Dielectric constant |
| (4) | Young's modulus |
| (5) | Magnetic field |
Choose the correct option:
| 1. | (2) and (4) |
| 2. | (3) and (5) |
| 3. | (1) and (4) |
| 4. | (1) and (5) |
Which of the following expressions have units of power?
| (A) | \(\dfrac{mv^2}{2t}\) |
| (B) | \(\dfrac{V^2}{R}\) |
| (C) | \(\dfrac{mgh}{t}\) |
| 1. | (A) and (B) only |
| 2. | (A) only |
| 3. | (B) and (C) only |
| 4. | (A), (B), and (C) |
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
| (a) | \(y = a\sin \left(2\pi t / T\right)\) |
| (b) | \(y = a\sin(vt)\) |
| (c) | \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\) |
| (d) | \(y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)\) |
(Symbols have their usual meanings.)
Choose the correct option:
| 1. | (a), (c) |
| 2. | (a), (b) |
| 3. | (b), (c) |
| 4. | (a), (d) |
IF \(P, Q\) and \(R\) are physical quantities, having different dimensions, which of the following combination/s can never be a meaningful quantity?
(a) \((P – Q)/R\)
(b) \(PQ – R\)
(c) \(PQ /R\)
(d) \((PR – Q^2)/R\)
(e) \((R + Q)/P\)
Choose the correct option:
1. (a), (e)
2. (a), (d), (e)
3. (a), (c), (d)
4. (b), (d)
Photon is a quantum of radiation with energy E = h, where is the frequency
and h is Planck's constant. The dimensions of h are the same as that of the following quantities.
(a) linear impulse
(b) angular impulse
(c) linear momentum
(d) angular momentum
Choose the correct option:
1. (a, d)
2. (b, d)
3. (c, d)
4. (a, b)
If Planck's constant \((h)\) and speed of light in a vacuum \((c)\) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass, and time in terms of the three chosen fundamental quantities?
| (a) | mass of the electron \((m_e)\) |
| (b) | universal gravitational constant \((G)\) |
| (c) | charge of an electron \((e)\) |
| (d) | mass of proton \((m_p)\) |
Choose the correct option from the given ones:
| 1. | (a), (c), and (d) only |
| 2. | (a), (b), and (d) only |
| 3. | (a), (b), and (c) only |
| 4. | (b), (c), and (d) only |
Which of the following ratios, express pressure?
| (a) | force/area |
| (b) | energy/volume |
| (c) | energy/area |
| (d) | force/volume |
Choose the correct option:
| 1. | (a), (c) |
| 2. | (a), (d) |
| 3. | (b), (d) |
| 4. | (a), (b) |
The following is/are not a unit of time:
| (a) | second |
| (b) | parsec |
| (c) | year |
| (d) | light year |
Choose the correct option:
| 1. | (a, c, d) |
| 2. | (a, c) |
| 3. | (b, d) |
| 4. | (b, c) |
| List-I | List-II | ||
| (a) | \({h} \) (Planck's constant) | (i) | \([MLT^{-1}]\) |
| (b) | \({E} \) (kinetic energy) | (ii) | \([ML^2T^{-1}]\) |
| (c) | \(V\) (electric potential) | (iii) | \([ML^2T^{-2}]\) |
| (d) | \(p\) (linear momentum) | (iv) | \([ML^2A^{-1}T^{-3}]\) |
Choose from the given option from the given ones;
| 1. | (a) → (iii), (b) → (iv), (c) → (ii), (d) → (i) |
| 2. | (a) → (ii), (b) → (iii), (c) → (iv), (d) → (i) |
| 3. | (a) → (i), (b) → (ii), (c) → (iv), (d) → (iii) |
| 4. | (a) → (iii), (b) → (ii), (c) → (iv), (d) → (i) |
Which of the following equations is dimensionally correct?
\((I)~~ v=\sqrt{\dfrac{P}{\rho}}~~~~~~(II)~~v=\sqrt{\dfrac{mgl}{I}}~~~~~~(III)~~v=\dfrac{Pr^2}{2\eta l}\)
(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. | \(I~ \text{and}~II\) |
| 2. | \(I~ \text{and}~III\) |
| 3. | \(II~ \text{and}~III\) |
| 4. | \(I,~II~\text{and}~III\) |
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