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# Match List-I with List-II: List-I List-II (a) $$h$$ (Planck's constant) (i) $$\left[ MLT^{-1} \right]$$ (b) $$E$$ (kinetic energy) (ii) $$\left[ ML^{2}T^{-1} \right]$$ (c) $$V$$ (electric potential) (iii) $$\left[ ML^{2}T^{-2} \right]$$ (d) $$p$$ (linear momentum) (iv) $$\left[ ML^{2}A^{-1}T^{-3} \right]$$ Choose the correct option: 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)

Subtopic:  Dimensions |
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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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Which of the following quantities have the same dimension?
(A) $$\frac{\text{(Magnetic flux)}^2}{\text{Electrical resistance}}$$                     (B) $$\text{Torque}\times\text{time}$$
(C) $$\text{Momentum}\times\text{length}$$          (D) $$\frac{\text{Power}}{\text{time}}$$

1.  B, C
2.  A, B, C
3.  B, D
4.  A, B, C, D
Subtopic:  Dimensions |
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Which of the quantities below have the same dimensions?

(A) $$\frac{\text{electric field }\times\text{ magnetic field}}{\mu_0}$$
(B) $$\frac{\varepsilon_0\times\text{(electric potential)}^2\times\text{ velocity}}{\text{area}}$$
(C) $$\frac{\text{power}}{\text{area}}$$

1.  A, B
2.  B, C
3.  A, C
4.  A, B, C
Subtopic:  Dimensions |
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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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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)

Subtopic:  Dimensions |
78%
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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)

Subtopic:  Dimensions |
76%
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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 electron ($$m_e$$) (b) universal gravitational constant ($$G$$) (c) charge of electron ($$e$$) (d) mass of proton ($$m_p$$)

Choose the correct option:
1. (a), (c), (d)
2. (a), (b), (d)
3. (a), (b), (c)
4. (b), (c), (d)
Subtopic:  Dimensions |
60%
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Photon is a quantum of radiation with energy E = h$\mathrm{\nu }$, where $\mathrm{\nu }$ 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)

Subtopic:  Dimensions |
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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)

Subtopic:  Dimensions |
55%
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