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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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Match the units mentioned in List-I with the units in List-II.

 List-I List-II (a)  H/s (i)  s2 (b)  H×A (ii)  Wb (c)  H×F (iii)  s (d)   $$\Omega$$×F (iv)  $$\Omega$$

 1 (a) – (ii), (b) – (iv), (c) – (i), (d) – (iii) 2 (a) – (iv), (b) – (ii), (c) – (i), (d) – (iii) 3 (a) – (iv), (b) – (ii), (c) – (iii), (d) – (i) 4 (a) – (ii), (b) – (iii), (c) – (iv), (d) – (i)
Subtopic:  Dimensions |
64%
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Match the following quantities in List-I with their dimensions in List-II.
 List-I List-II (a) acceleration (i) $$[M^0L^0T^0 ]$$ (b) torque (ii) $$[ML^{-1}T^{-2} ]$$ (c) absorptive power (iii) $$[LT^{-2} ]$$ (d) pressure (iv) $$[ML^2T^{-2} ]$$

 1 a - (iii), b - (iv), c - (i), d - (ii) 2 a - (iii), b - (ii), c - (i), d - (iv) 3 a - (iii), b - (i), c - (ii), d - (iv) 4 a - (ii), b - (iv), c - (iii), d - (i)
Subtopic:  Dimensions |
86%
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Match the units of some physical quantities in List-I with their corresponding dimensions in List-II.
 List-I List-II (a) Ohm (i) $$[ML^2T^{-2}A^{-1}]$$ (b) Farad (ii) $$[ML^2T^{-2}A^{-2}]$$ (c) Henry (iii) $$[M^{-1}L^{-2}T^4A^2]$$ (d) Weber (iv) $$[ML^2T^{-3}A^{-2}]$$
 1 (a) - (i), (b) - (ii), (c) - (iv), (d) - (iii) 2 (a) - (iv), (b) - (iii), (c) - (i), (d) - (ii) 3 (a) - (ii), (b) - (iii), (c) - (i), (d) - (iv) 4 (a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)
Subtopic:  Dimensions |
64%
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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 |
67%
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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 |
90%
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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 |
77%
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