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Four students measure the height of a tower. Each student uses a different method and each measures the height many times. The data for each are plotted below. The measurement with the highest precision is:

 (I) (II) (III) (IV)

1. I
2. II
3. III
4. IV

Subtopic:  Errors |
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In the expressions below: $$g$$ = gravitational acceleration; $$h$$ = height; $$m$$ = mass; $$R$$ = electrical resistance; $$t$$ = time; $$v$$ = velocity; $$V$$ = voltage. Which of the following expressions have units of power?
(a) $$\frac{mv^2}{2t}$$
(b) $$\frac{V^2}{R}$$
(c) $$\frac{mgh}{t}$$

 1 (a) and (b) only 2 (a) only 3 (b) and c) only 4 (a), (b) and (c)
Subtopic:  Dimensions |
72%
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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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NEET - 2022
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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 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 |
65%
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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 |
85%
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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 |
65%
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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)
Subtopic:  Dimensions |
71%
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AIPMT - 2008
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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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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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