Plane angle and solid angle have:
 1 both units and dimensions 2 units but no dimensions 3 dimensions but no units 4 no units and no dimensions
Subtopic: Â Dimensions |
Â 79%
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NEET - 2022
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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: Â Dimensions |
Â 70%
From NCERT
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: Â Dimensions |
Â 67%
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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

Subtopic: Â Dimensions |
Â 81%
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A physical quantity is measured and the result is expressed as $$nu$$ where $$u$$ is the unit used and $$n$$ is the numerical value. If the result is expressed in various units then:
1. $$n\propto \mathrm{size~of}~u$$
2. $$n\propto u^2$$
3. $$n\propto \sqrt u$$
4. $$n\propto \frac{1}{u}$$

Subtopic: Â Dimensions |
Â 76%
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A dimensionless quantity,

 1 never has a unit 2 always has a unit 3 may have a unit 4 does not exist
Subtopic: Â Dimensions |
Â 78%
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$$\int \frac{\mathrm{dx}}{\sqrt{2 \mathrm{ax}-\mathrm{x}^{2}}}=\mathrm{a}^{\mathrm{n}} \sin ^{-1}\left[\frac{\mathrm{x}}{\mathrm{a}}-1\right]$$
The value of $$\mathrm{n}$$ is:
1. $$0$$
2. $$-1$$
3. $$1$$
4. none of these

Subtopic: Â Dimensions |
Â 51%
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Young's modulus of steel is $$1.9 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$$. When expressed in CGS units of $$\mathrm{dyne/cm^2}$$, it will be equal to: $$(1 \mathrm{~N}=10^5 \text { dyne, } 1 \mathrm{~m}^2=10^4 \mathrm{~cm}^2)$$
1. $$1.9 \times 10^{10}$$
2. $$1.9 \times 10^{11}$$
3. $$1.9 \times 10^{12}$$
4. $$1.9 \times 10^9$$

Subtopic: Â Dimensions |
Â 74%
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If momentum ($$\mathrm{p}$$), area ($$\mathrm{A}$$), and time ($$\mathrm{T}$$) are taken to be fundamental quantities, then energy has the dimensional formula:
1. $${\left[\mathrm{pA}^{-1} \mathrm{~T}^1\right]}$$
2. $${\left[\mathrm{p}^2 \mathrm{AT}\right]}$$
3. $${\left[\mathrm{pA}^{-1 / 2} \mathrm{~T}\right]}$$
4. $${\left[\mathrm{pA}^{1 / 2} \mathrm{~T}^{-1}\right]}$$

Subtopic: Â Dimensions |
Â 75%
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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) $$y = \left({a \over T}\right) \sin \left({t \over a}\right)$$
(d) $$y = a \sqrt 2 \left(\sin \left({2 \pi t \over T}\right) - \cos \left({2 \pi t \over T}\right)\right)$$
(Symbols have their usual meanings.)
Choose the correct option:
1. (a), (c)
2. (a), (b)
3. (b), (c)
4. (a), (d)

Subtopic: Â Dimensions |
Â 63%
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