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 78%

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Match List-I with List-II.

Choose the correct answer from the options given below:

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%

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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: 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 77%

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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 79%

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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 \(1.9 \times 10^{11} ~\text{N/m}^2\). When expressed in CGS units of \(\text{dyne/cm}^2\), it will be equal to: \((1 \mathrm{~N}=10^5 \text { dyne, } 1~ \text{m}^2=10^4 ~\text{cm}^2)\)

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 73%

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If momentum (\({p}\)), area (\({A}\)), and time (\({T}\)) are taken to be fundamental quantities, then energy has the dimensional formula:

1. | \( {\left[{pA}^{-1} {~T}^1\right]} \) | 2. | \( {\left[{p}^2 {AT}\right]} \) |

3. | \( {\left[{pA}^{-1 / 2} {~T}\right]} \) | 4. | \( {\left[{pA}^{1 / 2} {~T}^{-1}\right]}\) |

Subtopic: Â Dimensions |

Â 76%

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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) | \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\) |

(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) |

Subtopic: Â Dimensions |

Â 63%

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