If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as $\left[{\mathrm{\eta}}^{\mathrm{x}}{\mathrm{\rho}}^{\mathrm{y}}{\mathrm{r}}^{\mathrm{z}}\right]$, where $\mathrm{\eta},\mathrm{\rho}\mathrm{and}\mathrm{r}$ are the coefficient of viscosity of the liquid, the density of liquid and radius of the tube respectively, then the values of x, y and z, respectively, will be

1. 1, -1, -1

2. -1, -1, 1

3. -1, -1, -1

4. 1, 1, 1,

Subtopic: Dimensions |

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If energy (E), velocity (v) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:

1. [Ev^{-2}T^{-1}]

2. [Ev^{-1}T^{-2}]

3. [Ev^{-2}T^{-2}]

4. [E^{-2}v^{-1}T^{-3}]

2. [Ev

3. [Ev

4. [E

Subtopic: Dimensions |

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If force (F), velocity (v) and time (T) are taken as fundamental units, the dimensions of mass will be

1. [FvT^{-1}]

2. [FvT^{-2}]

3. [Fv^{-1}T^{-1}]

4. [Fv^{-1}T]

Subtopic: Dimensions |

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In an experiment, four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows :

P = $\frac{{a}^{3}{b}^{2}}{cd}$

Percentage error in P is :

P = $\frac{{a}^{3}{b}^{2}}{cd}$

Percentage error in P is :

1. 10%

2. 7%

3. 4%

4. 14%

2. 7%

3. 4%

4. 14%

Subtopic: Errors |

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The dimensions of ${\left({\mathrm{\mu}}_{0}{\mathrm{\epsilon}}_{0}\right)}^{-1/2}$ are

1. $\left[{\mathrm{L}}^{-1}\mathrm{T}\right]$

2. $\left[{\mathrm{LT}}^{-1}\right]$

3. $\left[{\mathrm{L}}^{-1/2}{\mathrm{T}}^{1/2}\right]$

4. $\left[{\mathrm{L}}^{-1/2}{\mathrm{T}}^{-1/2}\right]$

Subtopic: Dimensions |

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The dimensions of $\frac{1}{2}{\mathrm{\epsilon}}_{0}{\mathrm{E}}^{2}$ where ${\epsilon}_{0}$ is the permittivity of free space and E is the electric field, are:

1. [ML^{2}T^{-2}]

2. [ML^{-1}T^{-2}]

3. [ML^{2}T^{-1}]

4. [MLT^{-1}]

Subtopic: Dimensions |

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If the dimensions of a physical quantity are given by M^{a}L^{b}T^{c}, then the physical quantity will be:

1. Pressure if a = 1, b = -1, c = - 2

2. Velocity if a = 1, b = 0, c = - 1

3. Acceleration if a = 1, b = 1, c = - 2

4. Force if a = 0, b =-1, c = - 2

2. Velocity if a = 1, b = 0, c = - 1

3. Acceleration if a = 1, b = 1, c = - 2

4. Force if a = 0, b =-1, c = - 2

Subtopic: Dimensions |

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If the error in the measurement of the radius of a sphere is 2%, then the error in the determination of the volume of the sphere will be:

1. 4%

2. 6%

3. 8%

4. 2%

Subtopic: Errors |

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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

1. (2) and (4)

2. (3) and (5)

3. (1) and (4)

4. (1) and (5)

Subtopic: Dimensions |

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Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, length L, time T and current I, would be:

1. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}\right]$

2. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-2}\right]$

3. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-1}{\mathrm{I}}^{-1}\right]$

4. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-2}\right]$

Subtopic: Dimensions |

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