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If dimensions of critical velocity \({v_c}\) of a liquid flowing through a tube are expressed as \(\eta^{x}\rho^yr^{z}\), where \(\eta, \rho~\text{and}~r\) are the coefficient of viscosity of the liquid, the density of the liquid, and the 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 |

68%

From NCERT

NEET - 2015

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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. | \([E^{-2}v^{-1}T^{-3}]\) |

Subtopic: Dimensions |

69%

From NCERT

NEET - 2015

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If force (\(F\)), velocity (\(\mathrm{v}\)), 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 |

71%

From NCERT

AIPMT - 2014

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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:

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

Percentage error in \(P\) is:

1. \(10\%\)

2. \(7\%\)

3. \(4\%\)

4. \(14\%\)

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

Percentage error in \(P\) is:

1. \(10\%\)

2. \(7\%\)

3. \(4\%\)

4. \(14\%\)

Subtopic: Errors |

89%

From NCERT

AIPMT - 2013

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The pair of quantities having the same dimensions are:

1. | impulse and surface tension |

2. | angular momentum and work |

3. | work and torque |

4. | Young's modulus and energy |

Subtopic: Dimensions |

80%

From NCERT

NEET - 2013

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

1. $[$ ${L}^{-1}T$ $]$

2. $[$ $L{T}^{-1}$ $]$

3. $[$ ${L}^{1/2}{T}^{1/2}$ $]$

4. $[$ ${L}^{1/2}{T}^{-1/2}$ $]$

Subtopic: Dimensions |

80%

From NCERT

AIPMT - 2012

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

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

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

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

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

Subtopic: Dimensions |

85%

From NCERT

AIPMT - 2011

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The density of a material in a CGS system of units is \(4~\text{grams/cm}^3\). In a system of units in which the unit of length is \(10~\text{cm}\) and the unit of mass is \(100~\text{grams}\), the value of the density of the material will be:

1. \( 0.04 \)

2. \( 0.4 \)

3. \( 40 \)

4. \(400\)

Subtopic: Dimensions |

62%

From NCERT

AIPMT - 2011

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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 |

71%

From NCERT

AIPMT - 2010

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A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate \(g,\) the acceleration due to gravity. If the maximum percentage errors in the measurement of the distance and the time are \(e_1\)_{ }and \(e_2\) respectively, the percentage error in the estimation of \(g\) is:

1. ${e}_{1}+2{e}_{2}$

2. ${e}_{1}+{e}_{2}$

3. ${e}_{1}-2{e}_{2}$

4. ${e}_{2}-{e}_{1}$

Subtopic: Errors |

66%

From NCERT

AIPMT - 2010

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