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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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.  $\left[$ ${L}^{-1}T$ $\right]$

2.  $\left[$ $L{T}^{-1}$ $\right]$

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

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

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 $$4~\text{g/cm}^3$$. In a system of units in which the unit of length is $$10~\text{cm}$$ and the unit of mass is $$100~\text{g}$$, 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. [ML2T-2]

2. [ML-1T-2]

3.  [ML2T-1]

4.  [MLT-1]

Subtopic:  Dimensions |
71%
From NCERT
AIPMT - 2010
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If the dimensions of a physical quantity are given by $$[M^aL^bT^c],$$ 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 $$a=0,$$ $$b=-1,$$ $$c=-2$$
Subtopic:  Dimensions |
87%
From NCERT
AIPMT - 2009
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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%
From NCERT
AIPMT - 2008
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