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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. $${\left[\mathrm{FvT}^{-1}\right]}$$
2. $${\left[\mathrm{FvT}^{-2}\right]}$$
3. $${\left[\mathrm{Fv}^{-1} \mathrm{~T}^{-1}\right]}$$
4. $${\left[\mathrm{Fv}^{-1} \mathrm{~T}\right]}$$

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. $$14\%$$
Subtopic:  Errors |
89%
From NCERT
AIPMT - 2013
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The pair of quantities having the same dimensions is:
 1 Impulse and surface tension 2 Angular momentum and work 3 Work and torque 4 Young's modulus and energy
Subtopic:  Dimensions |
81%
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 |
81%
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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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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