If dimensions of critical velocity \({v_c}\) of a liquid flowing through a tube are expressed as ηxρyrz, where η, ρand 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 \(\mathrm{x},\) \(\mathrm{y},\) and \(\mathrm{z},\) 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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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 |
 68%
From NCERT
NEET - 2015
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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
Please attempt this question first.
Hints
Please attempt this question first.

The dimensions of (μ0ε0)-1/2 are:

1.  [ L-1T ]

2.  [ LT-1 ]

3.  [ L1/2T1/2 ]

4. [ L1/2T-1/2 ]

Subtopic:  Dimensions |
 81%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The dimensions of μ0ε0-1/2 are:

1.  L-1 T

2.  LT-1

3.  L-1/2 T1/2

4.  L-1/2 T-1/2

Subtopic:  Dimensions |
 85%
From NCERT
AIPMT - 2011
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The dimensions of 12ε0E2 where ε0 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
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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. e1+2e2
2. e1+e2
3. e1-2e2
4. e2-e1

Subtopic:  Errors |
 66%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh