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
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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 (μ0ε0)-1/2 are:

1.  [ L-1T ]

2.  [ LT-1 ]

3.  [ L1/2T1/2 ]

4. [ L1/2T-1/2 ]

Subtopic:  Dimensions |
 80%
From NCERT
AIPMT - 2012
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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 velocity \(v\) of a particle at time \(t\) is given by \(v=at+\frac{b}{t+c}\), where \(a,\) \(b\) and \(c\) are constants. The dimensions of \(a,\) \(b\) and \(c\) are respectively:

1. \(\left[\mathrm{LT}^{-2}\right],[\mathrm{L}] \text { and }[\mathrm{T}]\)
2. \( {\left[\mathrm{L}^2\right],[\mathrm{T}] \text { and }\left[\mathrm{LT}^2\right]}  \)
3. \( {\left[\mathrm{LT}^2\right],[\mathrm{LT}] \text { and }[\mathrm{L}]}  \)
4. \( {[\mathrm{L}],[\mathrm{LT}] \text { and }\left[\mathrm{T}^2\right]}\)
Subtopic:  Dimensions |
 81%
From NCERT
AIPMT - 2006
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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. [ML2T-3I-1]

2. [ML2T-2]

3. [ML2T-1I-1]

4. [ML2T-3I-2]

Subtopic:  Dimensions |
 67%
From NCERT
AIPMT - 2007
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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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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 |
 83%
From NCERT
AIPMT - 2008
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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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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
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