# 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 |
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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 |
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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

1.  (2) and (4)

2.  (3) and (5)

3.  (1) and (4)

4.  (1) and (5)

Subtopic:  Dimensions |
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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. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}\right]$

2. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-2}\right]$

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

4. $\left[{\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-2}\right]$

Subtopic:  Dimensions |
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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 |
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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 |
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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 |
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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:
$$P=$$  $\frac{{a}^{3}{b}^{2}}{cd}$
Percentage error in $$P$$ is:
1. $$10$$%
2. $$7$$%
3. $$4$$%
4. $$14$$%
Subtopic:  Errors |
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If force (F), velocity (v), and time (T) are taken as fundamental units, the dimensions of mass will be:
1. [FvT-1]
2. [FvT-2]
3. [Fv-1T-1]
4. [Fv-1T]

Subtopic:  Dimensions |
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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-2T-1]
2. [Ev-1T-2]
3. [Ev-2T-2]
4. [E-2v-1T-3]

Subtopic:  Dimensions |
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