M.C.Q (1 Marks)

MCQ 11 Mark

A dimensionless quantity:

A
Never has a unit.
B
Always has a unit
✓
May have a unit.
D
Does not exist.

Answer

Correct option: C.

May have a unit.

Dimensionless quantities may have units.

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MCQ 21 Mark

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

A
Length, mass and velocity.
✓
Length, time and velocity.
C
Mass, time and velocity.
D
Length, time and mass.

Answer

Correct option: B.

Length, time and velocity.

We define length and time separately as it is not possible to define velocity without using these quantities. This means that one fundamental quantity depends on the other. So, these quantities cannot be listed as fundamental quantities in any system of units.

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MCQ 31 Mark

The dimensions $\text{ML}^{-1}\text{T}^{-2}$ may correspond to:

A
Work done by a force.
B
Linear momentum.
✓
Pressure and Energy per unit volume.
D
None of these

Answer

Correct option: C.

Pressure and Energy per unit volume.

$[$Work done$] = \text{[ML}^2\text{ T}^{-2}]$
$[$Linear momentum$] = \text{[MLT}^{-1}]$
$[$Pressure$] = \text{[ML}^{-1}\text{T}^{-2}]$
$[$Energy per unit volume$] = \text{[ML}^{-1}\text{T}^{-2}]$
From the above, we can see that pressure and energy per unit volume have the same dimension, i.e., $\text{ML}^{-1}\text{T}^{-2}.$

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MCQ 41 Mark

A unitless quantity:

✓
Never has a non-zero dimension.
B
Always has a non-zero dimension.
C
May have a non-zero dimension.
D
Does not exist.

Answer

Correct option: A.

Never has a non-zero dimension.

A unitless quantity never has a non-zero dimension.

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MCQ 51 Mark

A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then:

A
$\text{n}\propto\text{size of u}$
B
$\text{n}\propto\text{u}^2$
C
$\text{n}\propto\sqrt{\text{u}}$
✓
$\text{n}\propto\frac{1}{\text{u}}$

Answer

Correct option: D.

$\text{n}\propto\frac{1}{\text{u}}$

The larger the unit used to express the physical quantity, the lesser will be the numerical value.
Example: 1kg of sugar can be expressed as 1000g or 10000mg of sugar.
Here, g (gram) is the larger quantity as compared to mg (milligram), but the numerical value used with gram is lesser than the numerical value used with milligram.

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MCQ 61 Mark

$\int\frac{\text{dx}}{\sqrt{2\text{ax}-\text{x}^2}}=\text{a}^{\text{n}}\sin^{-1}\Big[\frac{\text{x}}{\text{a}}-1\Big].$ The value of $n$ is:

✓
$0$
B
$-1$
C
$1$
D
None of these.

Answer

Correct option: A.

$0$

${[a x]=\left[x^2\right]}$
$\Rightarrow[a]=[x] \ldots(1)$
Dimension of $\text{LHS} =$ Dimension of $\text{RHS}$
$\Rightarrow\Big[\frac{\text{dx}}{\sqrt{\text{x}}^2}\Big]=\big[\text{a}^{\text{n}}\big]$
$\Rightarrow\Big[\frac{\text{L}}{\text{L}}\Big]=\big[\text{a}^{\text{n}}\big] \ ...(2)$
$\Rightarrow\big[\text{L}^{0}\big]=[\text{a}^{\text{n}}]$
$\text{n}=0$

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Physics M.C.Q (1 Marks)

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