Units and Measurements Test

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Units and Measurements Test - 40

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Weekly Quiz Competition

Question 1
1 / -0

If 'muscle times speed equals power', then what is the ratio of the $$SI$$ unit and the $$CGS$$ unit of muscle?

A
$$10^{5}$$

B
$$10^{3}$$

C
$$10^{7}$$

D
$$10^{-5}$$

Solution

Given :

Muscles $$\times$$ Speed $$=$$ Power

and we know that

Force $$\times$$ Speed $$=$$ Power

comparing both the equations;

Muscles $$=$$ Force

S.I. unit of force $$=$$ N $$=$$ Newton

CGS unit of force $$=$$ dyne

and $$1N = 10^5 dynes$$

So the SI unit of muscles will be

= $$N/ dyne=10^5$$
Question 2
1 / -0

Dimensional formula of $$\dfrac{megnetic\, flux}{electric\, flux}$$ is

A
$$[LT^{-1}]$$

B
$$[TL^{-1}]$$

C
$$[L^3T^2 A^{-2}]$$

D
$$[M^0L^0T^0]$$

Solution

Dimensional formula of magnetic flux $$=ML^2T^{-2}A^{-1}$$

Dimensional formula for electric flux $$=ML^3T^{-3}A^{-1}$$

Dimensional formula of $$\dfrac{Magnetic\, flux}{Electric flux}=\dfrac{[ML^2T^{-2}A^{-1}]}{[ML^3T^{-3}A^{-1}]}=[TL^{-1]}$$
Question 3
1 / -0

The dimensions of a modulus of elasticity are:

A
[$$MLT^{-2}$$]

B
[$$M^{2}L^{-1}T^{-2}$$]

C
[$$ML^{-1}T^{-2}$$]

D
[$$ML^{-2}T^{-2}$$]

Solution

Young modulus, $$\gamma =\dfrac{stress}{strain}=\dfrac{Force\,/\,Area}{\Delta L/L}=\dfrac{\left[ ML{{T}^{-2}} \right]/\,\left[ {{M}^{o}}{{L}^{2}}{{T}^{o}} \right]}{\left[ {{M}^{o}}L{{T}^{o}} \right]/\left[ {{M}^{o}}L{{T}^{o}} \right]}=\left[ M{{L}^{-1}}{{T}^{-2}} \right]$$

Hence, Dimension is $$\left[ M{{L}^{-1}}{{T}^{-2}} \right]$$ .
Question 4
1 / -0

Dimensional formula for pressure head is

A
$$[M^0L^0T^0]$$

B
$$[ML^{-1}T^{-2}]$$

C
$$[M^0L^1T^{-2}]$$

D
$$[M^0L^1T^0]$$

Solution

$$[Presure\,head]=\dfrac{[Pressure]}{[Density]\times [g]}$$

$$Pressure=\dfrac{Force}{Area}$$

But, $$Force=Mass \times Accelaration=[M][LT^{-2}]=[MLT^{-2}]$$

Then,

$$[Pressure]=\dfrac{[MLT^{-2}]}{[L^2]}=[ML^{-1}T^{-2}]$$

$$[Density]=\dfrac{[Mass]}{[Volume]}=\dfrac{[M]}{[L^{3}]}=ML^{-3}$$

Now,

$$[Presure\,head]=\dfrac{[Pressure]}{[Density]\times [g]}=\dfrac{[ML^{-1}T^{-2}]}{[ML^{-3}][LT^{-2}]}=[M^0L^1T^0]$$
Question 5
1 / -0

Round off to $$3$$ significant figures,
a) $$20.96$$
b) $$0.0003125$$

A
$$21.0, 312\times 10^{-4}$$

B
$$21.0, 3.12\times 10^{-4}$$

C
$$2.10, 3.12\times 10^{-2}$$

D
$$210, 3.12\times 10^{-4}$$

Solution

$$\begin{array}{l}\text { According to the rule }\\\text { of rounding off:}\end{array}$$

$$\text { (a) } 20.96^{}=21.0$$

$$\text{ (b) }0.0003125=3.125 \times 10^{-4} = 3.12 \times 10^{-4}$$
Question 6
1 / -0

The correct dimensional formula for impulse is given by

A
$$ML^2T^{-2}$$

B
$$MLT^{-1}$$

C
$$ML^2T^{-1}$$

D
$$MLT^{-2}$$

Solution

$$[Impulse]=[MLT^{-1}]$$
Question 7
1 / -0

Which one of the following does not have the same dimensions

A
Work and energy

B
Angle and strain

C
Relative density and refractive index

D
Plank constant and energy

Solution

The work and energy have the same dimensions whereas the option $$B$$ and $$C$$ have the quantities which are dimensionless.

For option $$D$$:-
[Planck constant]=$$[ML^2T^{-1}]$$
and [Energy]=$$[ML^2T^{-2}]$$

So, option $$D$$ is correct.
Question 8
1 / -0

Dimension of work done is

A
$$\left[ L ^ { 2 } M ^ { 1 } T ^ { -2} \right]$$

B
$$\left[ L ^ { 2 } M ^ { 2 } T ^ { 2 } \right]$$

C
$$\left[ L ^ { 2 } M ^ { 0 } T ^ { 0 } \right]$$

D
$$\left[ L ^ { 2 } M ^ { 2 } T ^ { -3 } \right]$$

Solution

We know that
Work done = Force $$\times $$ Displacement
$$W= MLT^{-2} \times L= [ML^2T^{-2}]$$
Question 9
1 / -0

$$L^{-1}M^{1}T^{-2}$$ are the dimension for________.

A
Pressure

B
Power

C
Force

D
Work

Solution

$$Pressure=\dfrac{Force}{Area}=\dfrac{Mass\times Acceleration}{Area}$$

$$=\dfrac{[M][LT^{-2}]}{[L^2]}=M^1L^{-1}T^{-2}$$

So, correct answer is option (A).
Question 10
1 / -0

Of the following pairs of physical quantities, which one is dimensionally odd?

A
Stress and pressure

B
Energy and work

C
Young's modulus and stress

D
Frequency and angle

Solution

All other pair have same dimensions while frequency and angle have different dimensions. The dimension of frequency is $$[T^{-1}]$$ while angle is a dimensionless quantity.

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Re-Attempt Weekly Quiz Competition

Units and Measurements Test - 40

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Units and Measurements Test - 40

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SHARING IS CARING

Question 1

$$10^{5}$$

$$10^{3}$$

$$10^{7}$$

$$10^{-5}$$

Solution

Question 2

$$[LT^{-1}]$$

$$[TL^{-1}]$$

$$[L^3T^2 A^{-2}]$$

$$[M^0L^0T^0]$$

Solution

Question 3

[$$MLT^{-2}$$]

[$$M^{2}L^{-1}T^{-2}$$]

[$$ML^{-1}T^{-2}$$]

[$$ML^{-2}T^{-2}$$]

Solution

Question 4

$$[M^0L^0T^0]$$

$$[ML^{-1}T^{-2}]$$

$$[M^0L^1T^{-2}]$$

$$[M^0L^1T^0]$$

Solution

Question 5

$$21.0, 312\times 10^{-4}$$

$$21.0, 3.12\times 10^{-4}$$

$$2.10, 3.12\times 10^{-2}$$

$$210, 3.12\times 10^{-4}$$

Solution

Question 6

$$ML^2T^{-2}$$

$$MLT^{-1}$$

$$ML^2T^{-1}$$

$$MLT^{-2}$$

Solution

Question 7

Work and energy

Angle and strain

Relative density and refractive index

Plank constant and energy

Solution

Question 8

$$\left[ L ^ { 2 } M ^ { 1 } T ^ { -2} \right]$$

$$\left[ L ^ { 2 } M ^ { 2 } T ^ { 2 } \right]$$

$$\left[ L ^ { 2 } M ^ { 0 } T ^ { 0 } \right]$$

$$\left[ L ^ { 2 } M ^ { 2 } T ^ { -3 } \right]$$

Solution

Question 9

Pressure

Power

Force

Work

Solution

Question 10

Stress and pressure

Energy and work

Young's modulus and stress

Frequency and angle

Solution

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