Units and Measurements Test

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Units and Measurements Test - 32

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Weekly Quiz Competition

Question 1
1 / -0

The dimensions of magnetic field in $$M, L, T$$ and $$C$$ (coulomb) are given as

A
$$[MLT^{-1}C^{-1}]$$

B
$$[MT^{2}C^{-2}]$$

C
$$[MT^{-1}C^{-1}]$$

D
$$[MT^{-2}C^{-1}]$$

Solution

Force $$F$$ acting on charge $$q$$ moving with velocity $$v$$ in magnetic field $$B$$ is given as $$F=qvB$$ thus $$B=\dfrac {F}{qv}$$
$$\therefore [B]=\dfrac {[F]}{[qv]}=\dfrac {MLT^{-2}}{C\times LT^{-1}}=[MT^{-1}C^{-1}]$$
Question 2
1 / -0

1 $$\mathring{A}$$ is equal to :

A
$$0.1$$ nm

B
$$10^{-10}$$ cm

C
$$10^{-8} m$$

D
$$10^{-4} \mu$$.

Solution

1 Angstorm = $$1 \times 10^{-10} $$ m = $$0.1 \ nm$$ ($$10^{-9}$$ m)
Question 3
1 / -0

Which of the following quantities has a unit but dimensionless?

A
Strain

B
Reynolds number

C
Angular displacement

D
Poisson's ratio

Solution

Angular displacement has unit (degree or radian) but it is dimensionless as it is the ratio of like quantities
Question 4
1 / -0

Using mass $$(M)$$, length $$(L)$$, time $$(T)$$ and current $$(A)$$ as fundamental quantities, the dimension of permeability is

A
$$\displaystyle \left [ M^{-1}LT^{-2}A \right ]$$

B
$$\displaystyle \left [ ML^{-2}T^{-2}A^{-1} \right ]$$

C
$$\displaystyle \left [ MLT^{-2}A^{-2} \right ]$$

D
$$\displaystyle \left [ MLT^{-1}A^{-1} \right ]$$

Solution

Magnetic permeability is a constant of proportionality that exists between magnetic induction and magnetic field intensity.

In SI units, permeability is measured in henries per meter $$H/m$$ or $$H m^{-1}$$.
Henry has the dimensions of $$[ML^2T^{-2}A^{-2}]$$.
Dimensions for magnetic permeability will be $$[ML^2T^{-2}A^{-2}]/[L]=$$$$[MLT^{-2}A^{-2}]$$
Question 5
1 / -0

Count total number of Significant Figures in 3.0800

A
3

B
5

C
1

D
2

Solution

S.F. = Five, as trailing zeros after decimal place are significant.
Question 6
1 / -0

Count total number of significant figures in 3500

A
1

B
2

C
3

D
4

Solution

S.F. = Two , the trailing zeros are not significant.
Question 7
1 / -0

Dimensional formula of power is :
(West Bengal/NTSE Stage-l/2013)

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

B
$$[ML^{2}T^{-3}]$$

C
$$[M^{2}LT^{-3}]$$

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

Solution

power$$=\cfrac{work}{time} ; work=force\times displacement ; $$
$$Force=mass\times acceleration $$;
$$acceleration=\cfrac{velocity}{time}$$ ;
$$velocity=\cfrac{displacement}{time}$$
$$acceleration=\cfrac{velocity}{time}=\cfrac{\left[ L \right]}{\left[ T^2 \right] }$$
$$P=\cfrac{Work}{Time}=\cfrac{Force \times displacement}{Time} =\cfrac{\left[ M \right] \times \cfrac{\left[ L \right]}{\left[ T^2 \right] } \times L}{T}=\cfrac{\left[ MLL \right] }{T^3}=\left[ ML^2T^{-3} \right] $$
Hence, option $$B$$ is correct.
Question 8
1 / -0

A physical quantity $$X$$ is expressed as velocity $$\displaystyle =\sqrt{\dfrac{X}{Density}}$$ The dimension of $$X$$ are

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

B
$$MLT^{-2}$$

C
$$MLT^{-1}$$

D
$$ML^{-1}T^{-3}$$

Solution

$$[X]=[(velocity)^{2}Density]$$
$$=[(L^{2}T^{-2})ML^{-3}]=[ML^{-1}T^{-2}]$$
Question 9
1 / -0

Count total number of significant figures in 0.00418

A
5

B
4

C
3

D
6

Solution

S.F. = Three, as leading zeros are not significant.
Question 10
1 / -0

The magnetic moment has dimensions of

A
$$\left [LA\right ]$$

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

C
$$\left [LT^{-1} A\right ]$$

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

Solution

Magnetic moment of a coil carrying current is,

$$M = I.A$$

[A is area of cross section and i is current]

Dimension of $$M = AL^{2}$$

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Units and Measurements Test - 32

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Units and Measurements Test - 32

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Question 1

$$[MLT^{-1}C^{-1}]$$

$$[MT^{2}C^{-2}]$$

$$[MT^{-1}C^{-1}]$$

$$[MT^{-2}C^{-1}]$$

Solution

Question 2

$$0.1$$ nm

$$10^{-10}$$ cm

$$10^{-8} m$$

$$10^{-4} \mu$$.

Solution

Question 3

Strain

Reynolds number

Angular displacement

Poisson's ratio

Solution

Question 4

$$\displaystyle \left [ M^{-1}LT^{-2}A \right ]$$

$$\displaystyle \left [ ML^{-2}T^{-2}A^{-1} \right ]$$

$$\displaystyle \left [ MLT^{-2}A^{-2} \right ]$$

$$\displaystyle \left [ MLT^{-1}A^{-1} \right ]$$

Solution

Question 5

3

5

1

2

Solution

Question 6

1

2

3

4

Solution

Question 7

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

$$[ML^{2}T^{-3}]$$

$$[M^{2}LT^{-3}]$$

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

Solution

Question 8

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

$$MLT^{-2}$$

$$MLT^{-1}$$

$$ML^{-1}T^{-3}$$

Solution

Question 9

5

4

3

6

Solution

Question 10

$$\left [LA\right ]$$

$$\left [L^{2}A\right ]$$

$$\left [LT^{-1} A\right ]$$

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

Solution

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