Units and Measurements Test

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Units and Measurements Test - 46

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Weekly Quiz Competition

Question 1
1 / -0

Of the four figures given below, $$x_0$$ is known value of the outcome in an experiment. Which of the following data plot a precise but not an accurate measurement?

A

B

C

D
Question 2
1 / -0

The dimensions of $$ \dfrac {L}{RCV} $$ ($$ L= $$ inductance, $$ R= $$ resistance, $$ C= $$ capacitance, $$ V= $$ potential difference) are

A
[$$A$$]

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

C
[$$AT$$]

D
dimensionless

Solution

We know that:
$$[V]=[iR]=[L\dfrac{di}{dt}]$$

$$[i][R]=\dfrac{[L][i]}{[t]}$$

Thus, $$[\dfrac{L}{R}]=[t]=T$$

$$[L]=\dfrac{[V][t]}{[i]}$$

Also, $$i=C\dfrac{dV}{dt}$$, or $$[CV]={[i][t]}={A}{T}$$

Thus, $$[\dfrac{L}{RCV}]=\dfrac{T}{AT}={A}^{-1}$$
Question 3
1 / -0

The dimensions of $$ (h/e) [h= $$ Planck's constant, $$ e= electronic \ charge] $$ are same as that of

A
Magnetic field

B
Magnetic flux

C
Electric field strength

D
Electric flux

Solution

Plancks constant (h) has joule-seconds. dimensions are =$$[ML^2T^{-1}]$$
electron charge (e) will have $$[TI]$$
Dimension for h/e will be
$$[ML^2T^{-2}I^{-1}]$$
From the given options,
Dimension for magnetic moment will be  $$[L^2A]$$
Dimension for magnetic flux will be  $$[ML^2T^{-2}I^{-1}]$$
Dimension for electric flux will be  $$[ML^3T^{-3}I^{-1}]$$
Dimension for electric field strength will be  $$[MLT^{-3}I^{-1}]$$
Both magnetic flux and h/e will have same dimensions.
Question 4
1 / -0

The dimension of the expression $$ \dfrac { 1 }{ MB } $$ is

A
$$[L]$$

B
$$ [M^{-2}I T^{2}] $$

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

D
$$ [T^{-1}] $$

Solution

$$\left[ \ { 1 } /MB \right] =\dfrac { 1 }{ \left[ M \right] \left[ B \right] } =\dfrac { 1 }{ \left[ M \right] \left[ M{ I }^{ -1 }{ T }^{ -2 } \right] } $$$$=\left[ { M }^{ -2 }{ I }^{ 1 }{ T }^{ 2 } \right] $$
Question 5
1 / -0

The dimensions of $$ \dfrac{{v}^{2}}{\mu g} $$ where $$\mu=$$ coefficient of friction, $$v=$$ the velocity, $$g=$$ acceleration due to gravity is same as that of

A
$$\dfrac {F}{Bq}$$

B
$$\mu F$$

C
$$\dfrac {F}{m}$$

D
None

Solution

Units of $$\dfrac {v^2}{\mu g}$$ are $$m$$
A) Units of $$\dfrac {F}{Bq}=\dfrac {qvB}{Bq}=v$$ are $$ms^{-1}$$
B) Units of $$\mu F$$ are $$kgms^{-2}$$
C) Units of $$\dfrac {F}{m}=a$$ are $$ms^{-2}$$
D) Units of $$qvB=F$$ are $$kgms^{-2}$$
Question 6
1 / -0

The dimensional formula for magnetic permeability $$ \mu $$ is

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

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

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

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

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 7
1 / -0

What are the number of significant figures in the measurement $$ 0.0040\times10^{-15}m $$?

A
1

B
2

C
4

D
5

Solution

Zeroes before, any non zero digit are not significant, while zeroes after non zero digit after the decimal are counted as significant.
Therefore, (B) is correct.
Question 8
1 / -0

The dimensional formula of modulus of rigidity is

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

B
$$[ML^{-1}T^{-3}]$$

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

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

Solution

Modulus of rigidity is the ratio of shear stress to the shear strain.
$$\eta =\displaystyle \frac {stress}{strain}$$
Strain is dimensionless, where as Stress has the dimensions of Pressure.
$$Stress=\displaystyle \frac {F}{a}=\frac {MLT^{-2}}{L^2}=ML^{-1}T^{-2}$$
Question 9
1 / -0

If $$L$$ and $$R$$ denote inductance and resistance respectively, then the dimensions of $$L/R$$ are

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

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

C
$$[M^2L^0T^2]$$

D
$$[MLT^2]$$

Solution

The ratio $$\dfrac {L}{R}=\dfrac {[ML^2T^{-2}A^{-2}]}{[ML^2T^{-3}A^{-2}]}=T=[M^0L^0T^1]$$
Question 10
1 / -0

Area of a square is $$(100\pm 2)m^2$$. Its side is:

A
$$(10\pm 1)m$$

B
$$(10\pm 0.1)m$$

C
$$(10\pm \sqrt 2)m$$

D
$$10\pm \sqrt 2$$ %

Solution

$$Area=(Length)^2$$
$$Length =(Area)^{1/2}$$
$$=(100\pm 2)^{1/2}$$
$$=(100)^{1/2}\pm \dfrac {1}{2}\times 2$$
$$=(10\pm 1)m$$

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Units and Measurements Test - 46

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Units and Measurements Test - 46

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Question 1

Question 2

[$$A$$]

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

[$$AT$$]

dimensionless

Solution

Question 3

Magnetic field

Magnetic flux

Electric field strength

Electric flux

Solution

Question 4

$$[L]$$

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

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

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

Solution

Question 5

$$\dfrac {F}{Bq}$$

$$\mu F$$

$$\dfrac {F}{m}$$

None

Solution

Question 6

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

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

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

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

Solution

Question 7

1

2

4

5

Solution

Question 8

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

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

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

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

Solution

Question 9

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

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

$$[M^2L^0T^2]$$

$$[MLT^2]$$

Solution

Question 10

$$(10\pm 1)m$$

$$(10\pm 0.1)m$$

$$(10\pm \sqrt 2)m$$

$$10\pm \sqrt 2$$ %

Solution

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