Units and Measurements Test

Result

Units and Measurements Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

The dimensions of universal gas constant are

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

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

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

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

Solution
Question 2
1 / -0

Dimensions of impulse are

A
$[MLT^{-1}]$

B
$[MLT^{2}]$

C
$[MT^{-2}]$

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

Solution

Impulse $=$ Force $\times$ time $=MLT^{-2}T=MLT^{-1}$
Question 3
1 / -0

Which of the following set have different dimensions?

A
Pressure, Young's modulus, Stress

B
Emf, Potential difference, Electric potential

C
Heat, Work done, Energy

D
Electric dipole moment, Electric flux, Electric field

Solution

Electric dipole moment=charge $\times$ distance between charges $=[AT]\times [L]=[ALT]$
Electric flux $=$ Electric field strength x area $=[MLT^{-3}A^{-1}][L^2]=[ML^3T^{-3}A^{-1}]$
Electric field $=$ Force per unit charge $=[MLT^{-3}A^{-1}]$
Question 4
1 / -0

Which of these is dimensionless?

A
Force $/$ acceleration

B
Velocity $/$ acceleration

C
Volume $/$ area

D
Energy $/$ work

Solution

i) $\displaystyle \frac {Force}{acceleration}=\frac {kg.m.s^{-2}}{m.s^{-2}}=Kg$

ii) $\displaystyle \frac {Velocity}{acceleration}=\frac {m.s^{-1}}{m.s^{-2}}=s$

iii) $\displaystyle \frac {Volume}{Area}=\frac {m^3}{m^2}=m$

iv) $\displaystyle \frac {Energy}{Work}=\frac {J}{J}=1$
Question 5
1 / -0

The dimensions of Rydberg's constant are

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

B
$[MLT^{-1}]$

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

D
$[ML^0T^2]$

Solution

Using the relation, $\dfrac {1}{\lambda}=R\left (\dfrac {1}{n_1^2}-\dfrac {1}{n_2^2}\right )$ where ${ n }_{ 1 }\& { n }_{ 2 }$ denote orbit number and so are dimensionless
Therefore dimensions of $R=\frac {1}{L}=L^{-1}=[M^0L^{-1}T^0]$
Question 6
1 / -0

Which one of the following represents the correct dimensions of the coefficient of viscosity?

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

B
$[MLT^{-1}]$

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

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

Solution

From Stokes' law: $F_d=6\pi \eta Rv$
$\displaystyle \eta =\frac {F_d}{6\pi Rv}=\frac {MLT^{-2}}{(L)(LT^{-1})}=ML^{-1}T^{-1}$
Question 7
1 / -0

Identify the pair whose dimensions are equal.

A
Torque and work

B
Stress and energy

C
Force and stress

D
Force and work

Solution
Question 8
1 / -0

If $L$ denotes the inductance of an inductor through which a current $i$ is flowing, the dimensions of $Li^2$ are

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

B
$[MLT^{-2}]$

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

D
not expressible in $M, L, T$

Solution

Energy stored in an inductor $=\frac {1}{2}Li^2=[Energy]=[ML^2T^{-2}]$
Question 9
1 / -0

The dimensions of Hubble's constant are

A
$[T^{-1}]$

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

C
$[MLT^4]$

D
$[MT^{-1}]$

Solution

Hubble's constant, $H=\dfrac {velocity}{distance}=\dfrac {[LT^{-1}]}{[L]}$
The Hubble Constant is the unit of measurement used to describe the expansion of the universe.
Question 10
1 / -0

$[ML^2T^{-2}]$ are dimensions of

A
force

B
moment of force

C
momentum

D
power

Solution

Force $=[ML^1T^{-2}]$
Moment of force $=r\times F=[L][MLT^{-2}]=[ML^2T^{-2}]$ .....correct
Momentum $=[ML^1T^{-1}]$
Power $=[ML^2T^{-3}]$

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Units and Measurements Test - 29

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Units and Measurements Test - 29

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Question 1

[L2M1T−2K−1][L^2M^1T^{-2}K^{-1}][L2M1T−2K−1]

[L1M2T−2K−1][L^1M^2T^{-2}K^{-1}][L1M2T−2K−1]

[L1M1T−2K−1][L^1M^1T^{-2}K^{-1}][L1M1T−2K−1]

[L2M2T−2K−1][L^2M^2T^{-2}K^{-1}][L2M2T−2K−1]

Solution

Question 2

[MLT−1][MLT^{-1}][MLT−1]

[MLT2][MLT^{2}][MLT2]

[MT−2][MT^{-2}][MT−2]

[ML−1T−3][ML^{-1}T^{-3}][ML−1T−3]

Solution

Question 3

Pressure, Young's modulus, Stress

Emf, Potential difference, Electric potential

Heat, Work done, Energy

Electric dipole moment, Electric flux, Electric field

Solution

Question 4

Force///acceleration

Velocity///acceleration

Volume///area

Energy///work

Solution

Question 5

[M0L−1T][M^0L^{-1}T][M0L−1T]

[MLT−1][MLT^{-1}][MLT−1]

[M0L−1T0][M^0L^{-1}T^0][M0L−1T0]

[ML0T2][ML^0T^2][ML0T2]

Solution

Question 6

[ML−1T−1][ML^{-1}T^{-1}][ML−1T−1]

[MLT−1][MLT^{-1}][MLT−1]

[ML−1T−2][ML^{-1}T^{-2}][ML−1T−2]

[ML−2T−2][ML^{-2}T^{-2}][ML−2T−2]

Solution

Question 7

Torque and work

Stress and energy

Force and stress

Force and work

Solution

Question 8

[ML2T−2][ML^2T^{-2}][ML2T−2]

[MLT−2][MLT^{-2}][MLT−2]

[M2L2T−2][M^2L^2T^{-2}][M2L2T−2]

not expressible in M,L,TM, L, TM,L,T

Solution

Question 9

[T−1][T^{-1}][T−1]

[M0L0T−2][M^0L^0T^{-2}][M0L0T−2]

[MLT4][MLT^4][MLT4]

[MT−1][MT^{-1}][MT−1]

Solution

Question 10

force

moment of force

momentum

power

Solution

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

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

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

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

$[MLT^{-1}]$

$[MLT^{2}]$

$[MT^{-2}]$

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

Force $/$ acceleration

Velocity $/$ acceleration

Volume $/$ area

Energy $/$ work

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

$[MLT^{-1}]$

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

$[ML^0T^2]$

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

$[MLT^{-1}]$

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

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

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

$[MLT^{-2}]$

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

not expressible in $M, L, T$

$[T^{-1}]$

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

$[MLT^4]$

$[MT^{-1}]$