Units and Measurements Test

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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

Result

Units and Measurements Test - 29

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Question 1

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

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

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

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

Solution

Question 2

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

$$[MLT^{2}]$$

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

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

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

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

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

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

$$[ML^0T^2]$$

Solution

Question 6

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

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

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

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

Solution

Question 7

Torque and work

Stress and energy

Force and stress

Force and work

Solution

Question 8

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

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

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

not expressible in $$M, L, T$$

Solution

Question 9

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

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

$$[MLT^4]$$

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

Solution

Question 10

force

moment of force

momentum

power

Solution

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