Units and Measurements Test

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Units and Measurements Test - 30

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Weekly Quiz Competition

Question 1
1 / -0

The dimensions of magnetic moment are

A
$$[L^2A^1]$$

B
$$[L^2A^{-1}]$$

C
$$[L^2/A^3]$$

D
$$[LA^2]$$

Solution

Magnetic moment is given as $$M=current\times area-AL^2=[L^2A^1]$$
Question 2
1 / -0

The unit and dimensions of impedance in terms of charge Q are

A
$$mho, [ML^2T^{-2}Q^{-2}]$$

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

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

D
$$ohm, [MLT^{-1}Q^{-1}]$$

Solution

Unit of impedance is $$ohm $$ and
Dimension of Impedance $$=\dfrac {V}{I}=\dfrac {W}{QI}=\dfrac {ML^2T^{-2}}{QQT^{-1}}$$$$=[ML^2T^{-1}Q^{-2}]$$
Question 3
1 / -0

If $$L$$ and $$R$$ denote inductance and resistance then dimension of $$L/R$$ is

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 4
1 / -0

The dimensional formula of current density is

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

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

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

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

Solution

Current density $$=\dfrac {Current}{area}=\dfrac {Q}{area\times t}=[M^0L^{-2}T^{-1}Q]$$
Question 5
1 / -0

The dimensional formula for relative refractive index is

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

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

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

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

Solution

Relative refractive index $$ { \mu }_{ r }$$is a ratio of refractive index of medium $$ \mu $$ to refractive index of vacuum $$ { \mu }_{ o }$$.
Hence dimensionless $$\mu_r=\dfrac {\mu}{\mu_0}=[M^0L^0T^0]$$
Question 6
1 / -0

Which physical quantities have same dimensions?

A
Moment of couple and work

B
Force and power

C
Latent heat and specific heat

D
Work and power

Solution

Moment of couple $$=$$ force $$\times$$ perpendicular distance $$=[M^1L^2T^{-2}]$$
Work $$= $$ force $$\times$$ distance $$=[M^1L^2T^{-2}]$$
They have the same dimension.
Question 7
1 / -0

The dimensions of Wien's constant are

A
$$[ML^0TK]$$

B
$$[M^0LT^0K]$$

C
$$[M^0L^0TK]$$

D
$$[MLTK]$$4

Solution

Here $${ \lambda }_{ m }$$ is maximum wavelength at temperature $$T$$
Wien's constant $$b$$ is given as $$b=\lambda_mT=LK=[M^0L^1T^0K^1]$$
Question 8
1 / -0

The dimensional formula of couple is

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

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

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

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

Solution

Dimensionally couple $$=Torque = Force\times distance=[MLT^{-2}][L]=[ML^{2}T^{-2}]$$
Question 9
1 / -0

The dimensional formula of arial velocity is

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

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

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

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

Solution

In classical mechanics, areal velocity is the rate at which area is swept out by a particle as it moves along a curve.
Areal velocity $$=\frac {area}{time}$$$$=[M^0L^{2}T^{-1}]$$
Question 10
1 / -0

If $$I$$ is the moment of inertia and $$\omega$$ the angular velocity, what is the dimensional formula of rotational kinetic energy, $$\dfrac {1}{2}I\omega^2$$?

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

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

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

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

Solution

Dimensionally rotational kinetic energy $$=Work$$ $$done=Energy$$ $$=[ML^{2}T^{-2}]$$

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Units and Measurements Test - 30

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Units and Measurements Test - 30

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SHARING IS CARING

Question 1

$$[L^2A^1]$$

$$[L^2A^{-1}]$$

$$[L^2/A^3]$$

$$[LA^2]$$

Solution

Question 2

$$mho, [ML^2T^{-2}Q^{-2}]$$

$$ohm, [ML^2T^{-1}Q^{-2}]$$

$$ohm, [ML^2T^{-2}Q^{-1}]$$

$$ohm, [MLT^{-1}Q^{-1}]$$

Solution

Question 3

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

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

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

$$[MLT^2]$$

Solution

Question 4

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

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

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

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

Solution

Question 5

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

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

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

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

Solution

Question 6

Moment of couple and work

Force and power

Latent heat and specific heat

Work and power

Solution

Question 7

$$[ML^0TK]$$

$$[M^0LT^0K]$$

$$[M^0L^0TK]$$

$$[MLTK]$$4

Solution

Question 8

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

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

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

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

Solution

Question 9

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

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

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

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

Solution

Question 10

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

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

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

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

Solution

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