Tag: measurements and units

Questions Related to measurements and units

Volume is a derived quantity of length. True or false

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. True

  2. False

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Correct Option: A
Explanation:
Volume is calculated by the multiplying length, breadth and height.
Volume  $V = l\times b\times h$
Thus volume is a derived quantity.

Identify the derived quantities among the following.

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. Gravitational constant

  2. Frequency

  3. Electric charge

  4. Electric current

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Correct Option: A,B,C
Explanation:

The derived quantities are the one which depends on the other fundamental quantities for their representation. Among the following quantities, an electric current is a fundamental quantity whereas gravitational constant, frequency and electric charge are the derived quantities.

Using dimensional analysis the resistivity in terms of fundamental constants $h, m _e, c, e, \varepsilon _o$ can be expressed as.

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. $\displaystyle\frac{h}{\varepsilon _0m _ece^2}$

  2. $\displaystyle\frac{\varepsilon _0m _ece^2}{h}$

  3. $\displaystyle\frac{h^2}{m _ece^2}$

  4. $\displaystyle\frac{m _e\varepsilon _0}{ce^2}$

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Correct Option: C
Explanation:

 SI base units of resistivity are written as $Kgm^3s^{-1}C^{-2}$.

For plank constant  $h$  SI base units are $Kgm^2s^{-1}$.
For $e$  SI unit is $C$.
For $c$  SI unit is $ms^{-1}$.
For $m _e$ SI unit is $Kg$.
For $\varepsilon _o$ SI unit is $C^2{Kg}^{-1}m^{-3}s^{2}$
Solving the dimensions of constants in option $C$,
$\dfrac{({Kgm^2s^{-1}})^2}{Kgms^{-1}C^2}=Kgm^3s^{-1}C^{-2}$
We get the dimensions of resistivity hence option $C$ is correct.

1 kg f cm$^{-2}$ .................. Nm$^{-2}$ .

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. $10^{3}$

  2. $10^{5}$

  3. $10^{4}$

  4. $10^{6}$

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Correct Option: B
Explanation:
$1kgf$ is the amount of gravitational force acting on $1kg$ of a body.
$1\ kgf\ =\ 10\ N$

And  $1m =100cm$ , 
so $1 kgf/cm^2 = 10\times10^4\ N/m^2$

we will get $10^5\ N/m^2$

Which of the following quantities has its unit as newton second?

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. Energy

  2. Torque

  3. Momentum

  4. Angular momentum

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Correct Option: C
Explanation:

Dimensional formula of newton second $=\left[ \dfrac { kgm }{ { S }^{ 2 } } \times S \right] $

$=\left[ { MLT }^{ -1 } \right] $
Dimensional formula of momentum $=\left[ { MLT }^{ -1 } \right] $
Hence, momentum has the unit as $Nsec$.

The SI unit of power is ....................... .

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. Watt

  2. Horsepower

  3. joules

  4. Kilowatt

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Correct Option: A
Explanation:
Power is defined as the rate of doing work or rate of energy consumption.
Power  $P = \dfrac{Energy}{time}$
SI unit of power is Watt.

m$^3$ is the MKS unit of ....................... .

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. Length

  2. Area 

  3. Volume

  4. mass

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Correct Option: C
Explanation:
Volume of the cuboid  $V = l\times b\times h$
So, unit of volume is  $m^3$.

Symbol for steradian is ....................... .

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. St

  2. Sa

  3. Sr

  4. Sn

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Correct Option: C
Explanation:

Steradian is a unit of solid angle. Symbol of steradian is Sr

Among the following identify derived quantities?

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. Speed

  2. Temperature

  3. Volume

  4. Mass

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Correct Option: A,C
Explanation:

(A) Speed $\displaystyle = \frac{distance}{time}$ - a derived quantity of length and time.
(B) Temperature - fundamental quantity.
(C) Volume (cube of length) - a derived quantity of length.
(D) Mass - fundamental quantity.

Which of the following is larger unit of density ?

physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

  1. $gm^{-3}$

  2. $gkm^{-3}$

  3. $kgm^{-3}$

  4. $gcm^{3}$

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Correct Option: D
Explanation:
m is the mass of an object divided by its volume. Density often has units of grams per cubic centimeter (g/cm3). Remember, grams is a mass and cubic centimeters is a volume (the same volume as 1 milliliter).