Tag: fundamental and derived units

Questions Related to fundamental and derived units

Identify the uncommon quantity

Weight, spring balance, newton, kilogram 

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

  1. kilogram

  2. Weight

  3. spring balance

  4. newton

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Correct Option: A
Explanation:

The spring balance is the device used for measurement of weight. The weight of a body is measured in terms of the newton. On the other hand, kilogram is the unit for the mass of the body.


Therefore, spring balance, weight and Newton are related to the same thing i.e.the weight of a body whereas the kilogram is related to the mass of the body. So, kilogram is different.

Identify the common unit used to measure energy?

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

  1. Newtons

  2. Joules

  3. Grams

  4. Meters

  5. Liters

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Correct Option: B
Explanation:

Newton is the unit of force.

Joules is the SI unit of energy. It is equivalent to newton-meter($N-m$).
Grams is a unit of mass.
Meter is the SI unit of distance.
A liter is a unit of volume and equivalent to $dm^3$.

Therefore option $B$ is correct.

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