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

Any unit which can be obtained by the combination of one or more fundamental units is called

  1. Fundamental unit

  2. Scale

  3. Derived unit

  4. Standard unit
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The units which can neither derived from one another nor resolved into any thing more basic are called fundamental unit. It is independent of any other unit. Any unit which can be obtained by the combination of one or more fundamental units is called derived unit.

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

Derived units can be defined in terms of one or multiple fundamental units.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The units of fundamental quantities (length, mass,time) are known as fundamental units(meter, kilogram, second).
The derived quantities are the quantities defined in terms of fundamental quantities via a quantitative equation. Hence, the units of these fundamental quantities involved in the equation defines the derived units.
Hence, the given statement is true.
Multiple choice physics measurements and units some examples of derived units fundamental and derived quantities fundamental and derived units

Which of the following has derived dimension?

  1. Velocity

  2. Acceleration

  3. Density

  4. All of the above

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The fundamental quantities are basically mass, length,  time etc. Velocity is defined as the rate of displacement with respect to time. Displacement has dimensions same as that of length. Velocity is a derived quantity. Acceleration is defined as the rate of change of velocity with respect to time. This is how when acceleration is dependent on time and velocity. It is also a derived quantity. Density is defined as the mass of a unit volume of a substance. Volume has the dimension of the cube of length. Hence density is also a derived quantity.

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

Which of the following physical quantities has neither dimensions nor unit?

  1. angle

  2. Luminous intensity

  3. Coefficient of friction

  4. Current
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Unit of angle is radian, that of luminous intensity is candela and that of current is Ampere. Coefficient of friction is unitless and dimensionless.

Coefficient of friction$=\dfrac{Applied force}{Normal reaction}$
$=\dfrac{[MLT^{-2}]}{[MLT^{-2}]}=$No dimensions
Unit $=\dfrac{N}{N}=$No unit.

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

Pressure depends on distance as, $P=\dfrac{\alpha}{\beta}exp\left(-\dfrac{\alpha z}{k\theta}\right)$, where $\alpha, \beta$ are constants, z is distance, k is Boltzmann's constant and $\theta$ is temperature. The dimension of $\beta$ are.

  1. $M^0L^0T^0$
  2. $M^{-1}L^{-1}T^{-1}$
  3. $M^0L^2T^0$
  4. $M^{-1}L^1T^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given, 

$P=\dfrac{\alpha}{\beta}e^{\dfrac{-\alpha z}{k\theta}}$

Since, the exponentials are devoid of dimensions, the exponential part of the equation is ignored.  

Rest we have, $P=\dfrac{\alpha}{\beta}$

Since, $\dfrac{\alpha z}{k\theta}=Dimensionless$

$\alpha=\dfrac{k\theta}{z}$

Kinetic energy $=\dfrac 32 kT$

$k=\dfrac{K.E}{T}$

$\implies [k]=[M^1L^2T^{-2}][K^{-1}]$

$\implies [z]=[L^{-1}]$

$\implies [\theta]=[K^{-1}]$

From these, we get the values of $\alpha$ as,

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

Now, we know the dimension of prressure, 

$[P]=M^1l^{-1}t^{-2}]$

$\beta=\dfrac{\alpha}{P}$

$\implies \beta=\dfrac{[M^1L^1T^{-2}]}{[M^1L^{-1}T^{-2}]}$

$\implies \beta=[M^0L^2T^0]$