Question

Write the units of the following:
a) Volume​
b) Speed
c) Force
d) Power
e) Momentum

Answer 1

Hint : All units in the SI can be expressed in terms of the base units. We need to define the terms and then derive their equation in terms of the seven base units.

Complete step by step answer
Derived quantities are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.
a) We know that volume of a body is the product of its length, breadth and height. Since the SI unit for all the three is $m$, the unit of Volume is: ${m^3}$.
b) Speed is distance covered in unit time. Mathematically, ${\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$.
Now we know, distance is the length of path traversed and the SI unit of length is metre (m and the SI unit of time is seconds(s).
Thus the unit of Speed is: $m/s$
c) Force exerted on a body is given by the product of its mass and acceleration. The SI unit of mass is $kg$. Acceleration is the rate of change of velocity and its unit is given by, $acceleration = \dfrac{{m/s}}{s} = m/{s^2}$
Thus the unit of Force is: $kgm/{s^2}$.
d) Power is the amount of energy transferred or converted per unit time. It is the rate of doing work.
Mathematically, $Power = \dfrac{{Work}}{{Time}} = \dfrac{{Force \times Displacement}}{{Time}}$
This implies, $\dfrac{{kgm/{s^2} \cdot m}}{s}$ where $kgm/{s^2}$ is the unit of force, $m$ is the unit of displacement and $s$ is the unit of time.
Thus, the unit of power is given by, $kg{m^2}/{s^3}$.
e) Momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.
Mathematically, $p = mv$ where $p$ is the momentum, $m$ is the mass and $v$ is the velocity.
Thus, the unit of momentum is given by $kgm{s^{ - 1}}$.

Note
The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the second, with the symbol s, which is the SI unit of the physical quantity of time; the metre, symbol m, the SI unit of length; kilogram (kg, the unit of mass); ampere (A, electric current); kelvin (K, thermodynamic temperature); mole (mol, amount of substance); and candela (cd, luminous intensity). Note that 'the choice of the base units was never unique, but grew historically and became familiar to users of the SI'. All units in the SI can be expressed in terms of the base units, and the base units serve as a preferred set for expressing or analysing the relationships between units. The system allows for an unlimited number of additional units, called derived units, which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier.