Question

Write the dimensional formula of work.

Answer 1

Hint: Work is something that makes you do some physical efforts for the completion of something. The work is considered as part of the force over a distance of displacement. Hence, it is defined as the product of force and its distance, Which represents the amount of energy needed to move the object at a certain distance against a force.

Complete step by step solution:
Work is defined as the motion of something under constant force and therefore in a straight line, it is the magnitude of the force times the distance moved. generally, for the motion along any curve, it is the line integral of the force over the curve.
We can express a Work done in Joules, which is Newton's time meters. Newton describes the force, which is mass times of acceleration.
To express the work in dimension,
Mass is represented by $[M]$, length by $[L]$ and time by $[T]$
We know that
 Work = $F.{\text{ }}d$
Dimension of d is $[L]$
The dimension of force is expressed as,
$F = ma = kg.Meter/se{c^2}$
Now it becomes,
$ = [M][L]/{[T]^2}$
Then the equation becomes as follows,
$ = [M][L][{T^ - }^2]$
Now combine force dimension and distance to get the dimension of force. I.e
$F = [ML{T^{^ - 2}}][L]$
The above equation becomes,
$ = [M]{[L]^2}{[T]^ - }2$
So dimension of work is as $\left[ {{M^1}\;{L^2}\;{T^{ - 2}}} \right].$

Note:
Work is described as force over a displacement.
No work is done when the force and the displacements are perpendicular to each other.
Work is related to Kinetic energy.
Kinetic energy is defined as the energy of a moving particle.