Question

Dimensional formula $M{L^2}{T^{ - 3}}$ represents
(A)Force
(B)Power
(C)Energy
(D)Work

Answer 1

In mathematics, a dimension is a measurement of length, width, or height extended in a certain direction. It measures a point or line extended in one direction, according to dimension definition. Every shape we see has a set of dimensions. In mathematics, there is no specific dimensional formula for the idea of dimension. The power to which the fundamental units are elevated to obtain one unit of any physical quantity is called its dimension.

Formula used:
$Work(W) = \;force \times distance$
$Power = \dfrac{{Work}}{{Time}}$

Complete step by step solution:
Here we are going to find the dimensional formula $M{L^2}{T^{ - 3}}$ represents which one of the given options.
For finding dimensions for work,
Dimension of work $(W) = \;force \times distance$
So, we should apply the dimension value of both force and distance.
Dimensional value of force $(F)$ - $ML{T^{ - 2}}$
Dimensional value of distance $(d)$ - $L$
As we are multiplying both dimensional values of force $(F)$ and distance $(d)$ we will get,
$= [ML{T^{ - 2}}] \times [L] = [M{L^2}{T^{ - 2}}]$
This is the dimension value for work $(W)$.
$Power = \dfrac{{Work}}{{Time}}$
Or,
$Power\left( P \right) = Work \times time{e^{ - 1}}$
It indicates that power is the rate at which work is completed, or, to put it another way, how much energy is transmitted from one system to another over a certain time period.
The amount of energy carried or converted per unit time is defined as power in physics. The watt is a unit of power that is equal to one joule per second in the International System of Units. In ancient literature, power was often referred to as activity. Power is a scalar quantity.
For finding the dimension value for power $(P)$ we should use that above formula and to apply their dimension value,
$P = \dfrac{{[M{L^2}{T^{ - 2}}]}}{{[T]}}$
Or,
$P = [M{L^2}{T^{ - 2}}] \times [{T^{ - 1}}]$
As we are calculating these values we get,
$P = M{L^2}{T^{ - 3}}$
This is the dimension formula for Power $(P)$.
Hence Option B is the correct answer for the given question.

Note: Applications of power:
Mechanical Power: Engines in automobiles, trains, planes, and other aircraft are an example.
Electric Power: All electric appliances, elevator motors, electric automobile engines, power cables, and other similar items are prohibited.
Power of Light Sources: X-ray devices, gamma-ray cannons, radio transmitters, and other home items are examples.
Thermal Power: Turbine rotation, steam engines.
Atomic Power: Polaris submarines, atomic power reactors, and nuclear weapons.