Question

Dimension of energy in terms of force(F), length (L) and time (T) is.

Answer 1

Hint: We know that dimensions are physical quantities that are expressed as the powers of the fundamental units. Here, we have to find the dimension of energy in terms of force(F), length (L) and time (T). This can be done by using the definition of energy.

Formula used:
$E=W=F\times d$

Complete step-by-step solution:
We know that dimensional analysis is the process of checking relations between physical quantities and their dimensions. The seven most basic or the fundamental dimensions , namely, the mass, length, time, electric current, temperature, intensity of light and quantity of substance. And two supplementary quantities, plane angle and solid angle. Other physical quantities are derived from the basic dimensions.
There exist dimension variables, with dimensions and no fixed value. These examples include acceleration and force. There also exists dimensionless variables, these as the name suggests neither have dimensions or a fixed value. Some examples include specific gravity , coefficient of friction and refractive index to name a few.
We know that energy is defined as the ability to do work. We also know that energy $E$ is nothing but the work done $W$ which can be expressed mathematically as follows:
$E=W=F\times d$, where $F$ is forced and $d$ is displacement, which is nothing but length.
Then, the dimension of energy in terms of force(F), length (L) and time (T) is
$E= FL$
Thus $E= FL$ is the required dimension.

Note: The dimensions are generally expressed in terms of the basic or the supplementary quantities. Here, however, since the question is asking us to express a different notion, we express it in terms of the given dimensions. Note that the above is not the standard form of expression.