Question

If \[E = m{c^2}\] where, \[m = \] mass of the body \[c = \] speed of light Guess the name of physical quantity \[E\].

Answer 1

Hint: We will be substituting the S.I. units of the physical quantities present on the right-hand side of the given equation to find the S.I. unit of physical quantity on the left side, which is E. According to the final unit obtained, we will define the name of physical quantity E.

Complete step by step solution:
It is given that m is mass of the body, and c is the speed of light. We are required to name the physical quantity Expressed in terms of mass and speed of light as below.
\[E = m{c^2}\]
Let us write the given equation in its unit's form.
\[{\rm{Unit of }}E = \left( {{\rm{unit of }}m} \right){\left( {{\rm{unit of }}c} \right)^2}\]……(1)
S.I. unit of mass of the body is the kilogram, denoted by kg.
S.I. unit of speed of light is \[{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}\].

Substitute kg for the unit of m and \[{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}\] for the unit of c in equation (1).
\[
{\rm{Unit of }}E = \left( {{\rm{kg}}} \right){\left( {{{\rm{m}} {\left/
 {\vphantom {{\rm{m}} {\rm{s}}}} \right.
} {\rm{s}}}} \right)^2}\\
 = {\rm{kg}} \cdot {{{{\rm{m}}^2}} {\left/
 {\vphantom {{{{\rm{m}}^2}} {{{\rm{s}}^2}}}} \right.
} {{{\rm{s}}^2}}}
\]……(2)

We know that Joule can be represented in the MKS system, and its value is as given below.
\[{\rm{J}} = {\rm{kg}} \cdot {{{{\rm{m}}^2}} {\left/
 {\vphantom {{{{\rm{m}}^2}} {{{\rm{s}}^2}}}} \right.
} {{{\rm{s}}^2}}}\]
Substitute J for \[{\rm{kg}} \cdot {{{{\rm{m}}^2}} {\left/
 {\vphantom {{{{\rm{m}}^2}} {{{\rm{s}}^2}}}} \right.
} {{{\rm{s}}^2}}}\] in equation (2).
\[{\rm{Unit of }}E = {\rm{J}}\]
We also know that Joule is the unit of energy, such as heat, work, etc.

Therefore, we can conclude that the physical quantity E is the given body's energy and its unit is Joule.

Note:
It would be an added advantage if we remember the unit conversions of some standard physical quantities units into their base units that are kg, meter, and second.
Additional information: The given equation \[E = m{c^2}\] is called Einstein's equation, which shows that a body's mass and energy can be transformed into each other.