What is the mechanical equivalent of heat $J$ ?
(A) A constant
(B) A physical quantity
(C) A conversion factor
(D) A dimensional quantity

Hint: - Mechanical work can be defined as the amount of energy which is transferred by the force. It is the scalar quantity. Mechanical work done is directly proportional to the heat produced which can be expressed as –
$ \Rightarrow W\alpha H$

Complete Solution: -
Mechanical work is the number of energy transferred by a force. It is the scalar quantity. The S.I unit of mechanical work is Joules which is also the S.I unit of energy. Heat conductivity isn't thought of to be a variety of work, since there's no macroscopically measurable force, solely microscopic forces occurring in atomic collisions.
Mechanical work done can be defined as the quantity which is directly proportional to the heat produced. It is not the physical quantity. It is denoted by $W$. Mathematically, this statement can be expressed as –
$
  W\alpha H \\
   \Rightarrow W = J \times H \\
 $
where, $H$ is the heat produced and $J$ is the mechanical equivalent of heat.
It is the dimensionless quantity and is not the constant value.
Now, we know that –
1 Joule (S.I unit) = 4.2kcal (C.G.S unit)
So, now, we can conclude that the mechanical equivalent of heat $J$ is the conversion factor, as we have seen above that we are converting the CGS system to S.I system.

Hence, the correct option and answer is (C).

Note: - The mechanical energy of a body is that a part of its total energy that is subject to alter by mechanical work. It embraces kinetic energy and potential energy Some notable styles of energy that it doesn't include are thermal energy.