We need mechanical equivalent of heat because:
1) It converts work into heat
2) In C.G.S system, heat is not measured in the units of work
3) In S.I., heat is measured in the units of work.
4) Of some reason other than those mentioned above.

Hint:In early days the mechanical equivalent of heat is given as the interchangeability between motion and heat the only condition is that the work done is completely converted to heat energy. It played an important part in conservation of energy.

Complete step by step solution:
There were many misconceptions about heat in the early days, it was considered to be a kind of fluid until the mid-19^th century, it was called a caloric theory of heat. It was considered to be massless liquid which flows from hotter to colder bodies. Later it was disapproved. The correct definition of heat is the flow of energy from a warmer to a colder substance. The need for the mechanical equivalent of heat rise because if one does any mechanical work there would be heat produced for example take your hands and rub them together you will notice that your hand is getting warmer as you continue to rub your hand, here the mechanical work of rubbing is converting into heat. In the ideal case all the work done should be converted into heat but this is not possible.

There are various ways to measure heat. In the C.G.S system heat is measured in calories or kilocalories at the same time as heat is a form of energy its S.I unit is in joules. To make the comparison easier we use a factor for conversion which is named as mechanical heat equivalent:

$1cal = 4.2 \times {10^7} = 4.2J$;

Final Answer:Option “2” is correct. In C.G.S system, heat is not measured in the units of work

Note:Here, we need to define heat and give a proper background as what was heat considered to be. Then explain about the need for the mechanical equivalent for heat and give a proper definition. Write the conservation factor which mediates the difference between the two units.