A calorie is a unit of heat or energy and it equals about where . Suppose we employ a system of units in which the units of mass equals , the units of length equals , the unit of time is . Show that a calorie has a magnitude in terms of the new units.
Step 1: Given
Unit of mass:
Unit of length:
Unit of time:
Step 2: State the dimensional formula of Joule
The units of Joules are
The formula for unit conversion,
Hence, the dimensional formula is
And,
Step 3: Convert using the formula of unit conversion
Hence, proved.