A calorie is a unit of energy and it equals about 4.2J where 1J=1Kgm2s-2. Suppose we employ a system of units in which the unit of mass equals αKg, the unit of length equals βm, and the unit of time is γs. Show that a calorie has a magnitude 4.2α-1β2γ2 in terms of new units.
we know that
1J=1kgm2s-2
and
1 calorie = 4.2 joule
so,
1 calorie = 4.2 x (1kgm2s-2)
or
1C = 4.2kgm2s-2
now,
a new system of units uses
mass unit = α kg
1kg = (1/α) new mass unit
or
length unit = β m
or
1m = (1/β) new length unit
time unit = γ s
or
1s = (1/ γ) new time unit
thus,
in new units
1C = 4.2x[(1/α).(1/β)2.(1/γ)-2]
thus,
1C = 4.2α-1β-2γ2