Question

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.

Answer 1

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