Question

A calorie is a unit of heat or energy and it equals about 4.2 J, where 1 J = 1 kgm²S^-2. Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β metere, the unit of time is second, show that a calorie has a magnitude 4.2 α^-1 β^-2 γ² in terms of the new units.

Answer 1

1 cal = 4.2kg m²s^-2

SI	New system
n1 = 4.2	n2 = ?
M1 = 1 kg	M2 = α kg
L1 = 1m	L2 = β meter
T1 = 1s	T2 = γ second

Dimensional formula of energy is [ML²T^-2]. Comparing with [M^aL^bT^c], we find that
a = 1, b = 2, c = -2