A calorie is a unit of heat or energy and it equals about 4.2 J, where 1 J = 1 kg m^(2) s^(-2). Suppose we employ a system of units in which the unit of mass equals alpha kg, the unit of length equals is beta m , the unit oftime is gamma s. Show tthat a calorie has a magnitude 4.2 alpha^(-1) beta^(-1) gamma^(2) in terms of the new units.

A calorie is a unit of heat or energy and it equals about 4.2 J, where

1.	A calorie is a unit of heat or energy and it equals about 4.2 J, where 1 J = 1 kg m^(2) s^(-2). Suppose we employ a system of units in which the unit of mass equals alpha kg, the unit of length equals is beta m , the unit oftime is gamma s. Show tthat a calorie has a magnitude 4.2 alpha^(-1) beta^(-1) gamma^(2) in terms of the new units.
Answer» SOLUTION :`n_(2)=n_(1)[(M_(1))/(M_(2))]^(a)((L_(1))/(L_(2)))^(B)((T_(1))/(T_(2)))^(c)` `=4.2((kg)/(alphakg))^(1)((m)/(BETAM))^(2)((s)/(gammas))^(-2)` `n_(2)=4.2alpha^(-1)beta^(-2)gamma^(2)`