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

The calorie is a unit of heat or energy and it equals about 4.2 J wher

1.	The calorie is a unit of heat or energy and it equals about 4.2 J where 1J=1kgm^(2)s^(-2). Suppose we employ a system of units in which the unit of mass equals alpha kg, the unit of length equals beta m and the unit of time isgamma s. Show that the calorie has a magnitude of 4.2alpha^(-1) beta^(-2) gamma^(2) in terms of the new units.
Answer» Solution :Calorie is the of HEAT energy. DIMENSIONAL FORMULA of energy is `ML^(2)T^(-2)` `n_(1)(M_(1)L_(1)^(2)T_(1)^(-2))=n_(2)(M_(2)L_(2)^(2)T^(-2))` Given `n_(1)=4.2, n_(2)=?` `M_(1)=1kgL_(1)=1mT_(1)=1s` `M_(2)=alpha kg L_(2)=betamT_(2)=GAMMAS` `n_(2)=n_(1)((M_(1))/(M_(2)))((L_(1))/(L_(2)))^(2)((T_(1))/(T_(2)))^(-2)=4.2(1/(alpha))(1/(beta))^(2)(1/(gamma))^(-2)` `n_(2)=4.2alpha^(-1)beta^(-2)gamma^(2)`