A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J= 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 betam, the unit of time is gammas. Show that a calorie has a magnitude 4.2alpha^(-1)beta^(-2)gamma^(2) in terms of the new units.

A calorie is a unit of heat (energy in transit) and it equals about 4.

1.	A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J= 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 betam, the unit of time is gammas. Show that a calorie has a magnitude 4.2alpha^(-1)beta^(-2)gamma^(2) in terms of the new units.
Answer» SOLUTION :1 clorie =4.2 J DIMENSIONAL formula of THEAT energy `=[M^(1)L^(2)T^(-2)]` `:.n_(2)[M_(1)^(2)L_(2)^(2)T_(2)^(-2)]=n_(1)[M_(1)^(1)L_(1)^(2)T_(1)^(-2)]` `n_(2)=n_(1)((M_(1))/(M_(2)))^(1) ((L_(1))/(L_(2)))^(2) ((T_(1))/(T_(2)))^(-2)` `=n_(1)((1)/(alpha))^(1)((1)/(beta))^(2)((1)/(GAMMA))^(-2)` `n_(2)=n_(1)(alpha^(-1)beta^(-2)gamma^(+2))` `n_(2)=4.2alpha^(-1) beta^(-2) gamma^(2)`