A new system of units is proposed in which unit of mass is alpha kg, unit of length betam and unit of time gammas. How much will 5J measure in this new system?

A new system of units is proposed in which unit of mass is alpha kg, u

1.	A new system of units is proposed in which unit of mass is alpha kg, unit of length betam and unit of time gammas. How much will 5J measure in this new system?
Answer» SOLUTION :[Energy] `=[ML^(2)T^(-2)]` Let `M_(1),L_(1),T_(2) and M_(2), L_(2), T_(2)`are units of mass, length and time in given two system, `:.M_(1)=kg, L_(1)=1m, T_(1)=1s` `M_(2)= alpha kg, L_(2)= beta m,T_(2) = gammas` The magnitude of a physical QUANTITY remains the same, whatever be the system of units of its MEASUREMENT i.e. `n_(1)u_(1)=n_(2)u_(2)` `n_(2)=n_(1)(u_(1))/(u_(2))=n_(1)([M_(1)L_(1)^(2)T_(1)^(2)])/([M_(2)L_(2)^(2)T_(2)^(-2)])=5` `[(M_(1))/(M_(2))]xx[(L_(1))/(L_(2))]^(2)xx[(T_(1))/(T_(2))]^(-2)` `=5[(1)/(alpha)]xx[(1)/(beta)]xx[(1)/(GAMMA)]^(-2)` `=5xx(1)/(alpha)xx(1)/(beta^(2))xx(1)/(gamma^(-2))` `n_(2)=(5gamma^(2))/(alpha beta^(2))` Thus, NEW unit of energy will be `(gamma^(2))/(alpha beta^(2))`