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A new system of units is proposed in which unit of mass is `alpha kg,` unit of length `beta` m and unit of time `lambda s.` How much will 5 J measure in this new system ?

Answer» We know that dimension of energy = `[ML^(2)T^(-2)]`
`"Let "M_(1), L_(1), T_(1) and M_(2), L_(2), T_(2)` are units of mass, length and time in given two systems.
`therefore M_(1)=1kg, L_(1)=1m, T_(1)=1s`
`M_(2)=alphakg, L_(2)=betam, 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)`
`Rightarrow 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/alphakg]xx[1/betam]^(2)xx[1/gammas]^(-2)`
= `5xx1/alphaxx1/beta^(2)xx1/gamma^(-2)`
`n_(2)=(5gamma^(2))/(alphabeta^(2))`
Thus, new unit of energy will be `(gamma^(2))/(alphabeta^(2))`.


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