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(B) The dimensional formula for energy is $[M L^2 T^{-2}]$.Let the two systems be $1$ $(SI)$ and $2$ (new system).In system $1$: $M_1 = 1 \ kg$,$L_1 =

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$5 \alpha^{-1} \beta^{-2} \gamma^2$

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(B) The dimensional formula for energy is $[M L^2 T^{-2}]$.Let the two systems be $1$ $(SI)$ and $2$ (new system).In system $1$: $M_1 = 1 \ kg$,$L_1 = 1 \ m$,$T_1 = 1 \ s$,and $n_1 = 5$.In system $2$: $M_2 = \alpha \ kg$,$L_2 = \beta \ m$,$T_2 = \gamma \ s$,and $n_2 = ?$.Using the principle of homogeneity,$n_1 u_1 = n_2 u_2$,so $n_2 = n_1 (M_1/M_2)^1 (L_1/L_2)^2 (T_1/T_2)^{-2}$.Substituting the values: $n_2 = 5 	imes (1/\alpha)^1 	imes (1/\beta)^2 	imes (1/\gamma)^{-2}$.$n_2 = 5 	imes (1/\alpha) 	imes (1/\beta^2) 	imes (\gamma^2)$.$n_2 = 5 \alpha^{-1} \beta^{-2} \gamma^2$.

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

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