1 , J of energy is to be converted into a new | vedclass

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

Vedclass · Accepted Answer

$36 	imes 10^{-1}$

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(D) The dimensional formula for energy is $[M L^2 T^{-2}]$.Let the $SI$ system be system $1$ and the new system be system $2$.In $SI$ system: $M_1 = 1 \, kg$,$L_1 = 1 \, m$,$T_1 = 1 \, s$.In the new system: $M_2 = 10 \, kg$,$L_2 = 10 \, m$,$T_2 = 1 \, minute = 60 \, s$.Using the conversion formula $n_2 = n_1 [M_1/M_2]^1 [L_1/L_2]^2 [T_1/T_2]^{-2}$:$n_2 = 1 	imes [1 \, kg / 10 \, kg]^1 	imes [1 \, m / 10 \, m]^2 	imes [1 \, s / 60 \, s]^{-2}$$n_2 = (1/10) 	imes (1/10)^2 	imes (1/60)^{-2}$$n_2 = (1/10) 	imes (1/100) 	imes (60)^2$$n_2 = (1/1000) 	imes 3600 = 3.6 = 36 	imes 10^{-1}$.

$1 \, J$ of energy is to be converted into a new system of units in which length is measured in $10 \, m$,mass in $10 \, kg$,and time in $1 \, minute$. The numerical value of $1 \, J$ in the new system is:

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