Suppose two students are trying to make a new measurement system so that they can use it like a ...
0Suppose two students are trying to make a new measurement system so that they can use it like a code measurement. Instead of taking \( 1 \mathrm{~kg}, 1 \mathrm{~m} \) and \( 1 \mathrm{~s} \), as the basic unit they took unit of mass as \( \alpha \mathrm{kg} \), the unit of length as \( \beta \mathrm{m} \) and the unit of time as \( \gamma \mathrm{s} \). They called the new system
as ACME. Column I represents the units of the physical quantities, Column II represents the ACME units and Column III represents the CGS units of the physical quantities.
\begin{tabular}{llll}
\hline \multicolumn{2}{l}{ Column I } & Column II & Column III \\
\hline (I) & \( 1 \mathrm{~N} \) in new system & (i) \( \left[\alpha^{-1} \beta^{-2} \gamma^{2}\right] \) & (J) \( \mathrm{g} \mathrm{cm}^{2} \mathrm{~s}^{-3} \) \\
(II) & \( 1 \mathrm{~J} \) in new system & (ii) \( \left[\alpha^{2} \beta^{2} \gamma^{-3}\right] \) & (K) dyne \( \mathrm{cm}^{-2} \) \\
(III) 1 Pa in new system & (iii) \( \left[\alpha^{-1} \beta^{1} \gamma^{2}\right] \) & (L) dyne \\
(IV) \( 1 \mathrm{~W} \) in new system & (iv) \( \left[\alpha^{-1} \beta^{-1} \gamma^{2}\right] \) & (M) erg \\
\hline
\end{tabular}
Which of the following represents the correct combination for tension?
(A) (I) (iv) (L)
(B) (III) (ii) (K)
(C) (IV) (iii) (M)
(D) (II) (i) (J)
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