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The velocity, acceleration and force in two systems of units are related as under:
(i) \( v^{\prime}=\frac{\alpha^{2}}{\beta} v \)
(ii) \( a^{\prime}=(\alpha \beta) a \)
(iii) \( F^{\prime}=\left(\frac{1}{\alpha \beta}\right) F \)
All the primed symbols belong to one system and unprimed ones belong to the other system. Here \( \alpha \) and \( \beta \) are dimensionless constants. Which of the following is/are correct?
(A) Length standards of the two systems are related by:
\[
L^{\prime}=\left(\frac{\alpha^{3}}{\beta^{3}}\right) L
\]
(B) Mass standards of the two systems are related by:
\[
m^{\prime}=\left(\frac{1}{\alpha^{2} \beta^{2}}\right) m
\]
(C) Time standards of the two systems are related by:
\[
T^{\prime}=\left(\frac{\alpha}{\beta^{2}}\right) T
\]
(D) Momentum standards of the two systems are related by:
\[
P^{\prime}=\left(\frac{1}{\beta^{3}}\right) P
\]
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