In two systems of relations among velocity , acceleration , and force are , respectively , `v_(2) = (alpha^(2))/( beta) v_(1) , a_(2) = alpha beta a_(1), and F_(2) = (F_(1))/( alpha beta)`. If `alpha and beta` are constants , then make relations among mass , length , and time in two systems.

Options

A. `M_(2)=(alpha)/(beta)M_(1),L_(2)=(alpha^(2))/(beta^(2))L_(1),T_(2)=(alpha^(3)T_(1))/(beta)`
B. `M_(2)=(1)/(alpha^(2)beta^(2))M_(1),L_(2)=(alpha^(3))/(beta^(3))L_(1),T_(2)=T_(1)(alpha)/(beta^(2))`
C. `M_(2)=(alpha^(3))/(beta^(3))M_(1),L_(2)=(alpha^(2))/(beta^(2))L_(1),T_(2)=(alpha)/(beta)T_(1)`
D. `M_(2)=(alpha^(2))/(beta^(2))M_(1),L_(2)=(alpha)/(beta^(2))L_(1),T_(2)=(alpha^(3))/(beta^(3))T_(1)`

Answer

B