Question

Velocity $(v)$ and acceleration $(a)$ in two systems of units $1$ and $2$ are related as $v_2=\frac{n}{m^2}{v}_1$ and $a_2=\frac{a_1}{mn}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are:

• A. $\frac{n^3}{m^3}{L}_1=L_2$ and $\frac{n^2}{m}{T}_1=T_2$
• B. $L_1=\frac{n^4}{m^2}{L}_2$ and $T_1=\frac{n^2}{m}{T}_2$
• C. $L_1=\frac{n^2}{m}{L}_2$ and $T_1=\frac{n^4}{m^2}{T}_2$
• D. $\frac{n^2}{m}{L}_1=L_2$ and $\frac{n^4}{m^2}{T}_1=T_2$

Answer 1

Answer: (A)

$\frac{L_2}{T_2}=\frac{n}{m^2}\frac{L_1}{T_1}$
$\frac{L_2}{T_2^2}=\frac{L_1}{T_1^2\times mn}$
$\frac{n}{m^2}\times \frac{T_2}{T_1}=\frac{T_2^2}{T_1^2\times mn}$
$\frac{n^2}{m}=\frac{T_2}{T_1}$
$\frac{L_2}{L_1}=\frac{n^4}{m^2}\times \frac{1}{mn}$
$\frac{L_2}{L_1}=\frac{n^3}{m^3}$