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)

$\frac{n^3}{m_3}L_1=L_2$ and$\frac{n^2}{m}T_1=T_2$

Answer 2

The correct answer is (A) : $\frac{n^3}{m^3}L_1=L_2$ and $\frac{n^2}{m}T_1=T_2$
$[L]=\frac{[v^2]}{[a]}$
so
$\frac{[v_2]^2}{[a_2]}=\frac{[\frac{n}{m^2}v_1]^2}{[\frac{a_1}{mn}]}$
$\frac{[v_2]^2}{[a_2]}=\frac{n^3}{m^3} \frac{[v_1]^2}{[a_1]}$
or $[L_2]=\frac{n^3}{m^3}[L_1]$
Similarly
$[T]=\frac{[v]}{[a]}$
So,
$[T_2]=\frac{n^2}{m}[T1]$