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)

$\frac{ L _{2}}{ T _{2}}=\frac{ n }{ m ^{2}} \frac{ L _{1}}{ T _{1}}$
$\frac{ L _{2}}{ T _{2}^{2}}=\frac{ L _{1}}{ T _{1}^{2} \times mn }$
$\frac{ n }{ m ^{2}} \times \frac{ T _{2}}{ T _{1}}=\frac{ T _{2}^{2}}{ T _{1}^{2} \times mn }$
$\frac{ n ^{2}}{ m }=\frac{ T _{2}}{ T _{1}}$
$\frac{ L _{2}}{ L _{1}}=\frac{ n ^{4}}{ m ^{2}} \times \frac{1}{ mn }$
$\frac{ L _{2}}{ L _{1}}=\frac{ n ^{3}}{ m ^{3}}$