Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as V _{2}=frac{ n }{ m ^{2}} v

Q: 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 $a_{2}=\frac{a_{1}}{m n}$ respectively. Here $m$ and $n$ are constants. The relations for distance and time in two systems respectively are

a $\frac{ L _{2}}{ T _{2}}=\frac{ n }{ m ^{2}} \frac{ L _{2}}{ T _{1}}$ $\frac{ L _{2}}{ T _{2}^{2}}=\frac{ L _{1}}{ T _{1}^{2} \times mn }$ $\frac{ n }{ m ^{2}} \times \frac{ T _{2}}{ T _{1}}=\frac{ T _{2}^{2}}{ T _{1}^{2} \times mn }$ $\frac{ n ^{2}}{ m }=\frac{ T _{2}}{ T _{1}}$ $\frac{ L _{2}}{ L _{1}}=\frac{ n ^{4}}{ m ^{2}} \times \frac{1}{ mn }$ $\frac{ L _{2}}{ L _{1}}=\frac{ n ^{5}}{ m ^{3}}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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 $a_{2}=\frac{a_{1}}{m n}$ 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 $\frac{ n ^{4}}{ m ^{2}} T _{1}= T _{2}$

JEE MAIN 2022, Diffcult

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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