Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as V 2= n m 2 v 1 and a2= a1 m n respectively. Here m and n are constants. The relations for distance and time in two systems respectively are

(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 Mains · Physics · STD 11 - Units,dimensions and measurement

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

Pick an option to check your answer.

Verified Solution

Correct Answer

(A) \(\frac{ n ^{3}}{ m ^{3}} L _{1}= L _{2}\) and \(\frac{ n ^{2}}{ m } T _{1}= T _{2}\)

Detailed explanation

\(\frac{ L _{2}}{ T _{2}}=\frac{ n }{ m ^{2}} \frac{ L _{2}}{ T _{1}}\)

\(\frac{ L _{2}}{ T _{2}^{2}}=\frac{ L _{1}}{ T _{1}^{2} \times mn }\)

\(\frac{ n }{ m ^{2}} \times \frac{ T _{2}}{ T _{1}}=\frac{ T _{2}^{2}}{ T _{1}^{2} \times mn }\)

\(\frac{ n ^{2}}{ m }=\frac{ T _{2}}{ T _{1}}\)

\(\frac{ L _{2}}{ L _{1}}=\frac{ n ^{4}}{ m ^{2}} \times \frac{1}{ mn }\)

\(\frac{ L _{2}}{ L _{1}}=\frac{ n ^{5}}{ m ^{3}}\)

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