JEE Mains · Physics · STD 11 - 1. 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
- 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 & Solution
Correct Answer
(A) \(\frac{ n ^{3}}{ m ^{3}} L _{1}= L _{2}\) and \(\frac{ n ^{2}}{ m } T _{1}= T _{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{ L _{2}}{ T _{2}}=\frac{ n }{ m ^{2}} \frac{ L _{2}}{ T _{1}}\) \(\frac{ L _{2}}{ T _{2}^{2}}=\frac{ L _{1}}{ T _{1}^{2} \times mn }\) \(\frac{ n }{ m ^{2}} \times \frac{ T _{2}}{ T _{1}}=\frac{ T _{2}^{2}}{ T _{1}^{2} \times mn }\)…
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