Looking for classes? Ksquare Career Institute, Bengaluru →
Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $v_{2} = (n/m^{2})v_{1}$ and $a_{2} = (a_{1}/mn)$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are:
Explanation
Given, $v_{2} = \frac{n}{m^{2}}v_{1} \Rightarrow \frac{L_{2}}{T_{2}} = \frac{n}{m^{2}} \cdot \frac{L_{1}}{T_{1}}$ and $a_{2} = \frac{a_{1}}{mn}$ $\frac{L_{2}}{T_{2}} = \frac{L_{1}}{T_{1}^{2}} \cdot \frac{1}{mn}$ Dividing (ii) by (i), we get, $\frac{L_{2}/L_{2}}{L_{2}/L_{2}^{2}} = \frac{{n/m}^{2} \cdot L_{1}/T_{1}}{L_{1}/T_{1}^{2} \cdot 1/mm} \Rightarrow T_{2} = \frac{n^{2}}{m} \cdot T_{1}$ as, $L_{2} = \frac{T_{2}}{T_{1}} \cdot L_{1}\frac{n}{m^{2}} = \frac{n^{2}}{m}L_{1}\frac{n}{m^{2}} = \frac{n^{3}}{m^{3}}L_{1}$