Velocities (V) and accelerations (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 \(\mathrm{m}\) and \(\mathrm{n}\) are constants. Dimensionally relations between distances \(\left(\mathrm{S}_1\right.\) and \(\left.\mathrm{S}_2\right)\) and times \(\left(\mathrm{t}_1\right.\) and \(t_2\) ) in the two systems are respectively.

1. A \(S_2=\left(\frac{n}{m}\right)^3 S_1\) and \(t_2=\frac{n^2}{m} t_1\)
2. B \(\mathrm{S}_2=\left(\frac{\mathrm{n}}{\mathrm{m}}\right)^3 \mathrm{~S}_1\) and \(\mathrm{t}_2=\frac{\mathrm{m}}{\mathrm{n}^2} \mathrm{t}_1\)
3. C \(S_2=\frac{m}{n^2} S_1\) and \(t_2=\frac{m^2}{n^4} t_1\)
4. D \(\mathrm{S}_2=\frac{\mathrm{n}^2}{\mathrm{~m}} \mathrm{~S}_1\) and \(\mathrm{t}_2=\frac{\mathrm{m}^2}{\mathrm{n}^4} \mathrm{t}_1\)