A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2 > m1).

Question

A light string passing over a smooth light pulley connects two blocks of masses \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\) (where \(\mathrm{m}_{2}>\mathrm{m}_{1}\)). If the acceleration of the system is \(\frac{\mathrm{g}}{\sqrt{2}}\), then the ratio of the masses \(\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}\) is :

(1) \(\frac{\sqrt{2}-1}{\sqrt{2}+1}\)

(2) \(\frac{1+\sqrt{5}}{\sqrt{5}-1}\)

(3) \( \frac{1+\sqrt{5}}{\sqrt{2}-1}\)

(4) \(\frac{\sqrt{3}+1}{\sqrt{2}-1} \)  

Answer 1

Correct option is : (1) \(\frac{\sqrt{2}-1}{\sqrt{2}+1}\)

\(\mathrm{a}=\frac{\left(\mathrm{m}_2\ -\ \mathrm{m}_1\right) \mathrm{g}}{\mathrm{m}_1\ +\ \mathrm{m}_2}\)

\(\mathrm{a}=\frac{\mathrm{g}}{\sqrt{2}}=\left(\frac{\mathrm{m}_2\ -\ \mathrm{m}_1}{\mathrm{~m}_1\ +\ \mathrm{m}_2}\right) \mathrm{g} \)

\((1+\sqrt{2})\ \mathrm{m}_1=(\sqrt{2}-1) \mathrm{m}_2\)

\(\frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{\sqrt{2}\ -\ 1}{\sqrt{2}\ +\ 1}\)