A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2>m_1$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$, then the ratio of the masses $\frac{m_1}{m_2}$ is:

• A

  $\frac{1+\sqrt{5}}{\sqrt{5}-1}$
• Correct answer
  B

  $\frac{\sqrt{2}-1}{\sqrt{2}+1}$
• C

  $\frac{1+\sqrt{5}}{\sqrt{2}-1}$
• D

  $\frac{\sqrt{3}+1}{\sqrt{2}-1}$

Solution

$\begin{aligned} & a=\left(\frac{M_2-M_1}{M_1+M_2}\right) g \\ & \frac{g}{\sqrt{2}}=\left(\frac{M_2-M_1}{M_1+M_2}\right) g \\ & \left(M_1+M_2\right)=\sqrt{2} M_2-\sqrt{2} M_1 \\ & \frac{M_1}{M_2}=\left(\frac{\sqrt{2}-1}{\sqrt{2}+1}\right)\end{aligned}$

Hence, the correct answer is option: 'B'.