Q 11-04-080JEE MainJEE Main 2024 (6 Apr, Shift 1)Medium
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 $\dfrac{g}{\sqrt2}$, then the ratio of the masses $\dfrac{m_1}{m_2}$ is
Answer: (B) $\dfrac{\sqrt2 - 1}{\sqrt2 + 1}$
$a = \dfrac{(m_2 - m_1)g}{m_1 + m_2} = \dfrac{g}{\sqrt2}$. With $r = \dfrac{m_1}{m_2}$:
$$\frac{1 - r}{1 + r} = \frac{1}{\sqrt2} \Rightarrow \sqrt2 - \sqrt2r = 1 + r \Rightarrow r = \frac{\sqrt2 - 1}{\sqrt2 + 1}$$
Solution by Sreeraj P, M.Sc Physics