Question

In the figure the spring is compressed by ${}^{\prime }{x}_0^{\prime }$ and released. Two blocks ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }2m^{\prime }$ , respectively , are attached at the ends of the springs. Blocks are kept on a smooth horizontal surface and released. then find the velocity of the blocks.

Answer 1

Two blocks A and B of masses $m$ and $2m$ respectively.

Let, $V_r$ be the relative velocity of the two.

Let, the reduced mass of the $2$ block system be $\mu$

$\mu =\frac{\left(m\right)\left(2m\right)}{m+2m}=\frac{2}{3}m$

From conservation of mechanical energy we have,

$\frac{1}{2}K{x}^2=\frac{1}{2}\mu v_r^{2}K{x}^2=\mu v_r^2=\frac{2}{3}m{v}_r^2{v}_r=\left(\sqrt{\frac{3K}{2m}}\right)x$