Two masses $m_1$ and $m_2$ are connected by a string of length $l$. They are held in a horizontal plane at a height $H$ above two heavy plates $A$ and $B$ made of different materials placed on the floor. Initially,the distance between the two masses is $a < l$. When the masses are released under gravity,they collide with $A$ and $B$ with coefficients of restitution $e_1 = 0.8$ and $e_2 = 0.4$ respectively. Find the time after the collision when the string becomes tight. (Assume $H >> l$)

• A
  $\frac{5}{2}\sqrt{\frac{l^2 - a^2}{2gH}}$
• B
  $\sqrt{\frac{2g}{H}}$
• C
  $\frac{3}{2}\sqrt{\frac{l^2 - a^2}{2gH}}$
• D
  None of these