$A$ dumbbell consisting of two masses $m$ each,connected by a light rigid rod of length $l$,falls from a height $h$ onto two pads of equal height,one steel and the other brass. The coefficients of restitution are $e_1$ and $e_2$ $(e_1 < e_2)$. To what maximum height will the centre of mass of the dumbbell rise after bouncing off the pads?

• A
  $\frac{h}{e_1 + e_2}$
• B
  $(e_1 + e_2)^2 \frac{h}{4}$
• C
  $\frac{e_1^2 + e_2^2}{4} \times h$
• D
  $\frac{4h}{e_1^2 + e_2^2}$