$A$ bullet of mass $m$ moving horizontally with speed $v_0$ hits a wooden block of mass $M$ that is suspended from a massless string. The bullet gets lodged into the block. If the block-bullet system swings to a maximum height $h$,how much of the initial kinetic energy of the bullet is lost in the collision?

• A
  $\frac{1}{2} m v_0^2 \left( \frac{M}{m+M} \right)$
• B
  $\frac{1}{2} m v_0^2 \left( \frac{M+m}{M} \right)$
• C
  $\frac{1}{2} m v_0^2 \left( \frac{M^2}{(m+M)^2} \right)$
• D
  $\frac{1}{2} m v_0^2 \left( \frac{(M+m)^2}{M^2} \right)$