$A$ block of mass $m$ is kept in an elevator which starts moving downward with an acceleration $a$ as shown in the figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. The observer $B$ (who is on the ground) finds that the work done by gravity on the block is:

• A
  $\frac{1}{2}m{g^2}t_0^2$
• B
  $-\frac{1}{2}m{g^2}t_0^2$
• C
  $\frac{1}{2}mgat_0^2$
• D
  $-\frac{1}{2}mgat_0^2$