Mechanics Challenge 2 (Reposted)

Jimmy had a rectangular box of dimensions $2r \times r$ . One day, his younger sister Jane cut a semicircle with diameter as the length $2r$ because she want it for a school project. When Jimmy got to know that his box is no longer a rectangle and his calculation about where center of mass is, has gone in vain. He has blamed Jane for everything and wants her to find out how much the center of mass has sifted.

Jane is only a 9-yr old girl. Can you help her? Jimmy has although helped Jane a little by telling that the width of the box was nearly $1 m$ according to his calculation.

If the shift is $\delta$ , then Jimmy wants the answer as $\left \lfloor 10000 \delta \right \rfloor$ .