The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to 200 MPa stress, respectively, are

The correct option is 0.01 and 0.02.

To find the elastic and plastic strains corresponding to a stress of 200 MPa, we analyze the loading-unloading curve shown in the figure:
1. Total Strain (${\epsilon }_t$): The metal is loaded up to point A, where the stress reaches $200\text{ MPa}$. The vertical projection of point A onto the strain axis (point C) indicates that the total strain at this stress level is:
${\epsilon }_t=0.03$

2. Permanent (Plastic) Strain (${\epsilon }_p$): When the metal is unloaded from point A, it follows the unloading path AB. At point B, the stress is completely removed (0 MPa), leaving a permanent or plastic strain. The value on the strain axis at point B is labeled as:
${\epsilon }_p=0.02$

3. Elastic Strain (${\epsilon }_e$): The elastic strain is the strain that is recovered during the unloading process (represented by the segment BC along the strain axis). It is calculated as the difference between the total strain and the plastic strain:
${\epsilon }_e={\epsilon }_t-{\epsilon }_p$
Substituting the values from the graph:
${\epsilon }_e=0.03-0.02=0.01$

Therefore, the elastic strain is 0.01 and the plastic strain is 0.02, which matches the correct option.