Given the fact that the motor cortex controls movement of contralateral body parts, if your grandfather experiences damage to his right hemisphere motor cortex due to a stroke, it is likely that he will:

Have some paralysis on left side of his body.

Explanation:

In contralateral paralysis, the damage caused to the brain on one side but its effect occurs on the other side of the body. For example, on the right side of the brain if a stroke occurs than the paralysis will occur on the left leg. Thus, the grandfather is likely to be affected on his leg due to stroke in his right-hemispheric motor cortex.