When will I be able to move my hand after 10 weeks on cast?

Depends. A good rule of thumb for the time it takes to recover motion after a period of immobilization is about the same amount of time you were immobilized.
Ask your doctor. Why are you being casted? Once the reason you have the cast on is healed enough, your physician will remove the cast and instruct you on what to do. Since you have been in a cast for 10 weeks, I am guessing you may have a fracture that is slow to heal, like a scaphoid fracture. Motion is allowed once adequate healing is confirmed with x-ray or ct scan.