Family Responsibilities on the Common App

Is it worth mentioning family responsibilities that include: grocery shopping, aiding grandparents/parents to go to the doctor/physical therapy, and staying home to help family members with severe depression?

These things take up a lot of my time and prevent me from doing other activities so should I put them on or does it seem like I’m adding it to fill up space (I have 9 other activities listed anyway)?

It’s not about filling up space (or not). It’s about who you are and how you are balancing your interestss, passions, needs, and responsibilities. Are these family and domestic involvements a big part of who you are as a person? If you have 9 other activities, there’s no need to explain. But if these are be central to who you are, you might want to include them It’s your call.