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Sep 24, 2016 at 3:44 comment added bpedit There is no force pulling the ball back from either frame of reference. The ball has inertia which, for this question, can be defined as resistance to acceleration. Since the ball is tethered to the car, it must accelerate with the car. This means the string must exert an unbalanced force in the forward direction. So the string must acquire a horizontal component to accomplish this. The "inertial force", if you care to use that term, would be the ball pulling back on the string.
Sep 23, 2016 at 17:59 comment added Kosala Great explanation Dr. Bill. Thanks for dissecting the situation and explaining stepwise. This helps. Do you have any idea about the situation with respect to someone in the car? Can we say this as inertial force? Obviously it is pseudo force, but I am looking for the correct term.
Sep 23, 2016 at 17:42 history answered Bill N CC BY-SA 3.0