The force responsible for the downward motion of a ball dropped from rest is gravity.
The force responsible for the downward motion of the ball is the force of gravity. When a ball is dropped from rest, gravity pulls it downward, causing it to accelerate.
For example, when a ball is released from the top of a building, gravity pulls it towards the ground, causing it to gain speed as it falls.
Gravity, as described by Newton's law of universal gravitation, is the force of attraction between two masses, in this case, the ball and the Earth.
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