A large negatively charged object is placed on a wooden table. A neutral metallic ball rolls straight towards the object but stops before it touches it. A second neutral metallic ball rolls up along the path followed by the first ball, strikes the first ball driving it a bit closer to the negatively charged object and stops. After all balls have stopped rolling, the first ball is closer to the negatively charged object than is the second ball. At no time did either ball touch the charged object. Which statement is correct concerning the final charge on each ball

the charge of each small sphere, which is + Q / 2

Explanation:

For this exercise we must use the fact that a charged object induces charges on nearby bodies

Induced charge comes from the fact that charges of the same sign repel and charges of different signs attract.

In this case the large, fixed ball with a -Q charge induces a positive charge in the nearest part and the negative charges are repelled to the furthest point, but the net charge on the metallic sphere remains zero. It should be emphasized that since the charges are of different signs, there is an attractive force between the two spheres.

This first metallic sphere now has a negative charge on the back, this charge induces a positive charge on the second sphere, as the charges are of a different sign, they attract each other, which is why the force is attractive.

When the first sphere stops the second sphere hits it, at this moment the charge of the two spheres is equal, therefore the induced charge in the two spheres is + Q. When the two spheres are separated, the charge on each of them is half, that is, the sphere has a charge + Q / 2 and the second sphere has a charge + Q / 2.

Therefore the first sphere is subjected to two forces: an attractive force with the large sphere of charge -Q and a repulsive force with the second sphere of charge + Q / 2.

So the first sphere must approach the big ball and the second sphere must move away from the big sphere.

This is the process of the movement of this exercise, unfortunately the statements with which to compare this process do not appear, but one of the most common questions of what is the charge of each small sphere, which is + Q / 2

the bal will not change its velocity.