Question

how is momentum conserved when the big rolling ball hits the smaller rolling ball?
the big ball transfers some of its momentum to the small ball, but it keeps going forward, too.
the small ball had no momentum before the collision, and afterward it has all the momentum.
momentum is not conserved when the two balls collide.
the big ball gives all of its momentum to the small ball.

Explanation:

Momentum conservation means the total momentum before and after a collision remains the same. In a collision between two objects (here, the big and small rolling balls), momentum is transferred. The big ball doesn't lose all its momentum (so options stating it gives all or the small ball has all after - when it had none before are wrong). Momentum is conserved in such collisions (so the option saying it's not conserved is wrong). The big ball transfers some momentum to the small ball and still moves forward.

Answer:

The big ball transfers some of its momentum to the small ball, but it keeps going forward, too.