The cork is attached by a light spring to the bottom of the water vessel. Both the cork and the spring are completely immersed in the water. Will the length of the spring increase or decrease if the vessel moves vertically up (down) with constant acceleration?

A pipe of diameter $d$ is lowered into a vessel with water. A ball of the same diameter is placed in the pipe. The center of the ball is at a depth $h$. Find the density of the substance of the ball. There is no gap between the pipe and the ball. The frictional force between them is zero.