Question

Make two tiny holes, of the same size, at equal heights from bottom in a plastic bottle. Cover them and fill the bottle with water. Let the ‘covers’ be now removed. State the ‘observations’, and the ‘conclusions’, based on this activity.

Answer 1

Hint: In order to solve this question we need to understand buoyancy. We know from Newton’s laws of motion that any material opposes the change in its state so when water or any liquid is being pressed by some object then water opposes this behavior in its change of state and hence it exerts an upward or buoyant force on the volume of object inside liquid, this is known as buoyancy.

Complete step by step answer:
Before opening the lid water is filled in under pressure so it’s obvious that if some exit point is there then water tries to exit from it and release the pressure inside it.
Observations:
-If the holes are uncovered then water exits from both holes with the same pressure.
-Velocity with which liquid flows out of hole is the same.
-Range of water during efflux from holes is same

Conclusions:
-For explanation of the same pressure. Since the pressure inside liquid is given by,
$P = \rho gh$
Where, $\rho $ is density of liquid, $g$ is acceleration due to gravity, $h$ is height of liquid above hole and $p$ is pressure at that point.
-So for both liquid height and every other component is same, hence pressure would be equal.

For explanation of same velocity:
-From Torricelli’s theorem, velocity of efflux is defined as, $v = 2gh$.
-So for both the holes, height and acceleration due to gravity is same so velocity of efflux is same.

For explanation of same range covered by water:
Water effluxing out from both holes trace the projectile motion, so the range covered by water is given as,
$R = \sqrt {2h(H - h)} $
Here, $H$ is the height of liquid and $h$ is the height of liquid above hole. Since for both the holes H and h is same so water effluxing would cover the same range.

Note: It should be remembered that water flowing out of hole would trace only projectile motion is evident from the fact that motion is happening only under one acceleration and that is under acceleration due to gravity and it is only in y direction. If the water bottle is spined up after removing the cover then it may not cover the same range although velocity and pressure would be the same.