## stability of submerged and floating bodies

**INTRODUCTION: **Laboratory experiment 2 is an exercise in hydrostatics. It is designed to demonstrate the stability of a floating cylinder and to familiarize the student with the concept of buoyancy, metacenter, and metacentric height. It is also an experimental verification of the theory presented in the textbook.

The center of the buoyancy (C, the centroid of the displaced volume of fluid) of a floating body depends on the shape of the body and on the position in which it is floating. If the body is disturbed by a small angle of heel, the center of buoyancy changes because the shape of the submerged volume is changed. The point of intersection of the lines of action of the buoyancy force before and after heel is called the metacenter (M) and the distance between the center of gravity (G) and M, is called the metacentric height .

**Apparatus:**There are three components of the experimental set-up:

1. Large vertically-standing cylinder containing fresh water

2. Small cylinder with a detachable cap at one end

3. Sand and a metric balance to weigh the cylinders

**Procedures:**

1. Weigh the small cylinder and its cap together (m_{c})

2. Place the small empty cylinder into the large vertical cylinder containing fresh water and observe that it is unstable.

3. Pour a small amount of sand into the small cylinder (to give some ballast) and note if it is still unstable. Estimate how much of the cylinder is submerged, h, and then measure the height of sand, h_{b} .

4. Continue adding sand until the small cylinder remains vertical, i.e., stable. Measure the amount of cylinder that is submerged. Make sure that the open end of the small cylinder is capped when stability is reached.

5. Remove the small cylinder and measure its weight. Also measure the height of sand and record your results on the data sheet.

**Stability of Unconstrained Submerged Bodies in Fluid:**

- The equilibrium of a body submerged in a liquid requires that the weight of the body acting through its center of gravity should be collinear with equal hydrostatic lift acting through the center of buoyancy.
- In general, if the body is not homogeneous in its distribution of mass over the entire volume, the location of center of gravity G does not coincide with the center of volume, i.e., the center of buoyancy B.
- Depending upon the relative locations of G and B, a floating or submerged body attains three different states of equilibrium-

Let us suppose that a body is given a small angular displacement and then released. Then it will be said to be in

- Stable Equilibrium: If the body returns to its original position by retaining the originally vertical axis as vertical.
- Unstable Equilibrium: If the body does not return to its original position but moves further from it.
- Neutral Equilibrium: If the body neither returns to its original position nor increases its displacement further, it will simply adopt its new position.