Using a weight scale, a half-full beaker of pure water at 20oC, a small solid un

Question

Using a weight scale, a half-full beaker of pure water at 20oC, a small solid uniform sphere on a long thin piece of thread, and nothing else, explain how you could accurately measure the density of the sphere. We know that the density of the sphere is known to be between 5 grams/mm3 and 8 grams/mm3. Mention any concepts, assumptions, or approximations that you use. The sizes of the scale, beaker, and sphere are as shown in the picture.

Using a weight scale, a half-full beaker of pure water at 20oC, a small solid uniform sphere on a long thin piece of thread, and nothing else, explain how you could accurately measure the density of the sphere. We know that the density of the sphere is known to be between 5 grams/mm3 and 8 grams/mm3. Mention any concepts, assumptions, or approximations that you use. The sizes of the scale, beaker, and sphere are as shown in the picture.

Explanation / Answer

1. First measure the weight of te solid ball in the weight scale given. From this, we obtain the 'mass' of the solid ball.

We know that density=mass/volume. So we are yet to find out the volume of the solid ball. For tis we follow the following procedure.

2. First measure the weight of the glass half full with water. We know that the density of water is 1000kg/m3. So from the mass of water, we can find out the initial volume of water.

Assumption, here we for now assume that the mass of te glass is negligable compared to that of water

3. Then immerse the solid ball completely in the glass of water. Thus, the solid ball displaces some volume of water.

Then measure the weight of the glass again.

From, Archimedes law of Buoyancy: The volume of a body is equal to the volume of water it displaces.

Thus, from te new mass of water obtained, we can find the new volume of water since we know that density of water=1000kg/m3.

4. Now Volume of solid=volume of water displaced=New volume-old volume (both these values are measured before)

Thus density= mass of solid/volume of solid

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