Question

A flask of water rests on a scale that reads 100 NN. Then, a small block of unknown material is held completely submerged in the water. The block does not touch any part of the flask, and the person holding the block will not tell you whether the block is being pulled up (keeping it from falling further) or pushed down (keeping it from bobbing back up). Assume that no water spills out of the flask. (Figure 1)

Rank these blocks on the basis of the scale reading when the blocks are completely submerged.

Rank from largest to smallest. To rank items as equivalent, overlap them.

A, B, C, D, E, F

If the blocks were released while submerged, which, if any, would sink to the bottom of the flask?

Enter the correct letters from the table in alphabetical order without commas or spaces (e.g., ABC).

Answer 1

We are given that scale reads with water. We know that when the block is submerged in the flask of water then upward buoyant force act on the block will act.

The buoyant force is given as:

Where is the density of the water, is the mass of the water displaced by block, is the volume submerged block i.e. equal displaced volume of water due to block is completely submerged, and   is the gravitational acceleration.

The normal weight of the block in the air is given as:

Block has apparent weight once the block is completely submerged into the water which is given as:

Where is the density of the block.

Let's say, we have following blocks:

Since the sinking depends on the density of the block, reading on the scale depends on volume of the block in this case. When the volume of the blocks is equal to each other, then, reading on the scale depends on the mass of the block. Whichever block has the highest volume and lowest mass will cause to give highest reading on the scale. Therefore, the rank of the blocks based on reading on the scale from highest to lowest is .