Question

How do I answer this buoyancy question?

Using a block that is 12.0 cm wide, 7.0 cm long and 9.0 cm tall answer the following questions.

A. If the block weights 500.0 grams how much of the block will be below the surface of the water?

B. How much would the block have to weigh so that it floats half way under water?

C. If the entire block was under water how much water would it displace?

Answer 1

please see below

Explanation:

Let,`x cm` of the block will be below the surface of the water,so for equilibrium,weight of the block must get balanced by the buoyancy force of water on `12*7*x cm^3` volume of the block

So, `500 g = 12*7*x*1*g` (density of water = `1 g/ (cm^3)`)

So, `x=5.94 cm`

To,float half way under the water the block must weigh equals to the buoyancy force exerted by water on `12*7*(9/2) cm^3` volume of the cube,

i.e `12*7*(9/2)*1*g=370818` Dyne(unit of force in C.G.S)

If the entire block was under water,it would have displaced water equals to the buoyancy force exerted by the water on its full volume = `12*7*9*1*g=756g` Dyne weight of water or `756 gm` of water.