Question

a wooden dowel has diameter of 1.2 cm . it floats in water with 0.4 cm of diameter above water determine density of watrer

Answer 1

The density of water will be 0.935 g/
`cm^(3)`

Step-by-step explanation:

It is sufficient to solve this as a 2D problem since the length of the dowel does not matter. Let p be the density of the dowel in g/cm^3, and take water density 1g/cm^{3}

The area of the whole circle is
`\pi 0.6^(2)` = 1.130
`cm^(2)`

The angle from the center of the dowel to the two water line edges is

T = (2)arccos)
`(0.2)/(0.6)`

So the area exposed above water is sector minus triangle:

`(0.60T)/(2\pi -0.3)\sqrt{{0.6^(2) -0.4^(2)}`

= 0.642 - 0.447

= 0.195
`cm^(2)`

So, the weight of the dowel is balanced by the weight of water displaced:

1.130 p

= (1.130 - 0.195)

p = 0.935 g/
`cm^(3)`