Question

A wooden block immersed partially into water. There were 15% of the total volume of the block

exposed and 85% of the total volume immersed in water. Calculate a. the density of the wooden block

Answer 1

Density of wooden block is 850 kilogram per cubic meter

Solution:

Given that wooden block immersed partially into water

There were 15% of the total volume of the block exposed and 85% of the total volume immersed in water

To find: density of the wooden block

The upward force exerted by any fluid upon a body placed in it is called buoyant force

Buoyant force is balanced by weight force of block

Buoyant force is weight of water displaced by block

Buoyant force =
`\rho_(w) V_(2) g`

Density of water =
`\rho_w` = 1000 kg/m3

`V_2` = volume of block in water = 0.85 V

`V_1` = Volume of block in air = 0.15 V

Weight of block =
`\rho V g`

Therefore,

`\rho V g = \rho_(w) V_(2) g\\\\\rho V = \rho_(w) V_(2)\\\\ \rho V = 1000 * 0.85V\\\\\rho = 1000 * 0.85\\\\\rho = 850`

Thus density of wooden block is 850 kilogram per cubic meter