A cube of oak with sides 15cm long floats upright in water with 10.5cm of its depth submerged. What is the density of the oak?

The weight of the oak equals the weight of a 15 x 15 x 10.5 cm block filled with water (since that is the buoyancy force). That is the displaced volume of water.

The density of the block is
(water density)x(15 x 15 x 10.5)/(15 x 15 x 15) = 1 x 10.5/15
= 0.70 gm/cm^3

To find the density of the oak, we need to use the principle of buoyancy.

The buoyant force acting on the floating object is equal to the weight of the water displaced by the object. The weight of the water displaced can be calculated by multiplying the volume of the submerged part of the object by the density of water.

Given that 10.5 cm of the cube's depth is submerged, the volume of the submerged part can be calculated as follows:

Volume submerged = length x width x depth
Volume submerged = 15 cm x 15 cm x 10.5 cm

Volume submerged = 2362.5 cm3

The density of water is approximately 1 g/cm3.

So, the weight of the water displaced by the oak cube is 2362.5 g.

Now, we need to find the mass of the oak cube. The mass can be calculated by multiplying the density of oak by the volume of the cube (since density = mass/volume).

Let's assume the density of the oak cube is represented by the symbol "p".

Density of oak = Weight of the water displaced / Volume of the cube
Density of oak = 2362.5 g / (15 cm x 15 cm x 15 cm)
Density of oak = 2362.5 g / 3375 cm3
Density of oak = 0.7 g/cm3

Therefore, the density of the oak is 0.7 g/cm3.

To calculate the density of the oak, we need to know the mass of the cube and its volume. However, only the dimensions of the cube and the depth to which it is submerged are provided.

To find the volume of the cube, we use the equation V = s^3, where s represents the length of the sides, which in this case is 15 cm. Plugging in the value, we calculate the volume of the cube:
V = 15^3 = 3375 cm^3.

Since the cube is floating in water, the buoyant force acting on it is equal to the weight of the water displaced by the submerged portion of the cube. This buoyant force is equal to the weight of the cube itself, which is given by the equation:
Weight = volume x density x gravitational acceleration.

Let's label the density of the oak as ρ_oak. The equation can be rearranged to solve for density:
density = weight / (volume x gravitational acceleration).

We know that the weight of the cube is equal to its mass times the gravitational acceleration (9.8 m/s^2). Since the weight is equal to the buoyant force, we can rewrite the equation as:
density = (density of water) x (volume of submerged portion) / (volume of the cube).

The density of water is approximately 1000 kg/m^3 or 1 g/cm^3.

To convert the volumes to consistent units, we need to multiply the volume of the submerged portion by 10^-3 to convert it from cm^3 to m^3, and the volume of the cube by (10^-2)^3 to convert it from cm^3 to m^3.

Now, let's calculate the density of the oak:
density = (1 g/cm^3) x (10.5 cm^3 x 10^-3) / (3375 cm^3 x (10^-2)^3).

Simplifying the equation, we have:
density = 1 x 10.5 x 10^-3 / 3375 x (10^-2)^3.

density = 0.000311.

Therefore, the density of the oak is 0.000311 g/cm^3.

Part inside = 10.5 /15

And inside also equal to d1/d2
And u get the answer 0.70
G/cm3