Question

What will be the weight of the 10 x 10 x 20 cm wooden box (density 2 g/ml) in the water?

Answer 1

Question 27238

The density of wood is $\rho = 2\frac{g}{ml} = 2000\frac{kg}{m^3}$ .

Usual weight is given by $P = mg = \rho gV$ .

In case if body is immersed into fluid or gas, buoyancy force acts on this body vertically up. The value of this force is $F_{b} = \rho_{\text{fluid}} g V$ , where $\rho_{\text{fluid}}$ is the density of fluid, $g = 9.81 \frac{m}{s^2}$ is the gravitational constant and $V$ is the volume of immersed part of the body. For water, $\rho_{\text{water}} = 1000 \frac{kg}{m^3}$ .

The weight in water is the difference of weight $P = mg$ and buoyancy force:

$$P ^ {\prime} = P - \rho_ {\text {water}} g V = 9.81 \mathrm {m} / \mathrm {s} ^ {2} \cdot (0.1 \cdot 0.1 \cdot 0.2) \mathrm {m} ^ {3} \cdot 2000 \frac {\mathrm {kg}}{\mathrm {m} ^ {3}} - 1000 \frac {\mathrm {kg}}{\mathrm {m} ^ {3}} \cdot 9.81 \frac {\mathrm {m}}{\mathrm {s} ^ {2}} \cdot (0.1 \cdot 0.1 \cdot 0.2) \mathrm {m} ^ {3} = 19.62 \mathrm {N}$$

Hence, the weight of box in the water is $P' = 19.62N$ .