Question

A 100g object floats in a liquid of relative density 1.2.calculate

a)mass of the liquid displaced by the object.

Answer 1

By the definition, the buoyant force is equal to the weight of the liquid displace:

$$F_B=\rho_{liquid}V_{liquid}g,$$ $$m_{liquid}g=\rho_{liquid}V_{liquid}g,$$ $$m_{liquid}=\rho_{liquid}V_{liquid}.$$

We can find $\rho_{liquid}$ from the definition of relative density:

$$RD=\dfrac{\rho_{liquid}}{\rho_{water}},$$ $$\rho_{liquid}=RD\rho_{water}=1.2\cdot1000\ \dfrac{kg}{m^3}=1200\ \dfrac{kg}{m^3}.$$

Since the floating object displaces the volume of water equivalent to its own volume, we can write:

$$m_{liquid}=\rho_{liquid}V_{liquid}=m_{liquid}=\rho_{liquid}V_{obj}.$$

Unfortunately, we don't know the volume of the object. Let's suppose that the volume of the object equals $10\ cm^3$.

Then, we get:

$$m_{liquid}=1200\ \dfrac{kg}{m^3}\cdot10\ cm^3\cdot(\dfrac{1\ m}{100\ cm})^3=1.2\cdot10^{-2}\ kg.$$