Answer to Question #145203 in Physics for Harrison

Question

A solid cylinder has a density of 8.9g/cm^3 and weighs 72g. Find its apparent weight when immersed totally in a liquid of density 0.8g/cm^3.

Answer 1

By the definition of the apparent weight, we have:

$$W_{A}=W_{c}-F_B,$$

here, $W_{A}$ is the apparent weight of the solid cylinder, $W_c$ is the weight of the cylinder in air, $F_B=\rho_{liquid}V_{liquid}g$ is the buoyant force that acts on the solid cylinder when it submerged in liquid, $\rho_{liquid}=800\ \dfrac{kg}{m^3}$ is the density of the liquid, $V_{liquid}=V_{c}$ is the volume of the liquid displaced that is equal to the volume of the solid cylinder and $g=9.8\ \dfrac{m}{s^2}$ is the acceleration due to gravity.

Let's first find the volume of the liquid displaced:

$$V_{liquid}=V_{c}=\dfrac{m}{\rho},$$ $$V_{liquid}=\dfrac{0.072\ kg}{8900\ \dfrac{kg}{m^3}}=8.1\cdot 10^{-6}\ m^3.$$

Finally, we can find the apparent weight of the solid cylinder:

$$W_{A}=W_{c}-F_B,$$ $$W_{A}=mg-\rho_{liquid}V_{liquid}g,$$

$W_{A}=0.072\ kg\cdot 9.8\ \dfrac{m}{s^2}-800\ \dfrac{kg}{m^3}\cdot 8.1\cdot 10^{-6}\ m^3\cdot 9.8\ \dfrac{m}{s^2}=0.64\ N.$

Answer:

$W_{A}=0.64\ N.$