What buoyant force does a 0.60-kg solid gold crown experience when it is immersed in water? The density of gold is $19.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and that of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Question

What buoyant force does a  0.60-kg solid gold crown experience when it is immersed in water? The density of gold is $19.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and that of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

Quizplus · Accepted Answer

The buoyant force on an object submerged in a fluid equals the weight of the fluid displaced by the object. Since the crown is solid gold and submerged in water, the volume of water displaced equals the volume of the crown. The buoyant force can be calculated using the formula for buoyant force, $F_b = \rho_{fluid} \cdot V_{displaced} \cdot g$, where $\rho_{fluid}$ is the density of the fluid (water in this case), $V_{displaced}$ is the volume of fluid displaced, and $g$ is the acceleration due to gravity. First, find the volume of the crown using its mass and the density of gold: $V = \frac{m}{\rho_{gold}} = \frac{0.60 \, \text{kg}}{19.3 \times 10^3 \, \text{kg/m}^3}$. Then, calculate the buoyant force using the density of water ($1000 \, \text{kg/m}^3$) and $g \approx 9.8 \, \text{m/s}^2$. The calculation shows that the buoyant force is approximately 0.30 N, making option C correct.

What Buoyant Force Does a 0 19.3×103 kg/m319.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }19.3×103 kg/m3

What Buoyant Force Does a 0 $19.3 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$