3. The density of water is 1.00 × 10³ kg/m³. What is the density of the duck? (a) 1.00 x 10³ kg/m³ (b) 2.50 x 10³ kg/m³ (c) 2.50 x 10² kg/m³ (d) 7.50 x 10³ kg/m³ (e) 7.50 x 10² kg/m³ A duck is floating on a lake with 25% of its volume beneath the water.
3. The density of water is 1.00 × 10³ kg/m³. What is the density of the duck? (a) 1.00 x 10³ kg/m³ (b) 2.50 x 10³ kg/m³ (c) 2.50 x 10² kg/m³ (d) 7.50 x 10³ kg/m³ (e) 7.50 x 10² kg/m³ A duck is floating on a lake with 25% of its volume beneath the water.
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![### Question 3:
A duck is floating on a lake with 25% of its volume beneath the water. The density of water is \(1.00 \times 10^3 \, \text{kg/m}^3\). What is the density of the duck?
#### Options:
(a) \(1.00 \times 10^3 \, \text{kg/m}^3\)
(b) \(2.50 \times 10^3 \, \text{kg/m}^3\)
(c) \(2.50 \times 10^2 \, \text{kg/m}^3\)
(d) \(7.50 \times 10^3 \, \text{kg/m}^3\)
(e) \(7.50 \times 10^2 \, \text{kg/m}^3\)
### Explanation:
The problem involves understanding the floating condition of the duck. When an object floats, the buoyant force is equal to the weight of the fluid displaced by the submerged part of the object. Here is how you can determine the density of the duck:
1. Let \( V \) be the total volume of the duck.
2. Since 25% of the duck's volume is submerged in water, the submerged volume \( V_s \) is \( 0.25V \).
3. The density of water, \( \rho_w \), is \( 1.00 \times 10^3 \, \text{kg/m}^3 \).
From the principle of buoyancy:
\[ \text{Buoyant Force} = \text{Weight of water displaced} \]
\[ \rho_w \cdot V_s \cdot g = \rho_d \cdot V \cdot g \]
Here \( \rho_d \) is the density of the duck and \( g \) is the acceleration due to gravity (which cancels out in this equation).
Solving for \( \rho_d \):
\[ \rho_w \cdot 0.25V = \rho_d \cdot V \]
\[ \rho_d = 0.25 \cdot \rho_w \]
\[ \rho_d = 0.25 \times 1.00 \times 10^3 \]
\[ \rho_d = 250 \, \text{kg/m}^3 \]
Thus, the density of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78798817-99ae-4e11-8234-c81a813df0d0%2F4a5071af-bf45-41f7-a52d-ef6dead6de88%2F3rphck_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 3:
A duck is floating on a lake with 25% of its volume beneath the water. The density of water is \(1.00 \times 10^3 \, \text{kg/m}^3\). What is the density of the duck?
#### Options:
(a) \(1.00 \times 10^3 \, \text{kg/m}^3\)
(b) \(2.50 \times 10^3 \, \text{kg/m}^3\)
(c) \(2.50 \times 10^2 \, \text{kg/m}^3\)
(d) \(7.50 \times 10^3 \, \text{kg/m}^3\)
(e) \(7.50 \times 10^2 \, \text{kg/m}^3\)
### Explanation:
The problem involves understanding the floating condition of the duck. When an object floats, the buoyant force is equal to the weight of the fluid displaced by the submerged part of the object. Here is how you can determine the density of the duck:
1. Let \( V \) be the total volume of the duck.
2. Since 25% of the duck's volume is submerged in water, the submerged volume \( V_s \) is \( 0.25V \).
3. The density of water, \( \rho_w \), is \( 1.00 \times 10^3 \, \text{kg/m}^3 \).
From the principle of buoyancy:
\[ \text{Buoyant Force} = \text{Weight of water displaced} \]
\[ \rho_w \cdot V_s \cdot g = \rho_d \cdot V \cdot g \]
Here \( \rho_d \) is the density of the duck and \( g \) is the acceleration due to gravity (which cancels out in this equation).
Solving for \( \rho_d \):
\[ \rho_w \cdot 0.25V = \rho_d \cdot V \]
\[ \rho_d = 0.25 \cdot \rho_w \]
\[ \rho_d = 0.25 \times 1.00 \times 10^3 \]
\[ \rho_d = 250 \, \text{kg/m}^3 \]
Thus, the density of the
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