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A large block of ice cuboid of height h and density 0.9g/cm^3 has a large vertical hole along it's axis . This block is floating in a water lake find the length of the rope required to raise the bucket of water through the hole. the answer for this is h/10.can u explain this ?
Most Upvoted Answer
A large block of ice cuboid of height h and density 0.9g/cm^3 has a la...
The density of ice is 0.9 therefore 90% of it is immersed in water and 10% is above water level
Hence length of the Rope required to raise the bucket of water through the hole is h/10
Hence length of the Rope required to raise the bucket of water through the hole is h/10
Community Answer
A large block of ice cuboid of height h and density 0.9g/cm^3 has a la...
Problem: Find the length of the rope required to raise a bucket of water through a vertical hole in a large block of ice cuboid floating in a water lake.
Solution:
Given:
- Height of the ice cuboid = h
- Density of the ice cuboid = 0.9 g/cm^3
Approach:
To solve this problem, we need to consider the principle of buoyancy. When an object is partially or completely submerged in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object.
Step 1: Calculation of Volume of Ice Cuboid:
The volume of the ice cuboid can be calculated using the formula:
Volume = Length × Width × Height
Here, since the ice cuboid is a block, its length and width will be greater than its height. Let's assume the length and width of the ice cuboid are L and W, respectively. Therefore, the volume of the ice cuboid is:
Volume = L × W × h
Step 2: Calculation of Weight of Ice Cuboid:
The weight of the ice cuboid can be calculated using the formula:
Weight = Density × Volume × g
Here, the density of the ice cuboid is given as 0.9 g/cm^3, and g is the acceleration due to gravity (approximately 9.8 m/s^2). However, we need to convert the density from g/cm^3 to kg/m^3 for consistent units. Therefore, the density becomes 900 kg/m^3.
Weight = 900 × (L × W × h) × 9.8
Step 3: Calculation of Buoyant Force:
The buoyant force acting on the ice cuboid is equal to the weight of the water displaced by the submerged portion of the ice cuboid. Since the ice cuboid is floating, the weight of the water displaced is equal to the weight of the ice cuboid.
Buoyant Force = Weight = 900 × (L × W × h) × 9.8
Step 4: Calculation of Length of Rope:
The length of the rope required to raise the bucket of water through the hole is equal to the submerged height of the ice cuboid. As the ice cuboid is floating, the submerged height is equal to the height of the ice cuboid.
Length of Rope = h
Result:
Therefore, the length of the rope required to raise the bucket of water through the hole is h.
Solution:
Given:
- Height of the ice cuboid = h
- Density of the ice cuboid = 0.9 g/cm^3
Approach:
To solve this problem, we need to consider the principle of buoyancy. When an object is partially or completely submerged in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object.
Step 1: Calculation of Volume of Ice Cuboid:
The volume of the ice cuboid can be calculated using the formula:
Volume = Length × Width × Height
Here, since the ice cuboid is a block, its length and width will be greater than its height. Let's assume the length and width of the ice cuboid are L and W, respectively. Therefore, the volume of the ice cuboid is:
Volume = L × W × h
Step 2: Calculation of Weight of Ice Cuboid:
The weight of the ice cuboid can be calculated using the formula:
Weight = Density × Volume × g
Here, the density of the ice cuboid is given as 0.9 g/cm^3, and g is the acceleration due to gravity (approximately 9.8 m/s^2). However, we need to convert the density from g/cm^3 to kg/m^3 for consistent units. Therefore, the density becomes 900 kg/m^3.
Weight = 900 × (L × W × h) × 9.8
Step 3: Calculation of Buoyant Force:
The buoyant force acting on the ice cuboid is equal to the weight of the water displaced by the submerged portion of the ice cuboid. Since the ice cuboid is floating, the weight of the water displaced is equal to the weight of the ice cuboid.
Buoyant Force = Weight = 900 × (L × W × h) × 9.8
Step 4: Calculation of Length of Rope:
The length of the rope required to raise the bucket of water through the hole is equal to the submerged height of the ice cuboid. As the ice cuboid is floating, the submerged height is equal to the height of the ice cuboid.
Length of Rope = h
Result:
Therefore, the length of the rope required to raise the bucket of water through the hole is h.
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A large block of ice cuboid of height h and density 0.9g/cm^3 has a large vertical hole along it's axis . This block is floating in a water lake find the length of the rope required to raise the bucket of water through the hole. the answer for this is h/10.can u explain this ?
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