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A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.
- a)It will float
- b)It will not float
- c)Data insufficient
- d)None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A solid cylinder of 15 cm diameter and 40 cm long, consists of two par...
AG = (weight of base*distance of C.G from base point A) + (weight of upper part*distance of C.G from point A)/ )weight of base + weight of upper part)
= 14.52
By principle of buoyancy,
Weight of cylinder = Weight of water displaced
h = 38.625
AB = 19.31
BG = 14.25 - 19.31 = -4.79
GM = Metacentric height = I/∀ -BG
= 6.16
As metacentric height is positive, it will float.
= 14.52
By principle of buoyancy,
Weight of cylinder = Weight of water displaced
h = 38.625
AB = 19.31
BG = 14.25 - 19.31 = -4.79
GM = Metacentric height = I/∀ -BG
= 6.16
As metacentric height is positive, it will float.
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A solid cylinder of 15 cm diameter and 40 cm long, consists of two par...
To determine whether the solid cylinder can float vertically in water, we need to compare the weight of the cylinder to the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the cylinder.
Given:
Diameter of the cylinder = 15 cm
Length of the cylinder = 40 cm
Length of the first part (base) = 1.5 cm
Specific gravity of the first part = 6.5
Specific gravity of the second part = 0.75
Let's calculate the volume and weight of each part separately and then determine the total weight of the cylinder.
1. Calculation for the first part:
- Diameter of the first part = 15 cm
- Length of the first part = 1.5 cm
- Radius of the first part = diameter/2 = 15/2 = 7.5 cm = 0.075 m
- Volume of the first part = π * (radius^2) * length = π * (0.075^2) * 1.5 = 0.0265 m^3
- Weight of the first part = density * volume * gravity = specific gravity * density of water * volume * gravity = 6.5 * 1000 kg/m^3 * 0.0265 m^3 * 9.8 m/s^2 = 1697.45 N
2. Calculation for the second part:
- Diameter of the second part = 15 cm
- Length of the second part = Total length - Length of the first part = 40 cm - 1.5 cm = 38.5 cm = 0.385 m
- Radius of the second part = diameter/2 = 15/2 = 7.5 cm = 0.075 m
- Volume of the second part = π * (radius^2) * length = π * (0.075^2) * 0.385 = 0.0687 m^3
- Weight of the second part = density * volume * gravity = specific gravity * density of water * volume * gravity = 0.75 * 1000 kg/m^3 * 0.0687 m^3 * 9.8 m/s^2 = 500.565 N
3. Calculation for the total weight of the cylinder:
- Total weight = Weight of the first part + Weight of the second part = 1697.45 N + 500.565 N = 2198.015 N
Now, let's calculate the buoyant force acting on the cylinder:
- Volume of the cylinder = π * (radius^2) * length = π * (0.075^2) * 40 = 0.7071 m^3
- Buoyant force = density of water * volume * gravity = 1000 kg/m^3 * 0.7071 m^3 * 9.8 m/s^2 = 6921.21 N
Since the weight of the cylinder (2198.015 N) is less than the buoyant force (6921.21 N), the cylinder will float vertically in water.
Therefore, the correct answer is option 'A': It will float.
Given:
Diameter of the cylinder = 15 cm
Length of the cylinder = 40 cm
Length of the first part (base) = 1.5 cm
Specific gravity of the first part = 6.5
Specific gravity of the second part = 0.75
Let's calculate the volume and weight of each part separately and then determine the total weight of the cylinder.
1. Calculation for the first part:
- Diameter of the first part = 15 cm
- Length of the first part = 1.5 cm
- Radius of the first part = diameter/2 = 15/2 = 7.5 cm = 0.075 m
- Volume of the first part = π * (radius^2) * length = π * (0.075^2) * 1.5 = 0.0265 m^3
- Weight of the first part = density * volume * gravity = specific gravity * density of water * volume * gravity = 6.5 * 1000 kg/m^3 * 0.0265 m^3 * 9.8 m/s^2 = 1697.45 N
2. Calculation for the second part:
- Diameter of the second part = 15 cm
- Length of the second part = Total length - Length of the first part = 40 cm - 1.5 cm = 38.5 cm = 0.385 m
- Radius of the second part = diameter/2 = 15/2 = 7.5 cm = 0.075 m
- Volume of the second part = π * (radius^2) * length = π * (0.075^2) * 0.385 = 0.0687 m^3
- Weight of the second part = density * volume * gravity = specific gravity * density of water * volume * gravity = 0.75 * 1000 kg/m^3 * 0.0687 m^3 * 9.8 m/s^2 = 500.565 N
3. Calculation for the total weight of the cylinder:
- Total weight = Weight of the first part + Weight of the second part = 1697.45 N + 500.565 N = 2198.015 N
Now, let's calculate the buoyant force acting on the cylinder:
- Volume of the cylinder = π * (radius^2) * length = π * (0.075^2) * 40 = 0.7071 m^3
- Buoyant force = density of water * volume * gravity = 1000 kg/m^3 * 0.7071 m^3 * 9.8 m/s^2 = 6921.21 N
Since the weight of the cylinder (2198.015 N) is less than the buoyant force (6921.21 N), the cylinder will float vertically in water.
Therefore, the correct answer is option 'A': It will float.
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A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?
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A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?.
A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?.
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A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A solid cylinder of 15 cm diameter and 40 cm long, consists of two parts made of different materials. The first part at the base is 1.5 cm long and of specific gravity = 6.5. The other part of the cylinder is made of the material having specific gravity 0.75. State, if the it can float vertically in water.a)It will floatb)It will not floatc)Data insufficientd)None of the mentionedCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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