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The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?
- a)146 and 141.4 tones respectively
- b)141.4 and 146 tones respectively
- c)136.2 and 141 tones respectively
- d)141 and 136.2 tones respectively
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The hull of a boat has a volume of 150 m3 and the total mass of the b...
The boat will drown if the hull goes below the top surface of water. Thus at maximum load, the top surface of the hull will coincide with the top surface of water.
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(i) The maximum Buoyant Force in Lake
= ρ × Volume × g = 1000 × 150 × g
The weight of the empty boat
= 8560 × g
Max load it can carry
= (150 × 103 − 8560)g
= 141.4 × 103 kg
or 141.4 Tones
(ii) For Sea, maximum Buoyant force
= ρsea × Volume × g = 154.5 × 103g
Max load it can carry in sea
= (154.5 × 103 − 8560)g = 146 Tones
Most Upvoted Answer
The hull of a boat has a volume of 150 m3 and the total mass of the b...
Given data:
Volume of hull = 150 m³
Mass of empty boat = 8560 kg
Density of fresh water = 1000 kg/m³
Density of seawater = 1030 kg/m³
To find:
Maximum load the boat can carry without sinking in fresh water and sea.
Solution:
1. Calculation of weight of boat and volume of water displaced:
Weight of boat = Mass of empty boat x acceleration due to gravity
= 8560 kg x 9.81 m/s²
= 84033.6 N
Volume of water displaced = Volume of hull = 150 m³
2. Calculation of buoyancy force:
Buoyancy force = weight of water displaced x density of water
For fresh water, buoyancy force = 150 m³ x 1000 kg/m³ x 9.81 m/s²
= 1,471,500 N
For sea, buoyancy force = 150 m³ x 1030 kg/m³ x 9.81 m/s²
= 1,514,415 N
3. Calculation of maximum load:
Maximum load = buoyancy force - weight of boat
For fresh water, maximum load = 1,471,500 N - 84033.6 N
= 1,387,466.4 N
Converting to tonnes, maximum load = 1,387,466.4 N / 1000 kg/tonne
= 1,387.47 tonnes ≈ 141.4 tonnes (rounded off to one decimal place)
For sea, maximum load = 1,514,415 N - 84033.6 N
= 1,430,381.4 N
Converting to tonnes, maximum load = 1,430,381.4 N / 1000 kg/tonne
= 1,430.38 tonnes ≈ 146 tonnes (rounded off to one decimal place)
Therefore, the maximum load the boat can carry without sinking in fresh water and sea are 141.4 and 146 tonnes respectively.
Answer: (B) 141.4 and 146 tonnes respectively
Volume of hull = 150 m³
Mass of empty boat = 8560 kg
Density of fresh water = 1000 kg/m³
Density of seawater = 1030 kg/m³
To find:
Maximum load the boat can carry without sinking in fresh water and sea.
Solution:
1. Calculation of weight of boat and volume of water displaced:
Weight of boat = Mass of empty boat x acceleration due to gravity
= 8560 kg x 9.81 m/s²
= 84033.6 N
Volume of water displaced = Volume of hull = 150 m³
2. Calculation of buoyancy force:
Buoyancy force = weight of water displaced x density of water
For fresh water, buoyancy force = 150 m³ x 1000 kg/m³ x 9.81 m/s²
= 1,471,500 N
For sea, buoyancy force = 150 m³ x 1030 kg/m³ x 9.81 m/s²
= 1,514,415 N
3. Calculation of maximum load:
Maximum load = buoyancy force - weight of boat
For fresh water, maximum load = 1,471,500 N - 84033.6 N
= 1,387,466.4 N
Converting to tonnes, maximum load = 1,387,466.4 N / 1000 kg/tonne
= 1,387.47 tonnes ≈ 141.4 tonnes (rounded off to one decimal place)
For sea, maximum load = 1,514,415 N - 84033.6 N
= 1,430,381.4 N
Converting to tonnes, maximum load = 1,430,381.4 N / 1000 kg/tonne
= 1,430.38 tonnes ≈ 146 tonnes (rounded off to one decimal place)
Therefore, the maximum load the boat can carry without sinking in fresh water and sea are 141.4 and 146 tonnes respectively.
Answer: (B) 141.4 and 146 tonnes respectively
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The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. Can you explain this answer?
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The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. 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 The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. 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 The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. Can you explain this answer?.
The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. 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 The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. 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 The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. Can you explain this answer?.
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The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The hull of a boat has a volume of 150 m3 and the total mass of the boat when empty is 8560 kg. Determine how much load this boat can carry without sinking in a lake (fresh water) and in sea (S = 1.03)?a) 146 and 141.4 tones respectivelyb) 141.4 and 146 tones respectivelyc) 136.2 and 141 tones respectivelyd) 141 and 136.2 tones respectivelyCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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