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A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :
- a)30 kg
- b)95 kg
- c)90 kg
- d)50 kg
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat...
Volume of water displaced = (4 x 1.5 x 0.015) m3 = 0.09 m3
Mass of man = Volume of water displaced x Density of water = 0.09 x 1000 = 90 kg
Hence, option 3.
Mass of man = Volume of water displaced x Density of water = 0.09 x 1000 = 90 kg
Hence, option 3.
Most Upvoted Answer
A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat...
Solution:
Given,
Length of the boat = 4 m
Breadth of the boat = 1.5 m
The boat sinks by 1.5 cm when a man gets on it.
Let the mass of the man be 'm' kg.
We know that,
Density = Mass/Volume
Volume of water displaced by boat = Volume of boat
= Length × Breadth × Height
= 4 × 1.5 × H
= 6H
Volume of water displaced by boat when a man gets on it = Volume of boat + Volume of man
= 4 × 1.5 × 0.015 + (4 × 1.5 × 0.015)
= 0.09 + 0.09
= 0.18 m³
Let the density of water be 'd' kg/m³.
Weight of water displaced by boat = Volume of water displaced by boat × Density of water
= 0.18 × d
Weight of water displaced by boat when a man gets on it = (0.18 × d) + (m × g)
Where,
g = Acceleration due to gravity = 9.8 m/s²
According to Archimedes principle,
Upthrust = Weight of water displaced by boat when a man gets on it
Therefore,
Upthrust = (0.18 × d) + (m × g)
We know that,
Upthrust = Weight of boat + Weight of man
Weight of boat = Density of boat × Volume of boat × g
= (mass of boat/volume of boat) × volume of boat × g
= Mass of boat × g
= 4 × 1.5 × 1000 × g
= 6000g
Therefore,
(0.18 × d) + (m × g) = 6000g + m × g
(0.18 × d) = 6000g + m × g - m × g
(0.18 × d) = 6000g
m = (0.18 × d)/g
Given,
d = 1000 kg/m³
m = (0.18 × 1000)/9.8
m = 18.37 ≈ 18 kg
Therefore, the mass of the man is 90 kg (Option C).
Given,
Length of the boat = 4 m
Breadth of the boat = 1.5 m
The boat sinks by 1.5 cm when a man gets on it.
Let the mass of the man be 'm' kg.
We know that,
Density = Mass/Volume
Volume of water displaced by boat = Volume of boat
= Length × Breadth × Height
= 4 × 1.5 × H
= 6H
Volume of water displaced by boat when a man gets on it = Volume of boat + Volume of man
= 4 × 1.5 × 0.015 + (4 × 1.5 × 0.015)
= 0.09 + 0.09
= 0.18 m³
Let the density of water be 'd' kg/m³.
Weight of water displaced by boat = Volume of water displaced by boat × Density of water
= 0.18 × d
Weight of water displaced by boat when a man gets on it = (0.18 × d) + (m × g)
Where,
g = Acceleration due to gravity = 9.8 m/s²
According to Archimedes principle,
Upthrust = Weight of water displaced by boat when a man gets on it
Therefore,
Upthrust = (0.18 × d) + (m × g)
We know that,
Upthrust = Weight of boat + Weight of man
Weight of boat = Density of boat × Volume of boat × g
= (mass of boat/volume of boat) × volume of boat × g
= Mass of boat × g
= 4 × 1.5 × 1000 × g
= 6000g
Therefore,
(0.18 × d) + (m × g) = 6000g + m × g
(0.18 × d) = 6000g + m × g - m × g
(0.18 × d) = 6000g
m = (0.18 × d)/g
Given,
d = 1000 kg/m³
m = (0.18 × 1000)/9.8
m = 18.37 ≈ 18 kg
Therefore, the mass of the man is 90 kg (Option C).
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A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer?
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A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer?.
A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat of length 4 m and breadth 1.5 m is floating on a lake. The boat sinks by 1.5 cm when a man gets on it. The mass of man is :a)30 kgb)95 kgc)90 kgd)50 kgCorrect answer is option 'C'. Can you explain this answer?.
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