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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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Verified Answer
A solid cylinder of 15 cm diameter and 40 cm long, consists of two par...
Explanation: 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.
Most Upvoted Answer
A solid cylinder of 15 cm diameter and 40 cm long, consists of two par...
Solution:
Given data:
Diameter of cylinder = 15 cm
Length of cylinder = 40 cm
Specific gravity of first part = 6.5
Length of first part = 1.5 cm
Specific gravity of second part = 0.75
We need to find if the cylinder can float vertically in water or not.
Density of a material = Specific gravity x Density of water
Density of water = 1000 kg/m³ (at 4°C)
Density of first part = 6.5 x 1000 = 6500 kg/m³
Density of second part = 0.75 x 1000 = 750 kg/m³
Volume of first part = (π/4) x D² x L
= (π/4) x (15/100)² x (1.5/100)
= 0.001989 m³
Volume of second part = (π/4) x D² x L
= (π/4) x (15/100)² x (38.5/100)
= 0.018085 m³
Total volume of cylinder = Volume of first part + Volume of second part
= 0.001989 + 0.018085
= 0.020074 m³
Total weight of cylinder = Density x Volume x g
where g = acceleration due to gravity = 9.81 m/s²
Weight of first part = Density of first part x Volume of first part x g
= 6500 x 0.001989 x 9.81
= 127.95 N
Weight of second part = Density of second part x Volume of second part x g
= 750 x 0.018085 x 9.81
= 130.61 N
Total weight of cylinder = Weight of first part + Weight of second part
= 127.95 + 130.61
= 258.56 N
Buoyant force on cylinder = Weight of water displaced by cylinder
= Density of water x Volume of cylinder x g
= 1000 x 0.020074 x 9.81
= 1.973 N
As the buoyant force on cylinder (1.973 N) is greater than the total weight of cylinder (258.56 N), the cylinder will float vertically in water.
Hence, the correct option is A) It will float.
Given data:
Diameter of cylinder = 15 cm
Length of cylinder = 40 cm
Specific gravity of first part = 6.5
Length of first part = 1.5 cm
Specific gravity of second part = 0.75
We need to find if the cylinder can float vertically in water or not.
Density of a material = Specific gravity x Density of water
Density of water = 1000 kg/m³ (at 4°C)
Density of first part = 6.5 x 1000 = 6500 kg/m³
Density of second part = 0.75 x 1000 = 750 kg/m³
Volume of first part = (π/4) x D² x L
= (π/4) x (15/100)² x (1.5/100)
= 0.001989 m³
Volume of second part = (π/4) x D² x L
= (π/4) x (15/100)² x (38.5/100)
= 0.018085 m³
Total volume of cylinder = Volume of first part + Volume of second part
= 0.001989 + 0.018085
= 0.020074 m³
Total weight of cylinder = Density x Volume x g
where g = acceleration due to gravity = 9.81 m/s²
Weight of first part = Density of first part x Volume of first part x g
= 6500 x 0.001989 x 9.81
= 127.95 N
Weight of second part = Density of second part x Volume of second part x g
= 750 x 0.018085 x 9.81
= 130.61 N
Total weight of cylinder = Weight of first part + Weight of second part
= 127.95 + 130.61
= 258.56 N
Buoyant force on cylinder = Weight of water displaced by cylinder
= Density of water x Volume of cylinder x g
= 1000 x 0.020074 x 9.81
= 1.973 N
As the buoyant force on cylinder (1.973 N) is greater than the total weight of cylinder (258.56 N), the cylinder will float vertically in water.
Hence, the correct option is 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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