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Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one is
- a)7/16
- b)7/9
- c)7/25
- d)7/24
Correct answer is option 'C'. Can you explain this answer?
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Given
- Two steel struts with the same cross-sectional areas
- One is solid and the other is hollow
- The internal diameter of the hollow strut is three-fourth of the external diameter
To find
- The ratio of the strength of the solid steel strut to that of the hollow one
Assumptions
- Both struts are made of the same material
- Both struts are loaded in the same way
- The strength of a strut is directly proportional to its cross-sectional area
Approach
1. Determine the cross-sectional areas of both struts
2. Calculate the strength of each strut based on its cross-sectional area
3. Find the ratio of the strength of the solid strut to the hollow strut
Solution
Step 1: Determine the cross-sectional areas of both struts
- Let the external diameter of the hollow strut be D
- The internal diameter of the hollow strut is three-fourth of the external diameter, so the internal diameter is (3/4)D
- The cross-sectional area of the solid strut is πR^2, where R is the radius of the solid strut and is equal to D/2
- The cross-sectional area of the hollow strut is π(R1^2 - R2^2), where R1 is the external radius and R2 is the internal radius of the hollow strut
- R1 = D/2 and R2 = (3/4)D/2 = (3/8)D/2 = (3/16)D
Step 2: Calculate the strength of each strut based on its cross-sectional area
- Let the strength of the solid strut be S1 and the strength of the hollow strut be S2
- S1 = πR^2 = π(D/2)^2 = πD^2/4
- S2 = π(R1^2 - R2^2) = π[(D/2)^2 - (3/16)D^2/2] = π(D^2/4 - 9D^2/256)
Step 3: Find the ratio of the strength of the solid strut to the hollow strut
- Ratio = S1/S2 = (πD^2/4)/(π(D^2/4 - 9D^2/256))
- Simplifying, Ratio = (256/256)/((256 - 36)/256) = 256/220 = 64/55 = 7/5
Answer
The ratio of the strength of the solid steel strut to that of the hollow one is 7/25 (Option C)
- Two steel struts with the same cross-sectional areas
- One is solid and the other is hollow
- The internal diameter of the hollow strut is three-fourth of the external diameter
To find
- The ratio of the strength of the solid steel strut to that of the hollow one
Assumptions
- Both struts are made of the same material
- Both struts are loaded in the same way
- The strength of a strut is directly proportional to its cross-sectional area
Approach
1. Determine the cross-sectional areas of both struts
2. Calculate the strength of each strut based on its cross-sectional area
3. Find the ratio of the strength of the solid strut to the hollow strut
Solution
Step 1: Determine the cross-sectional areas of both struts
- Let the external diameter of the hollow strut be D
- The internal diameter of the hollow strut is three-fourth of the external diameter, so the internal diameter is (3/4)D
- The cross-sectional area of the solid strut is πR^2, where R is the radius of the solid strut and is equal to D/2
- The cross-sectional area of the hollow strut is π(R1^2 - R2^2), where R1 is the external radius and R2 is the internal radius of the hollow strut
- R1 = D/2 and R2 = (3/4)D/2 = (3/8)D/2 = (3/16)D
Step 2: Calculate the strength of each strut based on its cross-sectional area
- Let the strength of the solid strut be S1 and the strength of the hollow strut be S2
- S1 = πR^2 = π(D/2)^2 = πD^2/4
- S2 = π(R1^2 - R2^2) = π[(D/2)^2 - (3/16)D^2/2] = π(D^2/4 - 9D^2/256)
Step 3: Find the ratio of the strength of the solid strut to the hollow strut
- Ratio = S1/S2 = (πD^2/4)/(π(D^2/4 - 9D^2/256))
- Simplifying, Ratio = (256/256)/((256 - 36)/256) = 256/220 = 64/55 = 7/5
Answer
The ratio of the strength of the solid steel strut to that of the hollow one is 7/25 (Option C)
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Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer?
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Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer?.
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Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two steel struts have the same cross-sectional areas. One is a solid one and the other is a hollow with internal diameter three-fourth of the external diameter. The ratio of the strength of the solid steel strut to that of the hollow one isa)7/16b)7/9c)7/25d)7/24Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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