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If all the dimensions of a prismatic bar of square cross-section suspended freely from the ceiling of a roof are doubled then the total’elongation produced by its own weight will increase
- a)eight times
- b)four times
- c)three times
- d)two times
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If all the dimensions of a prismatic bar of square cross-section suspe...
The area of bar will become 4 times, and the volume as well as weight wiii increase 8 times. So increase in elongation
Most Upvoted Answer
If all the dimensions of a prismatic bar of square cross-section suspe...
Weight of the bar will increase by a factor of 8.
Explanation:
Assuming the material of the bar remains the same, the weight of the bar is proportional to its volume. The volume of a prismatic bar of square cross-section is given by:
V = A * L
where A is the area of the square cross-section and L is the length of the bar. If all dimensions are doubled, the new volume becomes:
V' = (2A) * (2L) = 4AL
Since the material of the bar remains the same, its density remains constant. Therefore, the weight of the bar is directly proportional to its volume:
W' = 4W
where W is the weight of the original bar.
Therefore, the total weight of the bar increases by a factor of 4, or 8 times the original weight.
Explanation:
Assuming the material of the bar remains the same, the weight of the bar is proportional to its volume. The volume of a prismatic bar of square cross-section is given by:
V = A * L
where A is the area of the square cross-section and L is the length of the bar. If all dimensions are doubled, the new volume becomes:
V' = (2A) * (2L) = 4AL
Since the material of the bar remains the same, its density remains constant. Therefore, the weight of the bar is directly proportional to its volume:
W' = 4W
where W is the weight of the original bar.
Therefore, the total weight of the bar increases by a factor of 4, or 8 times the original weight.
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If all the dimensions of a prismatic bar of square cross-section suspended freely from the ceiling of a roof are doubled then the total’elongation produced by its own weight will increasea)eight timesb)four timesc)three timesd)two timesCorrect answer is option 'B'. Can you explain this answer?
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