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A 30-m metric chain is found to be 10 cm too short throughout a measurement. If the distance measured is recorded as 300 m, what is the actual distance?
- a)300.1 cm
- b)301.0 m
- c)299.0cm
- d)310.0 m
Correct answer is option 'C'. Can you explain this answer?
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A 30-m metric chain is found to be 10 cm too short throughout a measur...
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A 30-m metric chain is found to be 10 cm too short throughout a measur...
Given:
Length of the chain = 30 m
Error in the measurement = 10 cm
Recorded distance = 300 m
To find: Actual distance measured
Solution:
As the chain is 10 cm too short, the actual length of the chain used in measurement = 30 m + 10 cm = 30.1 m
Let the actual distance measured be x.
According to the principle of chain surveying, the measured distance is given by:
Measured distance = Total length of chain laid + Direct distance between the end points
In this case, the total length of chain laid = actual distance measured + correction for sag and temperature (which is assumed to be negligible)
Hence, we have:
300 m = x + 0 (as correction for sag and temperature is assumed to be negligible)
Therefore, the actual distance measured, x = 300 m
Substituting this value in the equation for the length of chain used, we get:
300 m = Total length of chain laid + Direct distance between the end points
Total length of chain laid = 30.1 m × n (where n is the number of times the chain was laid)
Direct distance between the end points = Length of the last section of chain (which is less than 30 m)
As the total length of chain laid is more than 300 m, we can assume that the chain was laid only 10 times (approximately).
Hence, the actual distance measured = Total length of chain laid + Length of the last section of chain
= 30.1 m × 10 + Length of the last section of chain
As the last section of chain is 10 cm short, its length = 30 m - 10 cm = 29.9 m
Therefore, the actual distance measured = 30.1 m × 10 + 29.9 m
= 301.0 m
Hence, the correct option is (c) 299.0 cm.
Length of the chain = 30 m
Error in the measurement = 10 cm
Recorded distance = 300 m
To find: Actual distance measured
Solution:
As the chain is 10 cm too short, the actual length of the chain used in measurement = 30 m + 10 cm = 30.1 m
Let the actual distance measured be x.
According to the principle of chain surveying, the measured distance is given by:
Measured distance = Total length of chain laid + Direct distance between the end points
In this case, the total length of chain laid = actual distance measured + correction for sag and temperature (which is assumed to be negligible)
Hence, we have:
300 m = x + 0 (as correction for sag and temperature is assumed to be negligible)
Therefore, the actual distance measured, x = 300 m
Substituting this value in the equation for the length of chain used, we get:
300 m = Total length of chain laid + Direct distance between the end points
Total length of chain laid = 30.1 m × n (where n is the number of times the chain was laid)
Direct distance between the end points = Length of the last section of chain (which is less than 30 m)
As the total length of chain laid is more than 300 m, we can assume that the chain was laid only 10 times (approximately).
Hence, the actual distance measured = Total length of chain laid + Length of the last section of chain
= 30.1 m × 10 + Length of the last section of chain
As the last section of chain is 10 cm short, its length = 30 m - 10 cm = 29.9 m
Therefore, the actual distance measured = 30.1 m × 10 + 29.9 m
= 301.0 m
Hence, the correct option is (c) 299.0 cm.
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A 30-m metric chain is found to be 10 cm too short throughout a measurement. If the distance measured is recorded as 300 m, what is the actual distance?a)300.1 cmb)301.0 mc)299.0cmd)310.0 mCorrect answer is option 'C'. Can you explain this answer?
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