A surveyor's 30-m steel tape is correct at 68° F. On a hot day, the tape has expanded to 30.02 m. On that day, the tape indicates a distance of 15.52 m between two points. The true distance between these points is : A) 15.50 m B) 15.53 m C) 15.54 m D) 15.51 m E) 15.52 m

As we know that due to increase in temperature the length of the tape shall increase thus it shall give incorrect measurements when we measure any length by it.

We know that

Error = Measured Value - True Value

Thus for the given tape

[tex]Error=32.02-32=0.02m[/tex]

Thus for the second observation we have

True Value = Measured Value - Error

[tex]\therefore TrueValue=15.52-0.02=15.50m[/tex]

Thus option 'a' is the correct answer.

andromache andromache · Answer 2 · 2022-02-22T14:53:46+01:00

The true distance between these points is option b. 15.53 m

Calculation of true distance:

Since tape has extended to 30.02 m length, therefore the true length(TL) of 30.02 m will be measured as 30 m.

Now

ML of 30 m corresponds to TL of 30.02 m.

Also,

1 m of ML = (30.02/30) m of TL

so,

15.52 m of ML = (15.52 x 30.02/30) m of TL

= 15.53 m

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