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Surveying - Engineering

Q1:

The ratio of the linear displacement at the end of a line, subtended by an arc of one second to the length of the line, is

A 1:206 300

B 1:3440

C 1:57

D 1:100.

ANS:A - 1:206 300

Correct answer (A)

S=r*angle.
Or s/r = angle in radians ...eq 1

S being the linear displacement.
r being the length of the line or radius.

Here Angle = 1 sec.

So, for 360 degrees the eq 1 becomes,
s/r = 2 π in radians.

As in radians 1 sec =2pi/(360*60*60), which gives us 1sec = 1/206265 radians.

And by the relationship in eq 1 above we know that,
s/r = 1/ 206265,
Or s:r = 1: 206265 close to 206300. S=r*angle.

S being the linear displacement.
R being the length of the line.

Here Angle = 1 sec.

So,l for 360 degrees s/r = 2 π in radians.

As 1 sec =2pi/(360*60*60),
So s/r = 1/ 206265,
Or s:r = 1: 206265 close to 206300.