Q1: The desired sensitivity of a bubble tube with 2 mm divisions is 30". The radius of the bubble tube should be

ANS:A - 13.75 m

Formulas:

alpha(") = s/nDsin1"
R = nLD/s.

Manipulating the formulas, we know that:
R = (1/alpha(")*sin(1"))*L,
R= 13.75. The formula is radius equals to the [sensitiveness] divided by [division (in seconds) multiplied by sine 1 second].

Radius= 2mm/30"
= 13750.987 mm (convert to meters)
= 13.75. It's quite simple guys.

As we know S=R* π --->1)
Where R is radius and π is Central angle in radian.
So S= 2mm.
π= 30" remember 1"= 0.00000484814 so 30" becomes 30* 0.00000484814= 0.0001454441 rad.

Equation (1)=> 2=R*0.0001454441.
R= 13750.98mm => 13.75 m. Angle = arc/radius or =(d/r) radians.

Because 1 Radian = 206265 second.
So, = (d/r) * 206265 second.
Given that d = 2mm or 2 * 10^-3m.
So, ={(2 * -10^-3) * 206265}÷ r.
Then @ = 412.53÷r.
Given, 30second.

So r = 412.53÷30,
r = 13.75meter.