$1'' = \dots \text{rad}$

Precise measurements of physical quantities are a need of science. For example,to ascertain the speed of an aircraft,one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War $II$. Think of different examples in modern science where precise measurements of length,time,mass,etc.,are needed. Also,wherever you can,give a quantitative idea of the precision needed.

What is the accuracy of an atomic clock?

$(a)$ The earth-moon distance is about $60$ earth radii. What will be the angular diameter of the earth (approximately in degrees) as seen from the moon?
$(b)$ The moon is seen to have an angular diameter of $(1/2)^{\circ}$ from the earth. What is its relative size compared to the earth?
$(c)$ From parallax measurement,the sun is found to be at a distance of about $400$ times the earth-moon distance. Estimate the ratio of sun-earth diameters.

The angle of $1^{\prime}$ (minute of arc) in radian is nearly equal to

In an experiment,a set of readings are obtained: $1.24 \ mm, 1.25 \ mm, 1.23 \ mm, 1.21 \ mm$. The expected least count of the instrument used in recording these readings is . . . . . . $mm$.