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 . . . . . . $mm$.

Explain the concepts of accuracy and precision in measurement with an example.

Explain the method for the measurement of the diameter of a planet or star.

$A$ celestial object is observed from two points $A$ and $B$ on the Earth,which are diametrically opposite. The angle between the two observation directions is $2.9 \times 10^{-4} \text{ rad}$. Taking the diameter of the Earth to be $1.28 \times 10^4 \text{ km}$,find the distance between the Earth and the object.

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes $0.01 \, cm^3$ of oleic acid per $cm^3$ of the solution. Then you make a thin film of this solution (monomolecular thickness) of area $4 \, cm^2$ by considering $100$ spherical drops of radius $\left(\frac{3}{40 \pi}\right)^{1/3} \times 10^{-3} \, cm$. Then the thickness of the oleic acid layer will be $x \times 10^{-14} \, m$. Where $x$ is ...... .

$A$ huge circular arc of length $4.4 \; ly$ subtends an angle of $4''$ (arcseconds) at the centre of the circle. How long would it take for a body to complete $4$ revolutions if its speed is $8 \; AU/s$?
Given: $1 \; ly = 9.46 \times 10^{15} \; m$,$1 \; AU = 1.5 \times 10^{11} \; m$.