The Sun's angular diameter is measured to be $1920^{\prime \prime}$. The distance $D$ of the Sun from the Earth is $1.496 \times 10^{11} \ m$. What is the diameter of the Sun?

Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms.

Substance	Atomic Mass $(u)$	Density $(10^3\,kg\,m^{-3})$
Carbon (diamond)	$12.01$	$2.22$
Gold	$197.00$	$19.32$
Nitrogen (liquid)	$14.01$	$1.00$
Lithium	$6.94$	$0.53$
Fluorine (liquid)	$19.00$	$1.14$

In an experiment to estimate the size of a molecule of oleic acid,$1\, mL$ of oleic acid is dissolved in $19\, mL$ of alcohol. Then $1\, mL$ of this solution is diluted to $20\, mL$ by adding alcohol. Now,$1$ drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water,forming a one-molecule-thick layer. Lycopodium powder is sprinkled evenly over the film,and its diameter is measured. Knowing the volume of the drop and the area of the film,we can calculate the thickness of the film,which gives us the size of the oleic acid molecule.
Read the passage carefully and answer the following questions.
$(a)$ Why do we dissolve oleic acid in alcohol?
$(b)$ What is the role of lycopodium powder?
$(c)$ What would be the volume of oleic acid in each $mL$ of the solution prepared?
$(d)$ How will you calculate the volume of $n$ drops of this solution of oleic acid?
$(e)$ What will be the volume of oleic acid in one drop of this solution?

$A$ 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.

How is time regulated in a wristwatch and a cesium clock?

It is a well-known fact that during a total solar eclipse,the disk of the Moon almost completely covers the disk of the Sun. From this fact and the information given below,determine the approximate diameter of the Moon.
Distance of the Moon from the Earth $= 3.84 \times 10^{8} \; m$
Distance of the Sun from the Earth $= 1.496 \times 10^{11} \; m$
Diameter of the Sun $= 1.39 \times 10^{9} \; m$