The distance of the Sun from the Earth is $1.496 \times 10^{11} \ m$ and the diameter of the Sun is $1.393 \times 10^9 \ m$. Find the angular diameter of the Sun in radians.

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)	$19.00$	$1.14$

$A$ far-off planet is estimated to be at a distance $D$ from the Earth. If its diametrically opposite extremes subtend an angle $\theta$ at an observatory situated on the Earth,the approximate diameter of the planet is .............

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?

The angle subtended by a plate of diameter $2 \, cm$ at a distance of $1000 \, cm$ from the eye is ..... (in $^\circ$)