The angular diameter of the Sun is measured to be $1920''$. If the distance of the Sun from the Earth is $1.496 \times 10^{11} \ m$,calculate the diameter of the Sun. (Given: $1'' = 4.85 \times 10^{-6} \ rad$)

$A$ 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 .............

It is claimed that two cesium clocks,if allowed to run for $100$ years,free from any disturbance,may differ by only about $0.02\; s$. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of $1\; s$?

The difference between the length of a mean solar day and a sidereal day is approximately .......... minutes.

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?

$A$ tachometer is a device used to measure: