Match List-$I$ (Event) with List-$II$ (Order of the time interval for happening of the event) and select the correct option from the options given below the lists:

List-$I$	List-$II$
$(1)$ Rotation period of earth	$(i)$ $10^5\, s$
$(2)$ Revolution period of earth	$(ii)$ $10^7\, s$
$(3)$ Period of light wave	$(iii)$ $10^{-15}\, s$
$(4)$ Period of sound wave	$(iv)$ $10^{-3}\, s$

The nearest star to our solar system is $4.29$ light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?

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.

The principle of 'parallax' is used in the determination of distances of very distant stars. The baseline $AB$ is the line joining the Earth's two locations six months apart in its orbit around the Sun. That is,the baseline is about the diameter of the Earth's orbit $\approx 3 \times 10^{11} \; m$. However,even the nearest stars are so distant that with such a long baseline,they show parallax only of the order of $1''$ (second of arc) or so. $A$ parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of $1''$ (second of arc) from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres?

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?

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