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?

Why is the parallax method not used to measure the distance of stars that are $100$ light-years away?

The magnitude of any physical quantity

Which of the following pairs is incorrect?

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 distance of the Sun from Earth is $1.5 \times 10^{11} \,m$ and its angular diameter is $2000 \,s$ when observed from the Earth. The diameter of the Sun will be ...........