To measure distance or length between two points, various methods are adopted which are categorised as direct and indirect methods. Direct methods are used to measure shorter but accessible distances while indirect methods are used for inaccessible distance. Large distances, such as the distance of a planet or star from earth can be measured by the Parallax method. Parallax is the change in position of an object with respect to fixed background when object is seen from two different positions. Parallex method is used for measuring distances of stars which are less than 100 light years away.
(i) Name the instruments that are used to measure distance of the order 10^{- 5} m.
(ii) Define the terms 'basis' and parallactic angle used in Parallax method for measuring distance.
(iii) What is the measure of basis in measuring distance of a nearby star by Parallax method?
(iv) Why Parallax method is used for measuring distances of nearby stars only?
(v) What is meant by angular diameter of moon?

In the study of Physics, we often have to measure the physical quantities. The numerical value of a measured quantity can only be approximate as it depends upon the least count of the measuring instrument used. The number of significant figures in any measurement indicates the degree of precision of that measurement. The importance of significant figures lies in calculation. A mathematical calculation cannot increase the precision of a physical measurement. Therefore, the number of significant figures in the sum or product of a group of numbers cannot be greater than the number that has the least number of significant figures because a chain cannot be stronger than its weakest link. The difference in the true value and the measured value of a quantity is the measure of error in measurement.
(i) What are significant figures?
(ii) Define least count
(iii) Is there any relation between precision and accuracy?
(iv) State the relationship between significant figures and precision.
(v) Determine the maximum error in the addition of two physical quantities.
(vi) How Systematic errors can be minimised?

The dimensional method is a very convenient way of finding the dependence of physical quantity on other physical quantities of a given system. This method has its own limitations. In a complicated situation, it is often not easy to guess the factors on which a Physical quantity will depend. Secondly, this method gives no information about the dimensionless proportionality constant. Thirdly this method is used only if a Physical quantity depends on the product of other physical quantities. Fourthly this method will not work if a physical quantity depends on another quantity being a trignometric or exponential function. Finally this method does not give complete information in cases where a Physical quantity depends on more than three quantities in problems in mechanics.
(i) What are Physical quantity? Write their types.
(ii) What are dimensional formula of a physical quantity?
(iii) Which principle does the method of dimensional analysis use?
(iv) What is principle of homogeneity?
(v) Write two limitations of dimensional analysis.
(vi) Write one use of dimensional analysis.