Explain propagation of errors in the difference of two quantities and also in the division of two quantities.

How will you determine the distance of moon from earth using parallax method?

Briefly explain the different types of errors and their causes with an example. How can these error be minimised?

Explain the propagation of errors in subtraction, quotient and power of a quantity.

Write the rules for "Rounding off" with example

The length of a rod as measured in an experiment was found to be 3.48m, 3.46m, 3.49m, 3.50m and 3.48 m. Find the average length, the absolute error in each observation and the percentage error.

The value Gin CGS system is 6.67\(\times\)10^-8 dyne cm² g^-2. Calculate the value in SI units.

Check the dimensional consistency of the following equations.
(i) de-Broglie wavelength, \(\lambda ={h\over mv}\)
(ii) Escape velocity, v = \({\sqrt{2GM\over R}}\)

A planet moves around the sun in nearly circular orbit. Its period of revolution 'T' depends upon.
(i) radius 'r' of orbit 
(ii) mass 'm' of the sun and
(iii) The gravitational constant G Show dimensionally that T² \(\propto\)r³.

One mole of an ideal gas at STP occupies 22.4 L. What is the ratio of molar volume to atomic volume of a mole of hydrogen? Why is the ratio so large? Take radius of hydrogen molecule to be 1^oA.

The frequency of vibration of a string depends of on,
(i) tension in the string
(ii) mass per unit length of string
(iii) vibrating length of the string
Establish dimensionally the relation for frequency.