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.