The velocity of water wave `v` may depend on their wavelength `lambda`, the density of water `rho` and the acceleration due to gravity `g`. The method of dimensions gives the relation between these quantities as

Experiments reveal that the velocity v of water waves may depend on their wavelength lambda , density of water rho , and acceleration due to gravity g . Establish a possible relation between v and lambda , g, rho .

The velocity of a freely falling body is a function of the distance fallen through (h) and acceleration due to gravity g . Show by the method of dimensions that v = Ksqrt(gh) .

The orbital velocity v of a satellite may depend on its mass m , the distane r from the centre of the earth and acceleration due to gravity g . Obtain an expression for its orbital velocity .

The largest mass (m) that can be moved by a flowing river depends on velocity (v), density (rho) of river water and acceleration due to gravity (g). The correct relation is

The mass m of the heaviest stone that can be moved by the water flowing in a river depends on speed (v) of water, density (d) of water and the acceleration due to gravity (g). Find the dimension of velocity on which mass of stone depends.

What do you understand by gravity and acceleration due to gravity. Establish a relation between g and G .

The time period T of a simple pendulum depends on length L and acceleration due to gravity g Establish a relation using dimensions.

If different planets have the same density but diferent radii then the acceleration due to gravity (g) on the surface of the planet will depend on its radius (R) as