Question 4.\ a. Dimensional analysis\ In a shallow pond of depth

h

, surface waves are propagating at speed

v

. The density of water is

p

and the gravitational acceleration of the Earth is

g

.\ i. What are the dimensions of quantities

h,v,\\\ ho

and

g

?\ [4 marks]\ ii. - Find numbers

a,b,c

, so that the combination

h^(a)\\\ ho ^(b)g^(c)

has the dimension of velocity.\ [4 marks]\ iii. If

g=9.81(m)/(s^(2)),\\\ ho =1000k(g)/(m^(3))

and the depth of the pond is

h=10cm

, what is your estimate of the velocity of the surface waves,

v

?\ [2 marks]

a. Dimensional analysis In a shallow pond of depth h, surface waves are propagating at speed v. The density of water is p and the gravitational acceleration of the Earth is g. i. What are the dimensions of quantities h,v, and g ? ii. Find numbers a,b,c, so that the combination habgc has the dimension of velocity. [4 marks] iii. If g=9.81m/s2,=1000kg/m3 and the depth of the pond is h=10cm, what is your estimate of the velocity of the surface waves, v ? [2 marks]