DIMENSIONAL ANALYSIS WORKSHEET

Question 1 The air bubble formed by explosion inside water perform oscillations with time period T which depends on pressure (p), density (ρ) and on energy due to explosion (E). Establish relation between T, p, E and ρ.

Question 2 The velocity v of a particle depends upon the time ‘t’ according to the equation V = (ab)^1/2 +bt + c/d+t 
Determine the units of a, b, c and d. What physical quantities they represent. All have SI units.

Question 3 The  position (x) of a particle at time t, is given by the 

relation, x(t)=v0/a(1-e-at), where v0 is a constant and a>0. Find the dimensions of v0 and a.

Question 4 The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation f=cmxky; where c is a dimensionless quantity. Find the value of x and y.


Question 5 The time of oscillation t of a small drop of a liquid under surface tension depends upon the density d , radius r and surface tension S . Derive the expression for the time of oscillation of the drop using method of dimensions.

Question 6 Check the dimensional consistency in the following cases:

(a) mgh = F.v/t  -1/2 mv²

^(b) Tanθ = v²/rg  - cosθ

Question 7 If  X = at + bt²  where x is the distance travelled by the body in kilometre while t is the time in second, find the units of a and b.

Question 8 If energy (E), velocity (V) and time are chosen as fundamental quantities, 
what are the dimensions of surface tension?
Question 9 What are the dimensions of a/b in the equation P = a – t² / bx ? (where p is the pressure, x is the distance and t is time.)
Question 10 In the relation P = α e^αx/t/β , p is the pressure , x is distance and t is time. 
what are the dimensions of β?