Question

If the velocity of light c , acceleration due to gravity is g and atmosphere pressure p are the fundal mental quantities.find the dimensions of length

Answer 1

Answer:

L=c2/g

Explanation:

Given:

velocity of light - c  

acceleration due to gravity - g  

pressure - p

 

Let 'L' be the length.

 

Let's assume,

 

L = cx gy pz ... (*)

 

Thus,  

[M0 L1 T0] = [M0 L1 T -1]x [M0 L1 T -2]y [M1 L-1 T -2]z  

 

[M0 L1 T0] = [Mz Lx+y-z T -x-2y-2z]

 

Applying principle of homogeneity,

 

z = 0,

x + y - z = 1,

Thus, x + y = 1 ... (1)  

 

- x -2y - 2z = 0,  

Thus,  

 

- x - 2y = 0 ... (2)  

 

Solving equations (1) and (2) simultaneously,

we get,

 

y = -1  

 

and thus, x = 2  

 

Thus,  

Substituting the values of x, y and z in (*) we get,

 

L = c2 g-1 p0  

 

Thus,  

L=c2/g