If the velocity of light in vacuum c, acceleration due to gravity g and atmospheric pressure p are the fundamental quantities,find the dimensions of length.

Asked by pb_ckt | 22nd May, 2019, 10:16: AM

Expert Answer:

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 thin space equals space c squared over g
 
 

Answered by Shiwani Sawant | 22nd May, 2019, 11:31: AM