suppose velocity of light (c) acceleration due to gravity (g) and pressure (p) are taken as fundamental units .what is the dimensional for mass in this system of unis.

Asked by akankshyadas9437 | 26th Apr, 2019, 09:03: AM

Expert Answer:

Given:
velocity of light - c 
acceleration due to gravity - g 
pressure - p
 
Let 'M' be the mass.
 
Let's assume,
 
M = cx gy pz ... (*)
 
[M1 L0 T0] = [M0 L1-1]x [M0 L1-2]y [M1 L-1-2]z 
 
Thus, [M1 L0 T0] = [Mz Lx+y-z T -x-2y-2z]
 
Applying principle of homogeneity,
 
 
z = 1, ... (1)
 
x + y - z = 0, ... (2)
 
- x - 2y - 2z = 0 ... (3) 
 
x + y = 1 ... (4)  (from (1) and (2))
 
- x - 2y = 2 ...(5)  (from (1) and (3))
 
Solving equations (4) and (5),
 
y = -3 ... (6) 
 
Substituting y = -3 in equation (4),
 
x = 4
 
Substituing values of x, y, z in (*), we get,
 
M = c4 g-3 p-1  
 
Thus, mass can be expressed as,   
 
 
M space equals fraction numerator c to the power of 4 space p to the power of 1 over denominator g cubed end fraction
 
 
 
 
 
 
 
 
 

Answered by Shiwani Sawant | 26th Apr, 2019, 12:37: PM