Question

if velocity of light , acceleration due to gravity and atmospheric pressure are taken as the fundamentals units ,what will be the units of mass, length and time?​

Answer 1

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

Explanation:

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