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?
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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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