The velocity of light (c), acceleration due to gravity (g), and atmospheric pressure (p) are chosen a fundamental units, then the dimensions of length will be

 Given: Velocity of light=C

Acceleration due to gravity – g

Pressure -P

Let ‘L’ be the length.

Let’s assume, L = CxgyPz …eq i)

Now putting all the values in above equation, [M0L1T0] = [M0L1T−1]x [M0L1T−2]y [M1L−1T−2]z

⇒ [M0L1T0] = [MzLx+y−zT−x−2y−2z]

Applying the principle of homogeneity, Comparing the powers of M, z=0

Compare the powers of L, x+y−z=1 ( As z=0)

⇒ x + y =1

⇒ x = 1−y …eq ii)

Compare the powers of T, −x−2y−2z=0 ( As z=0)

⇒ −x−2y=0 …eq iii)

Put the value of eq ii) in above equation, we get ⇒ −(1−y)−2y = 0

⇒ y = −1

Putting the value of y in eq ii),

we get ⇒ x = 2

Now, put the values of x, y and z in eq i)

Therefore, the dimensions of length will be: L = C2g−1P0

⇒ L=C2/g

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