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
Tags:
Physics