Question

if the velocity of light c, acceleration due to gravity and atmospheric pressure p are fundamental quantities, find the dimension of length.. urgently need answers

Answer 1

Units of...
c = m/s
g = m/s^2
P = (kgm/s^2) / m^2 = kg / (ms^2)

Dimensional formula of...
c = [LT^-1]
g = [LT^-2]
P = [ML^-1 T^-2]

c^a g^b P^c = [L] = [LT^-1]^a [LT^-2]^b [ML^-1 T^-2]^c

[L] = [L]^(a + b - c) [T]^(-a - 2b - 2c) [M]^c

From above equation
1 = a + b - c ——(1)
0 = -a - 2b - 2c —-(2)
0 = c ——(3)

Substitute c = 0 in equation (1) and (2)
1 = a + b ; a = -2b
From above equations
b = -1 and a = 2

Finally we got
a = 2
b = -1
c = 0

The dimension of length is therefore
c^a g^b P^c = c^2 g^-1 P^0 = (c^2) / g

Answer 2

here is the answer... comment and let me know..... if you find any difficulty ..in this question