If the velocity of light (c), acceleration due to gravity (g), and atmospheric pressure (p) are chosen as fundamental units, then the dimensions of length will be?
Step 1: Given parameters
Step 2: Formula used
Use the following expression to find the dimensions for length.
Where, ,, and are the powers to which , , and are raised.
The dimensions for the given quantities are as follows:
Step 3: Calculating dimension
Substitute equations (2), (3), and (4) in equation (1).
Apply the principle of homogeneity,
Comparing the powers on both sides, we get :
Comparing the powers of and ,
Comparing the powers of ,
Substitute equation (5) in equation (6).
Substitute value of in equation (5).
Substitute the values of ,, and in equation (1).
Hence, if the velocity of light, acceleration due to gravity, and atmospheric pressure are chosen as fundamental units, then the dimensions of length will be .