The period of oscillation (T) of a simple pendulum depends on the probable quantities such as mass 'm' of a bob, length 'l' of the pendulum and acceleration due to gravity 'g' at the place. Derive an equation using dimensional analysis.

Explanation

Let ` T prop m ^ x l ^y g ^ z `
i.e., ` T = Km^ x l^y g ^ z `
i.e., ` ( M^0L ^0 T^( 1)) = ( M^x L^(y + z ) T^( - 2z ) ) `
From the principle of homogeneity , equating the dimensions of M, L & T on either side we get
` x = 0 .... (1) " " y + z = 0........... (2) " " - 2z = 1 ............ (3) `
From (3) ` z = -1//2 and y -1//2 = 0 `, hence ` y = 1//2 `
Therefore ` T = Km^0 l^( 1//2) g ^( -1//2) `
i.e., ` T = K sqrt(( l ) /(g) ) `