Derive an expression for the time period (T) of a simple pendulum which may depend upon the mass (m) of the bob, length (l) of the pendulum and acceleration due to gravity (g).

Explanation

Let T `= km^x l^y g^z` where k is a dimensionaless constant.
Writing the equation in dimensional form, we have
`[M^0 L^0 T^(-1)] =[M]^X [L]^Y [LT^(-2)]^Z= [M^X L^(Y+Z) T^(-2Z)]`
Equating exponent of M , L and T on both sides,
we get x = 0 ,y + z = 0 , - 2x = 1
Solving the eq. we get x = 0 , y =1/2 , z=-1/2
Hence , `T = ksqrt(l/g)` , where k is constant .