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^(3) l^(@) g^(c )`
where k is a dimensionless constant.
Writing the equation in dimensional form, we have
`[M^(@)L^(@)T^(1)]= [M]^(a)[L]^(b)[LT^(-2)]^(c )=[M^(a)L^(b+c)T^(-2c)]`
Equating exponents of M, L and T on both sides,
we get a=0 , b+c=0 , -2c =1.
Solving the eq., we get a = 0 , b=1/2 c= -1/2
Hence , T=k`sqrt((l)/(g))`, where k is constant.