The time period Of oscillation of a simple pendulum depends on the following quantities
Length of the pendulum (l),
Mass of the bob (m), and
Acceleration due to gravity (g)
Derive an expression for Using dimensional method.

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.