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

Explanation

Let the time period of a sample pendulum depend upon the mass of bob `m`, length of pendulum `l`, and acceleration due to gravity `g`, then
`t prop m^(@)n l^(b) g^(c) implies t = km^(@) g^(c)`
`M^(0) L^(0) T^(1) = M^(a) L^(b)[LT^(-2)]^(e)`
`implies M%^(0) L^(0) T^(1) = M^(a) L^(b+c) T^(2c)`
comparing the powers of `M,L` and `T` on both sides, we get `a = 0, b + c = 0,-2c = 1`
`implies a = 0, b = 1//2` and `c = -1//2`.Putting these values,
we get `T = km^(0) (l^(1/2))/(g^(1/2)) implies T = k sqrt((l)/(g))`,
Which is the required realtion.