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).

Derive an expression for the time period (T) of a simple pendulum whic

1.	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).
Answer» Solution :Let `T= km^(a) l^(b) g^(c )` where k is a dimensionless constant. Writing the equation in dimensional FORM, we have `[M^(0) L^(0) 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.