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 which

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^(x) l^(y)g^(Z) ` where k is a DIMENSIONLESS 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,-2z=1`. Solving the eq., we get `x=0,y=1/2,z=-1/2` Hence , `T=ksqrt(l/g)`, where k is constant.