Question

the period of a simple pendulum depends on the mass (m), length (l) of the thread and acceleration due to gravity (g). derive an expression for its period using dimensional analysis

Answer 1

T=km^al^bg^c\\ [T]=[k][m]^a[l]^b[g]^c \\ T=1(M)^a(L)^b(LT^{-2})^c\\a=0,c=-0.5,b=0.5\\T=k\sqrt{\frac{l}{g}}