Question

The period T of a simple pendulum is assumed to be affected by the following quantities.1 mass of bulb m 2 length of pendulum l 3 acceleration due to gravity g

if the empirical formula for the period T is T =Kmlg .find the relationship between T and the products of these two quantities 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}}