Question

Find the form of expression of the period of vibration of simple pendulum as T=km^x L^y G^2 where k,x,G, and 2 are known terms?

Answer 1

answer:-

$T=km^xl^yg^z$

$[MLT]=Km^xL^yG^z\\ g=m/s^2\\$

where k is dimensionless constant of proportionality.

Writing the dimensions in terms of M, L, T on either side , we get

$[M^0L^0T^1]=K[M]^x[L]^{y+z}[T]^z$

Applying the principle of homogeneity of dimensions, we get

$x=0\\ y=\frac{1}{2}\\ z=\frac{-1}{2}$

so ,

$T=K \sqrt{\frac{L}{G}}$