Question

The time period of simple pendulum depends on mass of Bob length of stream and gravitational acceleration. Find expression of Time period using dimensional analysis

Answer 1

Considerjng dimensions on both sides.

[M^0 L^0 T^1] = [L^1]^x [M^1]^y [L^1 T^-2]^x

= [M]^y [L^x+z T^-2z]

X = 1/2 z = -1/2, y = 0

So...

T= kl^1/2 m^0 g^-1/2 = kl^1/2 g^-1/2

Or...

T = k√(l/g)