Using the dimension analysis show that the period of the pendulum is given by T=k√l\g where k is the dimensionless constant.with method
In order to show that the period of a pendulum is given by T = k√(l/g), we can use dimension analysis.
Let's break down the dimensions in the equation:
T (period) has dimensions of time (T)
l (length of the pendulum) has dimensions of length (L)
g (acceleration due to gravity) has dimensions of acceleration (LT^-2)
Let's assume k is a dimensionless constant, so it does not have any dimensions.
Now, let's plug these dimensions into the equation T = k√(l/g):
T = k√(l/g)
T = k√(L / LT^-2)
T = k√(LT^2)
T = kT
From this analysis, we can see that the dimensions on both sides of the equation are equal. Therefore, the equation T = k√(l/g) holds true with proper dimensions.