Question

the time period of a simple pendulum depends upon mass of the bob and length of the pendulum l and acceleration due to gravity G using dimensional analysis obtain the expression for time period of the pendulum ​

Answer 1

Answer:

We need the formula of constant of pendulum:

k = L/T^2

Consider the value of constant equivalent to g/(4pi^2) (g expresses the gravitational accelaration)

Set the equations g/(4pi^2) and L/T^2 equal, such that:

L/T^2 = g/(4pi^2)

So, time period would be,

g*T^2 = 4pi^2*L

T^2 = (4pi^2*L)/g => T = 2pi*sqrt(L/g)

Hence, the time period of pendulum,

T = 2pi*sqrt(L/g).