Question

Time period of vibration of a pendulum depends on mass of pendulum ,acceleration due to gravity and length of the simple pendulum. Derive dimension relation between them.

Answer 1

Answer:

Let Time period =T

      Mass of the bob = m

      Acceleration due to gravity = g

     Length of string = L

Let 

      

      

      

      ⇒a=0 ⇒ Time period of oscillation is independent of mass of the bob

     

      -2b=1

      ⇒b=-

      

      b+c = 0

      - + c =0

      c=

      

Giving values to a,b and c in first equation

      

      

The real expression for Time period is

      

Therefore time period of oscillation depends only on gravity and length of the string.

Not on mass of the bob.