Question

the period t of a simple pendulum depends on the lenght of the simple pendulum snd acceleration due to gravity at a place obtain an expression for time period t by a method of dimension​

Answer 1

Answer:

Explanation:

Let Time period =T

     Mass of the bob = m

     Acceleration due to gravity = g

    Length of string = L

Let  Tam^a g^b L^c

      (T)a(m)^a (g)^b (L)^c

      M^0 L^0 T^1 = M^a L^b T^-2b L^c

      M^0 L^0 T^1 = M^a L^b+c T^-2b

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

     

     -2b=1

     ⇒b=- 1/2

     

     b+c = 0

     -1/2 + c =0

     c= 1/2

     

Giving values to a,b and c in first equation

 Tam^0 g^-1/2 L^1/2    

 Ta square root L/g      

The real expression for Time period is

 T= 2 pie square root L/g    

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

Not on mass of the bob.