11. Consider a simple pendulum, having a bob attached to a string that

1.	11. Consider a simple pendulum, having a bob attached to a string thatoscillates under the action of the force of gravity. Suppose that the period3of oscillation of the simple pendulum depends on its length (1), mass of thebob (m) and acceleration due to gravity (g). Derive the expression for itstime period using method of dimensions.
Answer» let the time period of oscillation be t.from question,t= k l^a m^b g^c BY PRINCIPLE OF HOMOGENETY OF DIMENSIONS,M^0L^0T^1= L^a M^b (L^1 T^-2)^c=M^b L^a+c T^-2c THIS GIVES,b=0, a=1/2, c=-1/2 APPLYING THE VALUES INTO THE ASSUMED EQUATION 1,T=kl^1/2g1/2T= k sqr root l/ sqr root g

11. Consider a simple pendulum, having a bob attached to a string thatoscillates under the action of the force of gravity. Suppose that the period3of oscillation of the simple pendulum depends on its length (1), mass of thebob (m) and acceleration due to gravity (g). Derive the expression for itstime period using method of dimensions.

Answer»

let the time period of oscillation be t.from question,t= k l^a m^b g^c

BY PRINCIPLE OF HOMOGENETY OF DIMENSIONS,M^0L^0T^1= L^a M^b (L^1 T^-2)^c=M^b L^a+c T^-2c

THIS GIVES,b=0, a=1/2, c=-1/2

APPLYING THE VALUES INTO THE ASSUMED EQUATION 1,T=kl^1/2g1/2T= k sqr root l/ sqr root g

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