Question

A pendulum that moves through its equilibrium position once every 1.000 s is sometimes called a seconds pendulum (a) What is the period of any seconds pendulum? (b) In Cambridge, England, a seconds pendulum is 0.9942 m long. What is the free-fall acceleration in Cambridge? (Use 4 significant figures in your answer.) (c) In Virginia Beach, Virginia, a seconds pendulum is 0.99284 m long. What is the free fall acceleration in Virginia Beach, Virginia? (Use 5 significant figures in your answer.) m/s m/s

Answer 1

2 seconds

9.812 m/s²

9.7989 m/s²

Step-by-step explanation:

L = Length of pendulum

g = Acceleration due to gravity

T = Time period would be 1+1 = 2 seconds

Time period is given by

`T=2\pi\sqrt{(L)/(g)}\\\Rightarrow g=4\pi^2(L)/(T^2)\\\Rightarrow g=4\pi^2(0.9942)/((1+1)^2)\\\Rightarrow g=9.812\ m/s^2`

The free fall acceleration in Cambridge is 9.812 m/s²

`T=2\pi\sqrt{(L)/(g)}\\\Rightarrow g=4\pi^2(L)/(T^2)\\\Rightarrow g=4\pi^2(0.99284)/((1+1)^2)\\\Rightarrow g=9.7989\ m/s^2`

The free fall acceleration in Virginia Beach is 9.7989 m/s²