Answer:
Acceleration due to gravity at new location will be [tex]g=9.820022m/sec^2[/tex]
Explanation:
We have given time period of pendulum T = 2 sec
Acceleration due to gravity [tex]g=9.8m/sec^2[/tex]
Time period of pendulum is given by [tex]T_1=2\pi \sqrt{\frac{L}{g}}[/tex], here L is length and G is acceleration due to gravity
So [tex]2=2\pi \sqrt{\frac{L}{9.8}}[/tex]------eqn 1
In second case time period is 1.99796 sec
So [tex]1.99196=2\pi \sqrt{\frac{L}{g}}[/tex]--------eqn 2
Now dividing eqn 1 by eqn 2
[tex]\frac{2}{1.99796}=\sqrt{\frac{g}{9.8}}[/tex]
[tex]\sqrt{\frac{g}{9.8}}=1.00102[/tex]
Squaring both side
[tex]\frac{g}{9.8}=1.00204[/tex]
[tex]g=9.820022m/sec^2[/tex]
