Answer:
[tex]\frac{g_1}{g_2} = 1.00513[/tex]
Explanation:
As we know that time period of simple pendulum is given by the formula
[tex]T = 2\pi\sqrt{\frac{L}{g}}[/tex]
now here we have two pendulum of different length at two different positions
But the time period is same for both the pendulums
so here we can say
[tex]2\pi\sqrt{\frac{L_1}{g_1}} = 2\pi\sqrt{\frac{L_2}{g_2}}[/tex]
now we have
[tex]\frac{L_1}{g_1} = \frac{L_2}{g_2}[/tex]
[tex]\frac{0.99560}{g_1} = \frac{0.99052}{g_2}[/tex]
now we have
[tex]\frac{g_1}{g_2} = \frac{0.99560}{0.99052}[/tex]
[tex]\frac{g_1}{g_2} = 1.00513[/tex]
The ratio of the free-fall acceleration of gravity at the two cities ( [tex]\frac{g_{1} }{g_{2} }[/tex] ) = 1.00513
Given data :
period of each oscillation = 2 secs
Length of Alaska = 0.99560 m
Length of Kuala Lumpur = 0.99052 m
Applying the formula for the time period of simple pendulum
T = [tex]2\pi \sqrt{\frac{L}{g} }[/tex]
given that the lengths ( L ) are different but time period for both are the same
T = [tex]2\pi \sqrt{\frac{L_{1} }{g_{1} } } = 2\pi \sqrt{\frac{L_{2} }{g_{2} } }[/tex]
therefore :
[tex]\frac{g_{1} }{g_{2} }[/tex] = 0.99560 / 0.99052
= 1.00513
Hence we can conclude that The ratio of the free-fall acceleration of gravity at the two cities ( [tex]\frac{g_{1} }{g_{2} }[/tex] ) = 1.00513
Learn more about free-fall acceleration : https://brainly.com/question/71092
