Answer:
Explanation:
Length of pendulum l = 1.37 m
time period T = time /no of oscillation
= [tex]\frac{209}{108}[/tex]
= 1.935
Formula for time period of pendulum
[tex]T=2\pi\sqrt{\frac{l}{g} }[/tex]
g is acceleration due to gravity , l is length of pendulum and T is time period.
Substituting the given values
[tex]1.935=2\pi\sqrt{\frac{1.37}{g} }[/tex]
.095 = [tex]\frac{1.37}{g}[/tex]
g = 14.42 m /s².
The required value of gravitational acceleration is 14.42 m/s².
Time period of Pendulum:
The time taken by the bob of the pendulum attached with a string to complete one complete oscillation is known as the time period of a pendulum.
Given data:
The length of a simple pendulum is, L = 1.37 m.
The number of oscillations is n = 108.
The time interval is, t = 209 s.
The expression for the time period of simple pendulum is,
T = t/n
T = 209/108
T = 1.935 s
And another expression for the time period of simple pendulum is,
[tex]T = 2 \pi \sqrt{\dfrac{L}{g}}[/tex]
here,
g is the gravitational acceleration.
Solving as,
[tex]1.935 = 2 \pi \sqrt{\dfrac{1.37}{g}}\\\\ g = \dfrac{1.37}{0.095}\\\\ g = 14.42 \;\rm m/s^{2}[/tex]
Thus, we can conclude that the required value of gravitational acceleration is 14.42 m/s².
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