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Answer :
The mean value of g obtained from the measurements (9.852 m/s²) is very close to the accepted value of g (9.81 m/s²). The small difference may be due to experimental errors or uncertainties in the measurements.
To determine the mean value of g obtained from the three measurements, we can use the equation for the period of a simple pendulum, which is given by:
[tex]\[T = 2\pi\sqrt{\frac{L}{g}}\][/tex]
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
Let's calculate the values of g for each measurement:
For the first measurement with a length of 1.000 m and a time interval of 99.8 s for 50 oscillations:
[tex]\[T = \frac{99.8 \, \text{s}}{50} = 1.996 \, \text{s}\][/tex]
Using the equation [tex]\(T = 2\pi\sqrt{\frac{L}{g}}\)[/tex], we can rearrange it to solve for g:
[tex]\[g = \frac{4\pi^2L}{T^2} = \frac{4\pi^2 \cdot 1.000 \, \text{m}}{(1.996 \, \text{s})^2} = 9.853 \, \text{m/s}^2\][/tex]
For the second measurement with a length of 0.750 m and a time interval of 86.6 s for 50 oscillations:
[tex]\[T = \frac{86.6 \, \text{s}}{50} = 1.732 \, \text{s}\][/tex]
Using the equation [tex]\(T = 2\pi\sqrt{\frac{L}{g}}\)[/tex], we can rearrange it to solve for g:
[tex]\[g = \frac{4\pi^2L}{T^2} = \frac{4\pi^2 \cdot 0.750 \, \text{m}}{(1.732 \, \text{s})^2} = 9.860 \, \text{m/s}^2\][/tex]
For the third measurement with a length of 0.500 m and a time interval of 71.1 s for 50 oscillations:
[tex]\[T = \frac{71.1 \, \text{s}}{50} = 1.422 \, \text{s}\][/tex]
Using the equation [tex]\(T = 2\pi\sqrt{\frac{L}{g}}\)[/tex], we can rearrange it to solve for g:
[tex]\[g = \frac{4\pi^2L}{T^2} = \frac{4\pi^2 \cdot 0.500 \, \text{m}}{(1.422 \, \text{s})^2} = 9.844 \, \text{m/s}^2\][/tex]
To find the mean value of g, we can simply calculate the average of the three values:
Mean value of
[tex]\(g\) = \(\frac{9.853 + 9.860 + 9.844}{3} = 9.852 \, \text{m/s}^2\)[/tex]
Now, let's compare this mean value with the accepted value of g, which is approximately [tex]\(9.81 \, \text{m/s}^2\)[/tex].
Learn more about mean value
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