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  • A physics experiment involves measuring the acceleration due to gravity using a simple pendulum. The length of the pendulum is 0.8 m, and the time period of one oscillation is 1.6 s. The experiment

A physics experiment involves measuring the acceleration due to gravity using a simple pendulum. The length of the pendulum is 0.8 m, and the time period of one oscillation is 1.6 s. The experimental setup introduces an error in measuring the length of the pendulum as 0.02 m and an error in timing as 0.05 s. Determine the acceleration due to gravity.

Option: 1

8.45214 m/s2


Option: 2

5.42256 m/s2


Option: 3

6.24662 m/s2


Option: 4

10.35874 m/s2


Answers (1)

best_answer

Given values:

Length of pendulum (L) = 0.8 m
Time period (T) = 1.6 s
Error in length measurement (EL) = 0.02 m
Error in time measurement (ET ) = 0.05 s

The acceleration due to gravity (g) can be calculated using the formula:

                    g = \frac{4\pi^{2}L}{T^{2}}

Step 1: Calculate the acceleration due to gravity without errors:

             g_{actual} = \frac{4\pi^{2} * 0.8 m}{(1.6 s)^{2}} \approx 9.8696 m/s^{2}

Step 2: Calculate the maximum possible error in g due to errors in length and time measurements:

                    \Delta g = |\frac{\delta g}{\delta L}| E_{L} + |\frac{\delta g}{\delta T}| E_{T}

where,

 \frac{\delta g}{\delta L} = \frac{4\pi^{2}}{T^{2}}            and         \frac{\delta g}{\delta T} =- \frac{8\pi^{2}L}{T^{3}}

Substitute the values:

\Delta g = |\frac{4\pi^{2}}{(1.6 s)^{2}}| * 0.02 m + |-\frac{8\pi^{2} * 0.8 m}{(1.6 s)^{3}}| * 0.05 s \approx 0.4891 m/s^{2}

Step 3: Calculate the range of g values:

gmin = gactual - \Deltag \approx 9.8696 m/s2 - 0.4891 m/s2 \approx 9.3805 m/s2

gmax = gactual + \Deltag \approx 9.8696 m/s2 + 0.4891 m/s2 \approx 10.3587 m/s2

The acceleration due to gravity is estimated to be in the range of 9.3805 m/s2 to 10.3587 m/s2 based on the experimental setup and measurement errors.

Posted by

Kuldeep Maurya

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