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Question
Describe, briefly how can you calculate the value of ‘g’ with a simple pendulum.
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Solution
Simple pendulum: A simple pendulum consists of a small heavy mass in the form of a bob suspended by a light inelastic string.
The pendulum is suspended from suitable support (the thread may be held firmly between two halves of a cork held by a clamp and stand). The pendulum is allowed to oscillate and its time period for one oscillation is noted with the help of a stopwatch by observing a large number of oscillations. The length of the pendulum is changed several times and the time period is determined in each case. A graph is plotted between l, the length of the pendulum, and T2, the square of the time period.
We know, time period of a simple pendulum = T = `2πsqrt("l"/"g")`
where l = length of the pendulum and g = acceleration due to gravity.
T = `2πsqrt("l"/"g")`
Squaring both sides,
T2 = `4π^2(("l")/"g")`
⇒ g = `4π^2(("l")/"T"^2)`
By substituting the value of `"l"/"T"^2` in this equation, we can calculate the value of acceleration due to gravity.
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