Question

Describe, briefly how can you calculate the value of ‘g’ with a simple pendulum.

Answer 1

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.