Question

How does the time period (T) of a simple pendulum depend on its length (l)? Draw a graph showing the variation of T² with l. How will you use this graph to determine the value of g (acceleration due to gravity)?

Answer 1

The time period of a simple pendulum is directly proportional to the square root of its effective length.

`T ∝ sqrt(l)`

From this graph, the value of acceleration due to gravity (g) can be calculated as follows.

The slope of the straight line can be found by taking two points P and Q on the straight line and drawing normals from these points on the X- and Y-axis, respectively. Then, the value of T2 is to be noted at a and b, the value of l at c and d. Then,

Slope = `"PR"/"QR" = "ab"/"cd" = (T_1^2 - T_2^2)/(l_1 - l_2)`

This slope is found to be constant at a place and is equal to `(4pi^2)/"g"` , where g is the acceleration due to gravity at that place. Thus, g can be determined at a place from these measurements using the following relation:

`"g" = (4pi^2)/("Slope"  "of"   T^2  "Vs"  l  "graph")`