Question

How does the time period of a simple pendulum depends upon its length? Draw a graph showing the variation of T² and L. How will you use this graph to determine the value of acceleration to to gravity?​

Answer 1

Answer:

In a simple pendulum,

Time period is dependent on the length directly.

Time period is directly proportional to the square root of its effective length.

i.e., T α

1

The acceleration due to gravity (g) can be calculated from the above mentioned graph:

To find the slope of the straight line, two points P and Q can be taken on the straight line. Value of T2 can be noted at a and b. To note the value at 'I', consider the points c and d.

Slope=

BC

AC

=

1

1

−1

2

T

1

2

−T

2

2

The slope is observed to be constant at a point which is equal to

g

4x

2

,

g = acceleration due to gravity at that place.

Hence 'g' can be determined at a place with the help of these measurements with the help of this relation:

g=

SlopeofT

2

vsIgraph

4π

2