Page 78 - Physics - XI

Steps involved in plotting a graph are given below:

(a) Selecting the Dependent and Independent Variables: First of all in the given problem, the dependent
and independent variables should be selected. e.g. Consider an experiment in which the change in
length of a string occurs due to the corresponding increase in weight. So here, length is a dependent
variable and weight is an independent variable. The independent variable is selected to plot along
X-axis and the dependent variable along Y-axis.

(b) Finding the Range of Each Physical Variable: To fi nd the range of the two variables (i.e. dependent
and independent), one should know the minimum and maximum values of these two variables. The
diff erence between these two values gives the range of a physical variable.
(c) Selecting the Scale: This is an important step of plotting the graph that one should select the convenient
scale for both the variables. The scales should be selected in such a way that the graph will cover about
80% of the space of the graph paper.
(d) The Number of Readings: For plotting a graph, at least six to seven observations should be taken.

(e) Joining the Points: After pointing the various observations as points in the graph, one should mark the
crosses or enclose them in a small circle. Then, we join all these points.

(f) Portion of a Graph for Special Purpose: Sometime from plotted graph, a particular segment of the
line drawn is selected to determine the result. e.g. In case of a second's pendulum, having time period
of 2 s and length of 99.3 cm or about 100 cm, the observations should be taken in such a manner that
the 100 cm mark falls in the middle portion of the graph. It means that for the given time periods, the
corresponding lengths of the pendulum should be 75 cm, 85 cm, 95 cm, 105 cm, 115 cm, and 125 cm.
This type of graph helps to keep away from the error occurred in the results.

(g) Giving Name (or Title) of the Graph: Give the name of the graph at the top of the graph paper,
i.e. write the heading "Graph showing relation between x (independent variable) and y (dependent
variable)".

Procedure

Identifi cation of Dependent and Independent Variables
1. From the given data, it is clear that the length is increasing due to the corresponding increase in weight
or load. Take the load to be as an independent variable and it should be taken along X-axis and the
extension to be as dependent variable and it should be taken along Y-axis.

Determination of Range
2. Determine the range of load and of extension as well.
Range of load = 600 – 100 = 500 gf
Range of extension = 0.98 – 0.18 = 0.80 cm

Selection of Scale
3. Since, the given data have only positive values, so, take the origin at lower left corner of the graph
paper.
4. Now, fi nd the smallest division which is to be projected along X-axis and Y-axis for load and extension,
respectively.

Along X-axis (for load) 1 cm = 100 gf
Along Y-axis (for extension) 1 cm = 0.2 cm

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