Question

The slope of the graph of T2 plotted on the vertical axis against l on the horizontal axis is used to determine the value of -----------

A. frequency
B. period
C. phase
D. acceleration due to gravity

Answer 1

Answer on Question #55611, Physics / Mechanics | Relativity

The slope of the graph of $\mathsf{T}^2$ plotted on the vertical axis against $l$ on the horizontal axis is used to determine the value of ---

A. frequency

B. period

C. phase

D. acceleration due to gravity

Solution:

Consider the expression that relates the period of oscillation of a simple pendulum (T) with the length (l) of the pendulum.

$$T = 2 \pi \sqrt {\frac {l}{g}}$$

Plotting the graph of $\mathsf{T}^2$ on the vertical axis and $\ell$ on the horizontal axis will give us a straight line passing through the origin as shown in figure.

The slope or the gradient of the graph is given as

$$\frac {\Delta \mathrm {T} ^ {2}}{\Delta \ell} = \frac {\text {Increase in T} ^ {2}}{\text {Increase in} \ell} = \mathrm {m} = \frac {4 \pi^ {2}}{\mathrm {g}}$$

The value of $g$ , acceleration due to gravity may then be obtained, by substitution of values of known variables in the relation.

Answer: D. acceleration due to gravity

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