Question

In an experiment to determine the acceleration due to gravity g, T2 was plotted on the vertical axis and I on the horizontal axis. The value of g is obtainable from

A. intercept on T2 axis
B. intercept on I axis
C. Inverse of the ratio T2/I
D. Slope of the graph

Answer 1

Answer on Question 55371, Physics, Mechanics | Kinematics | Dynamics

Question:

In an experiment to determine the acceleration due to gravity $g$, $T^2$ was plotted on the vertical axis and $L$ on the horizontal axis. The value of $g$ is obtainable from

A. Intercept on $T^2$ axis

B. Intercept on $L$ axis

C. Inverse of the ratio $T^2 / L$

D. Slope of the graph

Solution:

The time period of a simple gravity pendulum for small amplitude of oscillations depends on the length of the pendulum $L$ and the acceleration due to gravity $g$, and can be expressed by the equation:

$$T = 2 \pi \sqrt {\frac {L}{g}}.$$

Let's square both sides of the equation:

$$T ^ {2} = \frac {4 \pi^ {2}}{g} L.$$

From this equation we can find the acceleration due to gravity $g$:

$$g = 4 \pi^ {2} \frac {L}{T ^ {2}}.$$

In order to find $g$ we must plot a graph of $T^2$ as a function of $L$ by taking $L$ along the horizontal $(x)$ axis and $T^2$ along the vertical $(y)$ axis. The graph is a straight line. The slope of the graph is the change in $y$ ($T^2$) divided by the change in $x$ ($L$), or the rise divided by the run:

Equation $T^2 = \frac{4\pi^2}{g} L$ is of the form $y = mx + b$ (the equation for the straight line), where $y = T^2$ , $m = \frac{4\pi^2}{g}$ , $x = L$ , and $b = 0$ . A graph of $T^2$ versus $L$ is a straight line whose slope $m = \frac{4\pi^2}{g}$ .

Finally, we can find $g$ from the equation for the straight line:

$$y = m x + b,$$ $$T ^ {2} = m L,$$

Where $m$ is the slope of line. Therefore, we can see that the value of $g$ is obtainable from the slope.

So, the correct answer is D.

**Answer:**

D. Slope of the graph

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