The graph shows the square of the period versus the length of a simple pendulum on a certain planet. The acceleration due to gravity on that planet is approximately A) 0.100 m/s² B) 10.0 m/s² C) 3.95 m/s² D) 395 m/s² E) 0.628 m/s²

Question

Quizplus · Accepted Answer

The graph shows that the square of the period (T^2) is directly proportional to the length (L) of the pendulum. That is, T^2 is proportional to L. Mathematically, T^2 = kL, where k is the constant of proportionality. Therefore, if we plot T^2 against L, we should get a straight-line graph with slope k.

We know that for a simple pendulum, the period (T) is given by T = 2π√(L/g), where g is the acceleration due to gravity. Squaring both sides, we get T^2 = 4π^2(L/g).

Comparing this with the equation T^2 = kL, we see that k = 4π^2/g. Therefore, the slope of the graph is 4π^2/g.

From the graph, we can measure the slope of the line, which is approximately 3.95 s^2/m. Substituting this into the equation for k, we get:

3.95 s^2/m = 4π^2/g
g = 4π^2/(3.95 s^2/m) ≈ 9.81 m/s^2

However, we need to express the answer in the given units of m/s^2. Converting 9.81 m/s^2 to cm/s^2, we get:

9.81 m/s^2 = 981 cm/s^2

Therefore, the acceleration due to gravity on that planet is approximately 3.95 m/s^2 or 395 cm/s^2. The best choice among the given options is C.

The Graph Shows the Square of the Period Versus the Length