Imagine that two space explorers discovered a new inhabitable planet in another

Question

Imagine that two space explorers discovered a new inhabitable planet in another galaxy. In order to measure the gravitational acceleration of the newly discovered planet, they set up a pendulum on the surface of the planet.

(a) The first explorer measures that the length of the pendulum is 1.95 m and that the pendulum swings with a period of 3.06 seconds when the amplitude of the pendulum's swing is very small. Based on these measurements, what is the gravitational acceleration of the planet?

______ kg m/s2

(b) In order to confirm the first explorer's results, the second explorer set up his own pendulum, and measured the period T of his pendulum by changing the length L of the pendulum. He found that the plot of T2 vs. L is a straight line with a positive slope. From the value of the slope, he concluded that his measurement results are in full agreement with those of the first explorer. What is the value of the slope (in T2 vs. L plot of the second explorer)?

_____ s2/m

Explanation / Answer

Here .

length , L = 1.95 m

T = 3.06 s

as T = 2pi*sqrt(L/g)

3.06 = 2pi*sqrt(1.95/g)

g = 8.22 m/s^2

the gravitational acceleration of the planet is 8.22 m/s^2

b)

for the slope of T^2 vs L

T^2 = 4pi^2 * L/g

T^2/L = 4pi^2/g

the slope is 4pi^2/g

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