Question

You have been abducted by aliens and find yourself on a strange planet. Fortunately, you have a meter stick with you. You observe that, if the stick oscillates around one end as a physical pendulum, it has a period of 0.85 s. What is the acceleration of gravity on this planet?

Answer 1

Answer:

$36.4276\ m/s^2$

Explanation:

m = Mass of stick

L = Length of stick = 1 m

h = Center of mass of stick = $\dfrac{1}{2}=0.5\ m$

g = Acceleration due to gravity

T = Time period = 0.85 s

Time period is given by

$T=2\pi\sqrt{\dfrac{I}{mgh}}$

Moment of inertia is given by

$I=m\dfrac{L^2}{3}$

$T=2\pi\sqrt{\dfrac{m\dfrac{L^2}{3}}{mgh}}\\\Rightarrow T=2\pi\sqrt{\dfrac{L^2}{3gh}}\\\Rightarrow g=\dfrac{4\pi^2L^2}{3hT^2}\\\Rightarrow g=\dfrac{4\pi^2\times 1^2}{3\times 0.5\times 0.85^2}\\\Rightarrow g=36.4276\ m/s^2$

The acceleration of gravity on this planet is $36.4276\ m/s^2$

Answer 2

Answer:

54.6 m/s^2

Explanation:

length of the pendulum, l = 1 m

time period of the pendulum, T = 0.85 s

According to the formula of time period of pendulum

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

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

$g = \frac{4\times 3.14\times 3.14\times 1}{0.85\times 0.85}$

g = 54.6 m/s^2

Thus, the acceleration due to gravity at this planet is 54.6 m/s^2.