Question

The free-fall acceleration on the moon is 1.62 m/s2 . What is the length of a pendulum whose period on the moon matches the period of a 2.00-m-long pendulum on the earth?

Answer 1

To find the length of a pendulum on the Moon that matches the period of a 2.00-m-long pendulum on Earth, we use the period formula for a pendulum. Equating the periods for Earth and the Moon and substituting the known values, we find that the required pendulum length on the Moon is approximately 0.33 meters.

Step-by-step explanation:

The question you're asking involves determining the length of a pendulum on the Moon that has the same period as a 2.00-m-long pendulum on Earth. Using the formula for the period of a pendulum (T = 2π ∙ √(L/g)), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity, we can set up an equation based on the fact that the period of a pendulum depends only on the length of the pendulum and the acceleration due to gravity.

Let Lmoon be the unknown length of the pendulum on the Moon, with gmoon = 1.62 m/s2. Since the period (T) of the pendulum is the same on both the Moon and Earth, we have:

Tearth = 2π ∙ √(Learth/gearth) = Tmoon = 2π ∙ √(Lmoon/gmoon)

Solving this equation for Lmoon, we get:

Lmoon = (T2 ∙ gmoon) / (4π2) = (Learth/gearth) ∙ gmoon

Plugging in the known values:

Lmoon = (2.00 m / 9.80 m/s2) ∙ 1.62 m/s2 ≈ 0.33 m

Therefore, the length of a pendulum on the Moon that would have the same period as a 2.00-m-long pendulum on Earth is approximately 0.33 meters.

Answer 2

0.331 m

Step-by-step explanation:

We are given that

Acceleration on the moon=
`1.62 m/s^2`

Acceleration due to gravity on earth=
`9.8 m/s^2`

Length of pendulum on the earth=2 m

We know that time period

T=
`2\pi\sqrt{(l)/(g)}`

Substitute the values then we get

T=
`2\pi\sqrt{(2)/(9.8)}`

Time period on moon=
`2\pi\sqrt{(l)/(1.62)}`

Time period on the moon=Time period on the earth

`2\pi\sqrt{(2)/(9.8)}=2\pi\sqrt{(l)/(1.62)}`

`(1)/(4.9)=(l)/(1.62)`

`l=(1.62)/(4.9)`

l=0.331 m

Hence, the length of pendulum on moon=0.331 m