Question

The Earth is 81.25 times as massive as the Moon and the radius of the Earth is 3.668 times the radius of the Moon. If a simple pendulum has a frequency of 2 Hz on Earth, what will be its frequency on the Moon? a) 0.407 Hz b) 0.814 Hz c) 1.34 Hz d) 1.22 Hz e) 1.63 Ha

Answer 1

option (b)

Step-by-step explanation:

Mass of moon = m

Mass of earth = 81.25 x mass of moon = 81.25 m

Radius of moon = r

radius of earth = 3.668 x radius of moon = 3.668 r

Frequency on earth = 2 Hz

Let the frequency on moon is f.

The formula for the frequency is given by

`f = (1)/(2\pi )* \sqrt{(g)/(l)}`

The value of acceleration due to gravity on earth is g.

ge = G Me / Re^2

ge = G x 81.25 m / (3.668 r)^2

ge = 6.039 x G m / r^2 = 6.039 x gm

ge / gm = 6.039

Now use the formula for frequency

`(fe)/(fm) = \sqrt{(ge)/(gm)}`

`(2)/(fm) = \sqrt{(6.039 gm)/(gm)}`

`(2)/(fm) = 2.46`

fm = 0.814 Hz