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

Answer:

option (b)

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

$f = \frac{1}{2\pi }\times \sqrt{\frac{g}{l}}$

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

$\frac{fe}{fm} = \sqrt{\frac{ge}{gm}}$

$\frac{2}{fm} = \sqrt{\frac{6.039 gm}{gm}}$

$\frac{2}{fm} = 2.46$

fm = 0.814 Hz