Question

Assuming that the Moon is a Sphere of Same Mean Density as that of the Earth and One Quarter of its Radius, the Length of a Seconds Pendulum on Moon.​

Answer 1

Answer :-

l = 24.82 cm

Explanation :-

Acceleration due to gravity at earth's surface is calculated as -

g = GM / R²

Putting M = ρ × V = (4 / 3)π R³ . ρ,

g = G × (4 / 3)π R³ . ρ / R²

= (4 / 3)π R G ρ

Similarly, Acceleration due to Gravity at Moon's Surface is given as -

g' = (4 / 3)π R' G ρ

Putting R' = R / 4,

g' = (4 / 3) π (R / 4) G ρ

= g / 4

= 9.8 / 4

= 2.45 m/s²

Length of seconds pendulum is given by formula -

l = g.(T / 2π)²

= 2.45 (2 / 2π)²

= 2.45 / 9.87

= 0.2482 m

= 24.82 cm

Therefore, length of seconds pendulum on moon is 24.82 cm.

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