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

Hey Dear,

◆ 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)πR^3.ρ,

g = G × (4/3)πR^3.ρ / R^2

g = (4/3)πRGρ

Similarly, acceleration due to gravity at moon's surface is given as -

g' = (4/3)πR'Gρ

Putting R' = R/4,

g' = (4/3)π(R/4)Gρ

g' = g/4

g' = 9.8/4

g' = 2.45 m/s^2

Length of seconds pendulum is given by formula -

l = g.(T/2π)^2

l = 2.45 (2/2π)^2

l = 2.45 / 9.87

l = 0.2482 m

l = 24.82 cm

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

Thanks dear...