Question

a) What is the gravity of a planet if a R = 3 meter circulating mass m = 1 kg connected to a mass M = 4 kg, takes 2 seconds to circle once? b) If this same mass and string were to swing on the Earth, what would its period be? Please show ALL work and explanations. Thank you in advance.

Answer 1

a )

given

R = 3 m

m = 1 kg

M = 4 kg

T = 2 sec

using equation for acceleration is

a = 4 x $\pi$ R² / T

= 4 x 3.14 x 3² / 2

so the acceleration a = 56.52 m/sec²

b )

g = 9.8 m/sec²

9.8 = 4 x $\pi$ R² / T

T = 4 x 3.14 x 3² / 9.8

T = 11.534 sec

so the time period is T = 11.54054 sec