Answer:
T = 184 seconds
Explanation:
First in order to solve this, we need to know which is the expression to calculate the period. This is an exercise of angular velocity, so:
T = 2π/w
Where w: angular speed (in rad/s)
So, let's calculate first the innitial angular speed:
w = 2π/T
Converting days to seconds:
25.4 days * 24 h/day * 3600 s/h = 2,194,560 s
Then the angular speed:
w = 2π / 2,194,560 = 2.863x10^-6 rad/s
Now, the innitial angular momentum is:
I = (2/5)Mr² replacing data:
I = 2/5* (6.96x10^8)² * M = 1.94x10^17m² * M
so the initial angular momentum would be:
L = Iω = 2.863x10^-6 * 1.94x10^17 M
L = 5.55x10^11 m²/s * M = final angular momentum
Now the final I = 2/5Mr²
Final I = 2/5 * (6.37x10^6)² * M = 1.62x10^13m² * M
Then 5.55x10^11m²/s * M = 1.62x10^13m² * M * ω → M cancels
ω = 3.42x10^-2 rad/s
Then the new period
T = 2π/ω = 2*3.14 / 3.42x10^-2
T = 184 seconds
= mass of 1st object = 500 kg
= mass of 2nd object = 20kg