Question

Hulk once became angry and pushed earth so hard that her radius became
half of the present value. How many hours would make a day now?
Please also give description about the formule (2/5 mR^2w)??

Answer 1

From the conservation of angular momentum:
I_1 ω_1=I_2 ω_2
The moment of inertia of the sphere is
I=2/5 mr^2.
Thus,
2/5 mr^2 ω_1=2/5 m(r/2)^2 ω_2
ω_2=4ω_1.
We know that:
T~1/ω.
Thus,
T_2=T_1/4=24/4=6 hours.