Hi there!
We can use the conservation of angular momentum to solve.
I = moment of inertia (kgm²)
ω = angular velocity (rad/sec)
Recall the following equations for the moment of inertia.
Begin by converting rev/sec to rad sec:
According to the above and the given information, we can write an equation and solve for ωf.
Answer:
K = G Mm / 9R
Explanation:
Expression for escape velocity V_e =
Kinetic energy at the surface = 1/2 m V_e ²
= 1/2 x m x 2GM/R
GMm/R
Potential energy at the surface
= - GMm/R
Total energy = 0
At height 9R ( 8R from the surface )
potential energy
= - G Mm / 9R
Kinetic energy = K
Total energy will be zero according to law of conservation of mechanical energy
so
K - G Mm / 9R = 0
K = G Mm / 9R