Answer:
ω₂=1.20
Explanation:
Given that
mass of the turn table ,M= 15 kg
mass of the ice ,m= 9 kg
radius ,r= 25 cm
Initial angular speed ,ω₁ = 0.75 rad/s
Initial mass moment of inertia
Final mass moment of inertia
Lets take final speed of the turn table after ice evaporated =ω₂ rad/s
Now by conservation angular momentum
I₁ ω₁ =ω₂ I₂
ω₂=1.20
Given,
Distance from the surface to the center of the earth, d=4000 miles
Distance from the center to you at a height of 8000 miles, a= 8000+4000=12000 miles
The gravitational force acting on a person at the surface is equal to his weight.
From Newton's Universal Law of Gravitation, the gravitational force is
Where G is the gravitational constant, M is the mass of the earth, m is the mass of the object/person, r is the distance between the center of the earth and the object/person
At the surface, this force is equal to the weight of the person, W=mg
i.e.
On substituting the of d,
At a height of 8000 miles from the surface, the gravitational force is equal to,
On dividing the above two equations,
Therefore,
Therefore at a height of 8000 miles above the surface of the earth, the force of gravity becomes 1/9 time your weight.