The last choice is your answer, I just did it.
Use the Formula PE=mgh to solve for height.
Answer:
(a)
(b)
Explanation:
<u>For Earth we have:</u>
- mass of earth,
- radius of earth,
- orbital radius,
- period of rotation,
- period of revolution,
(a)
Angular momentum,
∵...............................(1)
For a particle of mass m moving in a circular path at a distance r from the axis,
&
Putting respecstive values in eq. (1)
To model earth as a particle is reasonable because the distance between the sun and the earth is very large s compared to the radius if the earth.
(b)
For a uniform sphere of mass M and radius R and an axis through its center,
using eq. (1)
Here object is dropped from height "h"
so we can say its initial speed is zero
and it will accelerate downwards due to gravity
now we can say it will take time T to hit the ground
now we can use
now it is given that it will take 1 second to drop h/2 height to strike the ground
so here we have can say that in "T - 1" s it will cover the h/2 distance from start
now we can say
from above two equations we have
now we can find total height of the drop by first equation
As the radius increases the circumference increases.