if the acceleration due to gravity at the equator becomes zero then the time period of rotation of the earth will become
Answers
Answer:
Explanation:
We would like to start our answer by saying that we're sure you realize that this could never happen. The Earth has mass, just like every other solid object does (including you). It is the Earth's mass that causes it to have gravity, and so in order to not have gravity the Earth would have to not have mass. But if the Earth didn't have mass, it wouldn't be there anymore!
Having said that, though, let's now imagine that we could magically turn off the gravity while leaving the Earth behind. What would happen to the things on Earth depends on how they are attached. As you know, the Earth is rotating at quite a speed (you're moving at over a thousand miles per hour at the equator due to the Earth's rotation alone). Now if you spin something around your head on a string, it goes around in a circle until you let go of the string. Then it flies off in a straight line. If the circle is very big, then at first the straight line is almost the same as the circle -- however, after a short amount of time, the two paths will be very different, since the circle bends around but the straight line does not.
"Switching off" gravity is analogous to letting go of the string. Things not attached to the Earth in any other way would fly off into space in a straight line that would take them away from the surface of the Earth. In buildings, people would start floating gently upwards until they bumped into the ceiling. Outdoors, however (or in buildings with GIANT ceilings), things would start floating away from the Earth gently but eventually go much faster, as their straight lines took them farther and farther away from the circular path that the spinning Earth takes. The Earth's atmosphere itself would also float off into space, for the same reason! Some things (like trees and most buildings) are rooted into the Earth. They would not fly off because they are being held down. In fact, the force you would need to hold on and keep yourself from flying away from the Earth is very weak, only about 0.3% as strong as the force of gravity (and even weaker away from the equator). However, things which are holding on to the Earth would eventually have problems too -- the Earth itself would most likely break apart into chunks and float off into space, since it is only held together by gravity also!
Anyway, we hope that you enjoyed the answer. Like we said to start with, though, you should remember that this could never happen!
Explanation:
Acceleration due to gravity = Centrifugal force
g - acceleration due to gravity
v - velocity at the equator
w - angular velocity of earth
R - radius of earth at equator
g = v^2/R
v = √(g*R)
w = v/R
w = √(g/R)
T = 2*π/w
T = (2*π)/√(g/R)
Hence Time period of rotation
T = 2*π*√(R/g)