# Conversion related problem:

I am preparing for my campus and while i am solving old placement papers i stumbled upon a problem. If anyone knows the answer please post it.

QUESTION:If the earth diameter was halved then what would be the duration of 1 day?

## Replies

• Ramani Aswath
What has that to do with the price of fish?

Our moon's diameter is about 27% of Earth's. Its day is 29 of Earth days. Length of the day has to do with the rotation of the object on its axis and not its size.
• Sarathkumar Chandrasekaran
• Sindhu Chowdary
A.V.Ramani
What has that to do with the price of fish?

Our moon's diameter is about 27% of Earth's. Its day is 29 of Earth days. Length of the day has to do with the rotation of the object on its axis and not its size.
I just got a small doubt.If earth's diameter is halved,then the duration for which the sun light is exposed to a particular area on the earth also decreases,which makes the day seems to be shortened.
Or if the diameter is halved and if we assume that the mass of the earth also decreased,then he velocity with which the earth rotates automatically increases.This is because to escape the gravitational pull of the sun.In that way also the day is shortened.
I don't know if my analogy is right or wrong.Correct me if I am wrong.
• Ramani Aswath
Sindhu Chowdary
I just got a small doubt.If earth's diameter is halved,then the duration for which the sun light is exposed to a particular area on the earth also decreases,which makes the day seems to be shortened.
Or if the diameter is halved and if we assume that the mass of the earth also decreased,then he velocity with which the earth rotates automatically increases.This is because to escape the gravitational pull of the sun.In that way also the day is shortened.
I don't know if my analogy is right or wrong.Correct me if I am wrong.
If the speed of rotation does not change and remains 24 hours, the length of day will continue to be the same whatever the diameter.

Reduced mass has no effect on the speed of rotation. It alters the speed along the orbit around the sun thereby changing the length of the year.
• Shashank Moghe
#-Link-Snipped-# , Sir, I believe this is as good as giving the example of the ballet dancer rotating on the feet. If she is rotating with her hands extended, her speed is 'x', but if she brings her hands closer to her body, the speed of rotation increases. It has to do with conservation of angular momentum.

I believe the speed of earth will increase shortening the days (assuming mass of the earth still remains the same, essentially meaning the density is increased) as angular momentum needs to be conserved. Earth was formed (like all other planets) from cosmic gas clouds whose momentum gave earth the momentum it has. That momentum needs to be conserved.

I believe the angular momentum is given as L = m.r^2.w (m = mass of earth, r = radius of gyration, w = angular velocity). So as r goes to r/2, w must increase 4 fold, to conserve momentum.

Thus, if the radius of the earth becomes half of what it is today, one day will only last 6 hours. And that means lesser sleep for all of us ðŸ˜”

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