The Universe, a Metal Rod and gravity (Part 2)

Classical Mechanics Level 2

Continuation of part 1: https://brilliant.org/problems/the-universe-a-metal-rod-and-gravity-part-1/

After you find this peculiar rod, you get so excited that you have to show it to all your friends at NASA. So you rush back to Earth in a hurry, taking the metal rod with you, which is again 1 lightyear long and 10 cm in diameter. Every researcher on Earth is quite shocked as you are welcomed back from your trip to the vast nothingness of space.

Now you stand on Earth, with this metal rod in your right hand pointing perfectly radially away from the earth towards the skies where you came from. And a thought strikes you, harder than any rod had previously struck you: "What if I dropped this rod right now from the height of my shoulders?"

Assume, for the sake of simplicity, that Earth is spherical, smooth, not rotating, and is the only celestial body around. The rod cannot do any deformation, totally stiff.

You now drop the rod with the end in front of your shoulder. What do you see?

The rod falls a lot faster than usual objects The rod falls at the same speed as anything else on Earth The rod falls so slow that it seems floating The rod falls slow, but still reaches the ground within a minute

Aleksander Lund by Aleksander Lund , 25, Denmark

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2 solutions

Tausif Hossain
May 9, 2018

You can consider the very long rod now as a point particle located half a light year away as the rod would have a center of mass at about half a light year away and considering in this problem earth is the only celestial object, it’s distance to the center of mass of the rod is very large. So as gravity falls by the square of distance from center of earth of center of mass of rod; it’s force and hence acceleration on the rod would be very small so it’s center of mass now moves very slowly. Thus as the rod is rigid(whole of it moves with center of mass) it falls down very slowly.

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A I
Apr 11, 2018

This is a very interesting problem! A rod of one ly long would (I think) have a huge mass. Objects with a bigger mass needs a longer time to accelerate, hence it will fall very very very slowly!

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Not quite the right reason. If that was true, why do bowling balls and tennis balls fall at the same speed?

Aleksander Lund - 3 years, 2 months ago

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That is a good point that I didn't think about. Then shouldn't it because the difference in the force acting on the rod at different sections?

A I - 3 years, 1 month ago

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Yeah, Gravitaionall pull is given by f_g = G * (m*M)/R^2 = m * a R being length from any point on the rod to the center of the earth, since most of the rod is so far out that the gravitational pull is really small, so the net acceleration (a) is very small too since the length of the rod is much bigger than the earths radius.

Aleksander Lund - 3 years, 1 month ago

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