Gravity

What is the weight of a 40 kg man at the center of the earth?


The answer is 0.

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7 solutions

Dương Tươi
Apr 9, 2014

Let's prove Gravitational acceleration on earth's center equals to 0. Basically, we suppose that mass of every point of the earth are the same. Acceleration g at a surface point is g = G . M R 2 = G × ρ 4 3 π R 3 R 2 = 4 3 π ρ × G R g=\frac{G.M}{R^2}=G \times \rho\frac{4}{3}\pi\frac{R^3}{R^2}=\frac{4}{3}\pi\rho \times GR In the similar way, we have at an underground point: g = 4 3 π ρ × G ( R h ) g'=\frac{4}{3}\pi\rho \times G(R-h) . h is distance from surface to the point here. So, g g = R h R \frac{g'}{g}=\frac{R-h}{R} or g = g R h R g'=g\frac{R-h}{R} . In this problem, h = R h=R and g = 0 g'=0 . However, we can guess easily the answer. :D

Tu hi chaava

Samarth Rastogi - 7 years, 1 month ago
Prathamesh Raut
Mar 20, 2014

gravity is 0 on center of earth

Simple . Yet people make it complicated :P

Arif Khan - 7 years, 1 month ago

g' = g * ( 1 - (h/R) ) ... for going below the earth's surface.......... put h=r and get g' = 0

Mayank Holmes - 7 years ago

of curse the gravity must be 0

Emran Mani - 7 years, 2 months ago

seriously, i just think the man died when he reaches the center of the earth. he become ashes

Pushpkant Yadav
Oct 12, 2014

g=0 at the center of earth and weight W=mg=0 of any object

Robert Fritz
May 1, 2014

Gravitational forces cancel out.

You have got it wrong. Your answer might seem logically correct. Had that been the case, gravitational forces from all directions would have cancelled out, but that's far from reality. Here, what actually happens is, the value of "g" decreases as we move above or below the Earth's surface. And it becomes zero at the center of earth (the same would happen at some higher point, above the surface). If you want a more theoretical explanation, go for Dương Tươi's answer. Hope it helps...

Nandakishor S Nair - 6 years, 8 months ago
Alinjar Dan
Apr 23, 2014

factual one.

Vaibhav Pandey
Apr 13, 2014

since weight=mass gravity therefore weight at the center of the earth=4.08163265306 0=0

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