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You weigh 720 N. What would you weigh if the Earth weretwo times as massive as it is and its radiuswere six times its present value?Answer in units of N.

User Akshay Rajput
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1 Answer

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Weight = mass x acceleration due to gravity

The formula for calculating acceleration due to gravity is expressed as

acceleration due to gravity = GMe/Re^2

where

G is the gravitational constant

Me is the mass of the earth

Re is the radius of the earth

From the information given,

W = 720N

This means that

720 = mass x GMe/Re^2

Let the new weight be W1. The mass would remain constant because it is the quantity of matter in the body. It does not vary. At this new weight, the earth is two times as massive as it is and its radius were six times its present value. This means that

W1 = mass x G x 2Me/6^2Re^2 = mass x G x 2Me/36Re^2

W1 = mass x G x Me/18Re^2

By crossmultiplying both equations, we have

720 x mass x G x Me/18Re^2 = W1 x mass x GMe/Re^2

mass x G x Me/Re^2 cancels out on both sides of the equation. It becomes

W1 = 720/18

W1 = 40

Your new weight would be 40N

User Tumbleweed
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