# Question #c4f46

Dec 21, 2017

It is either 14 N or 9 N, depending on interpretation. See below.

#### Explanation:

The question can be interpreted 2 ways. I will give answers for both interpretations. I will be using the formula of Newton's Universal Law of Gravitation.

$F = \frac{G \cdot m \cdot M}{r} ^ 2$

The only parameter that is changing in the elevation of the body is r. When the body weighed 144 N, the value of r was R. So the weight at the new location would be different by the multiplication factor, 1/k, where

$k = {\left(\frac{\text{new distance from center of the earth}}{R}\right)}^{2}$

1. Assuming the body is now 3R from the center of the earth, the value of k is

$k = {\left(\frac{3 \cdot R}{R}\right)}^{2} = 9$

So the new weight is $\frac{144 N}{9} = 16 N$

1. Assuming the body 3R above the surface, it is now 4R from the center of the earth, the value of k is

$k = {\left(\frac{4 \cdot R}{R}\right)}^{2} = 16$

So the new weight is $\frac{144 N}{16} = 9 N$

I hope this helps,
Steve