Posted by **Natsi** on Friday, October 2, 2009 at 1:00pm.

It can be shown that for a uniform sphere the force of gravity at a point inside the sphere depends only on the mass closer to the center than that point. The net force of gravity due to points outside the radius of the point cancels.

How far would you have to drill into the Earth in kilometers, to reach a point where your weight is reduced by 4.5% ? Approximate the Earth as a uniform sphere.

- Science -
**bobpursley**, Friday, October 2, 2009 at 1:10pm
Me(r)=Me (r/re)^3 for r<re

so you want g' to be .955g

g= GMe/re^2

g'=.955GMe/re^2 =GMe(r/re)^3

which reduces to..

.955re=r^3 so

r=re *cubrt(.955)

check my work.

you want, of course, the depth of drilling, re-r

## Answer this Question

## Related Questions

- Physics Problem 6.22 - It can be shown that for a uniform sphere the force of ...
- Physics - It can be shown that for a uniform sphere the force of gravity at a ...
- Physics - It can be shown that for a uniform sphere the force of gravity at a ...
- Physics - A solid uniform sphere has a mass of 2.0 104 kg and a radius of 1.5 m...
- physics - A solid uniform sphere has a mass of 7.0 104 kg and a radius of 1.2 m...
- PHYSICS - A 494 kg uniform solid sphere has a radius of 0.390 m. Find the ...
- science - a sphere of mass 500.0g is released from point A 5m above the ground ...
- Science - 1) A block of mass 0.5 kg is placed at the highest point of a fixed ...
- physics - A solid sphere of mass m and radius r rolls with out slipping along ...
- Physics - An object is formed by attaching a uniform, thin rod with a mass of mr...