GREPhysics.NET: GR9277 #4

GR9277 #4

Problem

GREPhysics.NET Official Solution

\prob{4}
The magnitude of the Earth's gravitational force on a point mass is F(r), where r is the distance from the Earth's center to the point mass. Assume the Earth is a homogenous sphere of radius R.

What is $\frac{F(R)}{F(2R)}$

Mechanics $\Rightarrow$ }Gravitational Law

Recall the famous inverse square law determined almost half a millennium ago,

$F=\frac{k}{r^2}, <br />$

where $k=GMm$ .

The ratio of two inverse-square forces ( $r>R$ , where $R$ is the radius of the planet or huge heavy object) would be

$\frac{F(r_1)}{F(r_2)}=\frac{4r_2^2}{r_1^2}.<br />$

Thus, $\frac{F(R)}{F(2R)}=\frac{4R^2}{R^2}=4$ , which is choice (C).

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

bonghan_lee27
2016-05-22 17:07:38

Easy question. 97% obtained it right.\r\n

Reply to this comment

Manoj
2011-06-20 23:15:12

g/g'= r'*r'/r*r
Substituting the respective values the answer will be 4.

dwight5
2018-05-14 04:08:42

Agree!\r\ngmail sign up

Reply to this comment

solarclathrate
2009-06-22 08:38:19

Should not the LHS of the ratio of forces equation in the solution read $\frac{F(r_1)}{F(2 r_2)}$ ?

UTBphysics
2009-10-11 01:56:19

not exactly since R=r1 and r2=2R=2r1 the LHS is alright. The r2 on the RHS should be an r1, however.

Reply to this comment

emailzac
2007-11-02 16:11:10

Don't you have to take into account that the mass is not concentrated at the center? where $\rho$ = M / (4/3) $\pi$ R^3 you get a mass of M/8 then take into account the radial contribution of 4 to get a final answer of 1/2. Where'd i go wrong?

emailzac
2007-11-02 16:15:28

Sorry, thought this was problem 5, please ignore this comment :D

Reply to this comment

Post A Comment!

You are replying to:

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone