GREPhysics.NET
GR | # Login | Register
   
  GR9277 #4
Problem
GREPhysics.NET Official Solution    Alternate Solutions
\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 $\frac{F(R)}{F(2R)}$


  1. 32
  2. 8
  3. 4
  4. 2
  5. 1

Mechanics}Gravitational Law

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

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


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

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
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\nNEC
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
NEC
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.
Typo Alert!
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)\piR^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
NEC

Post A Comment!
Username:
Password:
Click here to register.
This comment is best classified as a: (mouseover)
 
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\int_0^\infty$
$\partial$
$\Rightarrow$
$\ddot{x},\dot{x}$
$\sqrt{z}$
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
$\vec{E}$
$\frac{a}{b}$
 
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...