- #1
Rmehtany
- 27
- 2
Note: I know this question has been asked before, but I wasn't allowed to ask my question on that thread
1. Homework Statement
The gravitational self potential energy of a solid ball of mass density ρ and radius R is E. What is the gravitational self potential energy of a ball of mass density ρ and radius 2R?
$$PE = -\frac{GMM}{R}$$
My attempt was dimensional analysis, because I had no other idea on how to approach this. The energy was somehow going to be related to G, radius, density, and other constants. PE has units $$kg \frac{m^2}{s^2}$$, density $$\frac{kg}{m^3}$$, and G in terms of $$\frac{m^3}{s^2}$$. I tried using E = $$k G^a \rho^b R^c$$, but I couldn't eliminate enough masses from the equation.
1. Homework Statement
The gravitational self potential energy of a solid ball of mass density ρ and radius R is E. What is the gravitational self potential energy of a ball of mass density ρ and radius 2R?
Homework Equations
$$PE = -\frac{GMM}{R}$$
The Attempt at a Solution
My attempt was dimensional analysis, because I had no other idea on how to approach this. The energy was somehow going to be related to G, radius, density, and other constants. PE has units $$kg \frac{m^2}{s^2}$$, density $$\frac{kg}{m^3}$$, and G in terms of $$\frac{m^3}{s^2}$$. I tried using E = $$k G^a \rho^b R^c$$, but I couldn't eliminate enough masses from the equation.