Question

Three uniform spheres, with masses $m_A=350kg,m_B=2000kg$, and $m_C=500kg$ have the $(x,y)$ coordinates $(0,0)cm,(-80,0)cm$ and $(40,0)cm$ respectively. The gravitational potential energy, $U$, of the system and change in its value in terms of increase or decrease, if the sphere of mass is removed, may be given as

• A. $U=-1.92\times 10^{-4}J$ and its value shall decrease if the sphere B is removed
• B. $U=-1.92\times 10^{-4}J$ and its value shall increase if the sphere B is removed
• C. $U=-1.43\times 10^{-4}J$ and its value shall decrease if mg is removed
• D. $U=-1.43\times 10^{-4}J$ and its value shall increase if $m_B$ is removed

Answer 1

Answer: (D)

$U=-G\left[\frac{m_A{m}_B}{r_{AB}}+\frac{m_B{m}_C}{r_{BC}}+\frac{m_C{m}_A}{r_{CA}}\right]$
$=6.7\times 10^{-11}\left[\frac{350\times 2000}{80\times 10^{-2}}+\frac{2000\times 500}{120\times 10^{-2}}+\frac{350\times 500}{40\times 10^{-2}}\right]$
$=-6.7\times 10^{-11}[8750+8333.33+4375]\times 10^{+2}$
$=-6.7\times 10^{-9}\times 21458.33$
$=-143770.81\times 10^{-9}$
$=-1.43\times 10^{-4}J$
Hence gravitational potential energy
$U=-1.43\times 10^{-4}J$
and its value shall increase if $m_B$ removed.