Question

Three uniform spheres, with masses $m_{A}=350\, kg , m_{B}=2000\, kg$, and $m_{C}=500 \,kg$ 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

The Correct Option is D

$U=-G\left[\frac{m_{A} m_{B}}{r_{A B}}+\frac{m_{B} m_{C}}{r_{B C}}+\frac{m_{C} m_{A}}{r_{C A}}\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.