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
Correct Answer: D
Solution :
\[U=-G\left[ \frac{{{m}_{A}}{{m}_{B}}}{{{r}_{AB}}}+\frac{{{m}_{B}}{{m}_{C}}}{{{r}_{BC}}}+\frac{{{m}_{C}}{{m}_{A}}}{{{r}_{CA}}} \right]\] \[=6.7\times {{10}^{-11}}\] \[\left[ \frac{350\times 2000}{80\times {{10}^{-2}}}+\frac{2000\times 500}{120\times {{10}^{-2}}}+\frac{350\times 500}{40\times {{10}^{-2}}} \right]\] \[=-6.7\times {{10}^{-11}}[8750+8333.33+4375]\times {{10}^{+2}}\] \[=-6.7\times {{10}^{-9}}\times 21458.33\] \[=-143770.81\times {{10}^{-9}}=-1.43\times {{10}^{-4}}J\] Hence gravitational potential energy\[U=-1.43\times {{10}^{-4}}J\] and its value shall increase if \[{{m}_{B}}\] removed.You need to login to perform this action.
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