Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m . They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J.

Work done by external agent :
\(w _{ ext }=\Delta U\)
\(U _{ i }=-\frac{ Gm _1 m_2}{ r _{ i }}-\frac{ Gm _2 m_3}{ r _{ i }}-\frac{ Gm _1 m_3}{ r _{ i }}: r _{ i }=20 m\)
\(U _{ f }=-\frac{ Gm _1 m_2}{ r _{ f }}-\frac{ Gm _2 m_3}{ r _{ f }}-\frac{ Gm _1 m_3}{ r _{ f }}: r _{ f }=25 m\)
\(U _{ i }=\frac{-6.67 \times 10^{-11}}{20}[200 \times 300+300 \times 400+200 \times 400]\)
\(=\frac{-6.67 \times 10^{-11}}{20} \times 26 \times 10^4=-86.71 \times 10^{-8} J\)
\(U_f=\frac{-6.67 \times 10^{-11}}{0.25}[200 \times 300+300 \times 400+200 \times 400]\)
\(=\frac{-6.67 \times 10^{-11}}{0.25} \times 26 \times 10^4=-693.68 \times 10^{-9}\)
\(=-69.36 \times 10^{-8} J\)
\(\Delta U = U _{ f }- U _{ i }=1.74 \times 10^{-7} J\)