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. (Gravitational constant G =6.7 10⁻¹¹ ~N ~m ² / kg ² )

Step-by-step solution

Work done equals negative change in gravitational potential energy. For three masses in an equilateral triangle, gravitational PE is U = -G ( m₁m₂ r₁₂ + m₂m₃ r₂₃ + m₁m₃ r₁₃ ) . Initial configuration (side 20 m): U_i = - G 20 (200 300 + 300 400 + 200 400) = - 260000G 20 = -13000G Final configuration (side 25 m): U_f = - G 25 (260000) = -10400G Work done: W = -(U_f - U_i) = -10400G + 13000G = 2600G = 2600 6.7 10⁻¹¹ = 1.742 10⁻⁷ J 1.74 10⁻⁷ J