A body of mass 2M splits into four masses m, M-m, m and M-m. They are arranged at the four vertices of a square as shown. For what ratio M/m = x:1 is the gravitational potential energy of the system maximum? Find x.
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Question

A body of mass 2M splits into four masses m, M-m, m and M-m. They are arranged at the four vertices of a square as shown. For what ratio M/m = x:1 is the gravitational potential energy of the system maximum? Find x.

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G1 Physics · Accepted Answer

Step 1: Gravitational potential energy is U = -Σ Gmᵢmⱼ/rᵢⱼ and orbital total energy is E = -GMm/(2r) for a circular orbit. Step 2: Conserve total energy or compute the difference between configurations. Step 3: Substitute the given separations/masses. Final: Option B. In this specific setup, apply the calculation to: A body of mass (2M) splits into four masses {m, M - m, m, M - m}, which are rearranged to form a square a.