Weights locate the gravity resultant

A horizontal massless rod carries 1 kg at x = 0 and 2 kg at x = 0.60 m. The local downward gravitational accelerations are 10 m/s² and 5 m/s² respectively, with parallel directions.

Where must one upward support force act to balance both force and torque?

Organize the givens & assumptions

Left mass: 1 kg, g = 10 m/s²
Right mass: 2 kg, g = 5 m/s²
Separation = 0.60 m

Fixed horizontal orientation, point masses, parallel gravitational forces with the stated local values, no additional force or applied couple. The requested point is the gravity-resultant location in this orientation.

A $0.60\ \mathrm m$
B $0.30\ \mathrm m$
C $0.40\ \mathrm m$
D $0.20\ \mathrm m$

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