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A body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not, state the condition under which work done over a closed path is always zero?

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Only when the conservative force acts along the body when it moves in a closed loop. The work done can be zero.  However, if a non-conservative force acts on the body when it moves in a loop (for example friction, electrostatic force, etc.), then the work done cannot be zero.

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