AS Daily A Level Physics question
On a long, light plank balanced on a frictionless pivot, a 30 N toolbox sits 0.50 m to the left of the pivot. A 20 N paint can is placed a distance x to the right so the plank is in horizontal equilibrium. The toolbox is then slid 0.20 m closer to the pivot. To re-balance the plank, what must happen to x?
Answer
The correct answer is A.
Correct: A — Decrease by 40% to 0.45 m from the pivot on the right. A: Initially 30×0.50 = 20×x gives x = 0.75 m; after sliding the toolbox to 0.30 m, 30×0.30 = 20×x′ gives x′ = 0.45 m, which is a 40% decrease, and it must remain on the right to oppose the left-hand moment. B: Increasing x is the wrong trend because the left moment has fallen (from 15 N m to 9 N m), and in the limiting case of the toolbox at the pivot the required right distance should shrink toward zero, not grow. C: A 20% decrease misapplies proportional reasoning to distances rather than moments—the left moment fell by 40%, so the required right distance must also fall by 40% for the same 20 N weight. D: Keeping 0.75 m assumes only weights matter, but equilibrium requires equal and opposite moments, which depend on both force and perpendicular distance.