AS Daily A Level Physics question
Which statement must be true when a uniform 3.0 m plank (mass 20 kg) is held level by two vertical spring scales at its ends, and a 10 kg toolbox initially 1.0 m from the left end is slid 0.50 m toward the right end? Assume g = 10 N kg^−1 and no acceleration.
Answer
The correct answer is A.
Correct: A — The left scale reading decreases by 10%, while the right increases by 12.5%. Taking upward forces equal to total weight (300 N) and balancing moments about the left end: initially R_R×3.0 = 200×1.5 + 100×1.0 ⇒ R_R = 133.3 N, R_L = 166.7 N; after sliding the toolbox to 1.5 m, R_R×3.0 = 200×1.5 + 100×1.5 ⇒ R_R = 150 N, R_L = 150 N; thus left drops by 16.7/166.7 ≈ 10% and right rises by 16.7/133.3 = 12.5%. A correct because it uses constant total force and the moment shift toward the right; at the limiting case of the toolbox at the centre, readings must be equal. B reverses the direction of change: moving mass right must increase the right support and decrease the left, not the other way around. C cannot be true because the total upward force is fixed at 300 N, so both readings cannot increase together; additionally the final state is equal readings (150 N each), not a same-percentage increase from unequal starting values. D ignores that the total must stay 300 N: if the right reading increases, the left must decrease; it cannot remain unchanged.