Mr. T has a faulty weighing balance — one arm of the beam is longer than the…
2023
Mr. T has a faulty weighing balance — one arm of the beam is longer than the other. When placed in the left pan, 1 kilogram balances 8 melons kept in the right pan; when placed in the right pan, 1 kilogram balances 2 melons kept in the left pan. If all the melons are equal in weight, what is the weight of a single melon?
- A.
150 gm
- B.
250 gm
- C.
300 gm
- D.
200 gm
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept: for a beam balance whose two arms are of unequal length, equilibrium is a moment (torque) balance, not a simple weight equality — the weight in a pan multiplied by that pan's arm length must equal the same product on the other pan. Because the arm-length ratio is fixed for a given balance, comparing the same reference weight (1 kg here) from the two different pans across two different scenarios lets that fixed ratio be eliminated algebraically to solve for the unknown weight.
Let the weight of one melon be m kg, and let L1 and L2 be the left and right arm lengths.
Scenario 1 — 1 kg on the left pan balances 8 melons on the right pan: 1 × L1 = 8m × L2, so L1/L2 = 8m.
Scenario 2 — 1 kg on the right pan balances 2 melons on the left pan: 2m × L1 = 1 × L2, so L1/L2 = 1/(2m).
Since both expressions equal the same fixed arm-length ratio, equate them: 8m = 1/(2m).
This gives 16m2 = 1, so m2 = 1/16, and m = 1/4 kg = 250 gm.
Cross-check: substituting m = 0.25 kg back — from Scenario 1, L1/L2 = 8(0.25) = 2; from Scenario 2, L1/L2 = 1/(2×0.25) = 2. Both scenarios give the same arm-length ratio, confirming the melon weighs 250 gm and is consistent with both weighings.