Two pans of a balance are…

Physics Questions

Two pans of a balance are 46.3 cm apart. The fulcrum of the balance has been shifted 0.633 cm away from the center by a dishonest shopkeeper. By what percentage is the true weight of the goods marked up by the shopkeeper? Please provide your answer in percentage (%).

Answer

By shifting the fulcrum of the balance, the shopkeeper artificially inflates the weight of the goods by about 6.08%. Explanation: When a balance’s fulcrum is moved away from its center, the measurements it provides become distorted. This can be examined through the principles of physics concerning torque and levers. Torque (œÑ) is the rotational force that depends on the applied force (F) and the distance from the pivot (r), expressed as œÑ = r * F. In this case, the arms of the balance are 46.3 cm apart, and the fulcrum has been displaced 0.633 cm from the center, giving one side a length of 22.467 cm and the other 23.833 cm. The shopkeeper positions the goods on the shorter arm (22.467 cm) and the weights on the longer one (23.833 cm) to maintain balance. However, for the balance to level out, the side with the goods must carry a greater weight. To ascertain the percentage increase of the actual weight when compared to the apparent weight, we use the lever balance formula: m1 * r1 = m2 * r2. The proportion of r1 to r2 (r1/r2) yields the percentage markup. Therefore, the percentage markup = ((23.833 / 22.467) – 1) * 100% ‚âà 6.08%. Hence, the weight of the goods is effectively marked up by around 6.08% as a result of the fulcrum’s relocation.

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