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A metal wire has mass (0.4±0.002) g, radius (0.3±0.001) mm and length (5±0.02) cm. The maximum possible percentage error in the measurement of density will nearly be

Asked in NEET 2023 · Percentage error in a derived quantity

• (1) 1.3%
• (2) 1.6%
• (3) 1.4%
• (4) 1.2%

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip reaches 1.3%: dropping the mass term gives 1.1%, dropping the length term gives 1.2%, and counting the radius once instead of twice gives 1.2%
• (3) comes from also out of reach: the four contributions are fixed at 0.5%, 0.33%, 0.33% and 0.4%, and no subset of them sums near 1.4%
• (4) comes from counting the radius only once: 0.5+0.33+0.4=1.23%, read off as the nearest listed 1.2%

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