Question 6 of 17beginner🔍 AnalyzeMCQ1 mark

Which of the following is the most precise device for measuring length:

Exercise: EXERCISES | Q: 1.6 | (Page 10)
For More Understanding

Explanation

Option (C) is correct. The precision of a measuring instrument depends on its least count — the smaller the least count, the more precise the instrument. For vernier callipers with 20 divisions, the least count is 1 mm/20 = 0.05 mm. For the screw gauge with pitch 1 mm and 100 divisions, the least count is Pitch/No. of divisions = 1 mm/100 = 0.01 mm. An optical instrument measuring within a wavelength of light can measure to approximately 10⁻⁷ m (about 0.0001 mm), which is much smaller than the least counts of both the vernier callipers and screw gauge. Hence, the optical instrument is the most precise device.

Solution Steps

  1. Step 1: Recall that precision depends on least count — smaller least count means higher precision.

  2. Step 2: Calculate least count of vernier callipers: 1 mm ÷ 20 = 0.05 mm = 5×105 \times 10⁻⁵ m

  3. Step 3: Calculate least count of screw gauge: 1 mm ÷ 100 = 0.01 mm = 1×101 \times 10⁻⁵ m

  4. Step 4: Wavelength of visible light ≈\approx 10⁻⁷ m, which is smallest among all three options.

  5. Step 5: Conclude that optical instrument (Option C) is most precise.

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