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MHT CET 2026 (19 Apr, Shift 2) · Errors in Measurement

Errors in Measurement question from MHT CET 2026 (19 Apr, Shift 2)

Q23MHT CET 2026 · 19 APR · SHIFT 2Medium

Errors in Measurement

A cuboid has volume V=l×l×lV = l \times l \times \sqrt{l}, where ll is the length of one side. When the length ll is measured by a meter scale of least count 11 mm, the relative percentage error in the measurement of its volume is 6.25%6.25\%. Then the relative percentage error in measurement of its length and the value of the length ll is

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Answer: (b)

  1. V=l2l=l5/2V = l^2\sqrt{l} = l^{5/2}, so ΔVV=52Δll\frac{\Delta V}{V} = \frac{5}{2}\frac{\Delta l}{l}
  2. 6.25%=2.5 Δll⇒Δll=2.5%6.25\% = 2.5\,\frac{\Delta l}{l} \Rightarrow \frac{\Delta l}{l} = 2.5\%
  3. With Δl=1 mm=0.1 cm\Delta l = 1\text{ mm} = 0.1\text{ cm}: l=0.10.025=4 cml = \frac{0.1}{0.025} = 4\text{ cm}
  4. So the answer is (b) 2.5%2.5\% and 44 cm.
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