JEE Advanced 2025 Paper 1 Q06 Physics Errors & Measurements Significant Figures Medium

JEE Advanced 2025 Paper 1 · Q06 · Significant Figures

Length, breadth and thickness of a strip having a uniform cross section are measured to be $10.5\text{ cm}$, $0.05\text{ mm}$, and $6.0\ \mu\text{m}$, respectively. Which of the following option(s) give(s) the volume of the strip in $\text{cm}^3$ with correct significant figures:

  1. A. $3.2 \times 10^{-5}$
  2. B. $32.0 \times 10^{-6}$
  3. C. $3.0 \times 10^{-5}$
  4. D. $3 \times 10^{-5}$
Reveal answer + step-by-step solution

Correct answer:D

Solution

Convert each measurement to cm: $L = 10.5\text{ cm}$ ($3$ sig figs), $b = 0.05\text{ mm} = 0.005\text{ cm} = 5 \times 10^{-3}\text{ cm}$ ($1$ sig fig), $t = 6.0\ \mu\text{m} = 6.0 \times 10^{-4}\text{ cm}$ ($2$ sig figs). Volume $V = L \cdot b \cdot t = 10.5 \times 5 \times 10^{-3} \times 6.0 \times 10^{-4} = 315 \times 10^{-7} = 3.15 \times 10^{-5}\text{ cm}^3$. The rule for multiplication: the result must be reported to the SAME number of significant figures as the factor with the FEWEST sig figs. Here the breadth $0.05\text{ mm}$ has only $1$ significant figure, so the volume must be quoted to $1$ sig fig $\Rightarrow$ $3 \times 10^{-5}\text{ cm}^3$. (A) and (C) have $2$ sig figs, (B) has $3$ sig figs — all overstate precision. Only (D) is consistent with the input data. Answer: (D).

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