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Vidaara.orgClass 11 · Physics
CodeVID-P11-01-ERR-01
Errors & Significant Figures — Assignment
Chapter: Units and Measurements
Topic: Errors & Significant Figures
Maximum Marks: 30
Time: 60 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The number of significant figures in $6.032 \\times 10^{4}$ is:
  • A.3
  • B.4
  • C.5
  • D.6
2.
For $Z = A/B$, the relative error in $Z$ is:
  • A.$\\Delta A + \\Delta B$
  • B.$\\dfrac{\\Delta A}{A} + \\dfrac{\\Delta B}{B}$
  • C.$\\dfrac{\\Delta A}{A} - \\dfrac{\\Delta B}{B}$
  • D.$\\dfrac{\\Delta A}{B}$
3.
Closeness of a measurement to the true value is its:
  • A.precision
  • B.accuracy
  • C.least count
  • D.resolution
4.
A zero error in a screw gauge is an example of:
  • A.random error
  • B.systematic error
  • C.gross error
  • D.no error
5.
The result of $1.2 \\times 3.45$ to correct significant figures is:
  • A.$4.14$
  • B.$4.1$
  • C.$4$
  • D.$4.140$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Distinguish between accuracy and precision in one line each.
7.
Find the number of significant figures in $0.0203$ and $4.700$.
8.
If $\\dfrac{\\Delta a}{a} = 0.02$, express the percentage error.
9.
Round $3.765$ to three significant figures (round-half-to-even).
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
The radius of a sphere is $(2.00 \\pm 0.02)\\,\\text{cm}$. Find the percentage error in its volume.
11.
Two masses are $(10.2 \\pm 0.1)\\,\\text{g}$ and $(8.6 \\pm 0.1)\\,\\text{g}$. Find their difference with error.
12.
Subtract $0.027\\,\\text{m}$ from $1.5\\,\\text{m}$ to correct significant figures.
13.
Classify with one example each: systematic and random error.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In an experiment $g$ is found from $g = \\dfrac{4\\pi^2 l}{T^2}$. If the error in $l$ is $1\\%$ and in $T$ is $2\\%$, find the percentage error in $g$.
15.
Five readings of a time period are $2.01, 2.10, 1.98, 2.05, 1.96\\,\\text{s}$. Find the mean, mean absolute error and percentage error.

Answer Key

Section A — Multiple Choice Questions
  1. (B) 4
  2. (B) $\\dfrac{\\Delta A}{A} + \\dfrac{\\Delta B}{B}$
  3. (B) accuracy
  4. (B) systematic error
  5. (B) $4.1$
Section B — Short Answer (2 marks)
  1. Accuracy: closeness to true value. Precision: agreement among repeated readings.
  2. $0.0203$ has 3; $4.700$ has 4.
  3. $2\\%$.
  4. $3.76$.
Section C — Short Answer (3 marks)
  1. $3 \\times 1\\% = 3\\%$ (since $V \\propto r^3$).
  2. $(1.6 \\pm 0.2)\\,\\text{g}$.
  3. $1.5\\,\\text{m}$ (one decimal place).
  4. Systematic: faulty calibration / zero error. Random: scatter from fluctuations in repeated readings.
Section D — Long Answer (5 marks)
  1. $\\dfrac{\\Delta g}{g} = \\dfrac{\\Delta l}{l} + 2\\dfrac{\\Delta T}{T} = 1\\% + 2(2\\%) = 5\\%$.
  2. Mean $= 2.02\\,\\text{s}$; mean absolute error $\\approx 0.044\\,\\text{s}$; percentage error $\\approx 2.2\\%$.
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