Least count, significant figures and errors in measurement
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See all →- A physical quantity P is related to four observations a, b, c and d as follows:P = a^3b^2 / c√(d)The percentage errors of measurement in a, b, c and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is Answer: 3. 13% Key idea: for P=a³b²/csqrt d , the maximum percentage error is the sum of (power × percentage error) of each quantity. Δ P/P×... 1
- The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are : Answer: 1. Random errors Errors that arise from unpredictable, irregular fluctuations in conditions such as temperature or voltage supply ar... 1
- 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: Answer: 4. 1.6% Density ρ=m/π r² l . The maximum fractional errors add, with the radius error counted twice because of r² . Δρ/ρ=Δ m/m+2Δ r/... 1
- The area of a rectangular field (in m^2) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is : Answer: 1. 14 × 10² Area =55.3×25=1382.5\ m² . In multiplication the answer keeps as many significant figures as the least precise number. 2... 1
- Taking into account of the significant figures, what is the value of 9.99 m - 0.0099 m ? Answer: 2. 9.98 m For subtraction, the result keeps as many decimal places as the number with the fewest decimal places. 9.99 has 2 decimals... 1
- In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = A^2 B^1/2C^1/3 D^3, will be : Answer: 2. 16% For a product or quotient, the maximum fractional error is the sum of each power times its fractional error. Δ X/X×100=2(1)+1... 1