Advertisements
Advertisements
Question
Define absolute error.
Advertisements
Solution
- For a given set of measurements of a quantity, the magnitude of the difference between mean value (Most probable value) and each individual value is called absolute error (Δa) in the measurement of that quantity.
- absolute error = |mean value - measured value|
Δa1 = |amean - a1|
Similarly,
Δa2 = |amean - a2|,
`\vdots \vdots \vdots`
Δan = |amean - an|
APPEARS IN
RELATED QUESTIONS
The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.
Define relative error.
Define percentage error.
If the measured values of the two quantities are A ± ΔA and B ± ΔB, ΔA and ΔB being the mean absolute errors. What is the maximum possible error in A ± B? Show that if Z = `"A"/"B"`
`(Delta "Z")/"Z" = (Delta "A")/"A" + (Delta "B")/"B"`
Answer the following question.
Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`
The masses of two bodies are measured to be 15.7 ± 0.2 kg and 27.3 ± 0.3 kg. What is the total mass of the two and the error in it?
The distance travelled by an object in time (100 ± 1)s is (5.2 ± 0.1) m. What are the speed and its maximum relative error?
In a workshop, a worker measures the length of a steel plate with Vernier calipers having a least count 0.01 cm. Four such measurements of the length yielded the following values: 3.11 cm, 3.13 cm, 3.14 cm, 3.14 cm. Find the mean length, the mean absolute error, and the percentage error in the measured value of the length.
In Ohm’s experiments, the values of the unknown resistances were found to be 6.12 Ω, 6.09 Ω, 6.22 Ω, 6.15 Ω. Calculate the (mean) absolute error, relative error, and percentage error in these measurements.
Solve the numerical example.
If the formula for a physical quantity is X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))` and if the percentage error in the measurements of a, b, c and d are 2%, 3%, 3% and 4% respectively. Calculate percentage error in X.
Measure of two quantities along with the precision of respective measuring instrument is A = 2.5 ms–1 ± 0.5 ms–1 B = 0.10 s ± 0.01 s. The value of A B will be ______.
The mean length of an object is 5 cm. Which of the following measurements is most accurate?
The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.
Time for 20 oscillations of a pendulum is measured as t1 = 39.6 s; t2 = 39.9 s; t3 = 39.5 s. What is the precision in the measurements? What is the accuracy of the measurement?
A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a2 b3 c5/2d–2. The percentage error in the measurement of a, b, c and d are 1%, 2%, 3% and 4%, respectively. What is the percentage error in quantity X? If the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result.
In a Screw Gauge, the fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation, the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with the reference line. Calculate the true reading.
If the zero of the vernier lies on the right-hand side and the fourth division coincides with the main scale division when the jaws are in contact so the correction will be ______.
A thermometer always reads 2°C higher than the actual temperature because its zero mark is incorrect. What type of error is this?
A weighing scale that always reads a constant +0.2 kg because its zero mark is misaligned is a clear example of a(n):
A student reads a measuring cylinder from above the liquid level, causing the reading to be higher than the actual value. What type of error is this?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
Zero error of an instrument introduces ______.
Error due to non-removal of parallax between pointer and its image in case of magnetic compass needle causes ______.
The reason behind holding thermometer in the mouth instead of the armpit is to reduce ______.
