Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given, physical quantity is X = a2 b3 c5/2d–2
The maximum percentage error in X is
`(Δx)/x xx 100 = +- [2((Δa)/a xx 100) + 3((Δb)/b xx 100) + 5/2((Δc)/c xx 100) + 2((Δd)/d xx 100)]`
= `+- [2(1) + 3(2) + 5/2 (3) + 2(4)]%`
= `+- [2 + 6 + 15/2 + 8]`
= `+- 23.5%`
∴ Percentage error in quantity X = ± 235%
Mean absolute error in X = ± 0.235 = ± 0.24 ......(Rounding-off upto two significant digits)
The calculated value of x should be round-off up to two significant digits.
∴ X = 2.8
APPEARS IN
RELATED QUESTIONS
Define absolute error.
Answer the following question.
Show that if Z = `"A"/"B"`, `(triangle"Z")/"Z" = (triangle"A")/"A" + (triangle "B")/"B"`
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.
Solve the numerical example.
If the length of a cylinder is l = (4.00 ± 0.001) cm, radius r = (0.0250 ± 0.001) cm and mass m = (6.25 ± 0.01) g. Calculate the percentage error in the determination of density.
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^2B^(1/2))/(C^(1/3)D^3)`, will be:
You measure two quantities as A = 1.0 m ± 0.2 m, B = 2.0 m ± 0.2 m. We should report correct value for `sqrt(AB)` as ______.
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.
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 E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M−5G−2 are ______.
The least count of the main scale of a screw gauge is 1 mm. The minimun number of divisions on its circular scale required to measure 5 µm diameter of a wire is ______.
A thermometer always reads 2°C higher than the actual temperature because its zero mark is incorrect. What type of error is this?
Which statement best describes the effect of systematic errors on measurements?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
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 ______.
