Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given: X = `("a"^4"b"^3)/("c"^(1//3)"d"^(1//2))`
The percentage error in a, b, c, d is respectively 2%, 3%, 3% and 4%.
`(Δ"x")/"x" xx 100` = 4 × % error of a + 3 × % error of b + `1/3` × % error of c + `1/2` × % error of d
i.e. X `= [(4 xx 2) + (3 xx 3) + (1/3 xx 3) + (1/2 xx 4)]`
Percentage error in X = [8 + 9 + 1 + 2] = 20%
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 absolute error.
Define Mean absolute error.
Define relative error.
Define percentage error.
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.
Find the percentage error in kinetic energy of a body having mass 60.0 ± 0.3 g moving with a velocity of 25.0 ± 0.1 cm/s.
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.
The relative density of a metal may be found by hanging a block of the metal from a spring balance and nothing that in air, the balance reads (5 .00 ± 0.05)N while in water, it reads (4.00 ± 0.05)N. The relative density would be quoted as ______.
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.
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?
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.
A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is ______ × 10-6 m.
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 ______.
Systematic errors cause all measurements to shift in the same direction. What does this primarily affect?
What are random errors?
Which of the following is an environmental error?
If the pointer of the voltmeter is not exactly at the zero of the scale, then the error is called ______.
Instrumental error can be minimised by ______.
