Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given, t1 = 39.6 s, t2 = 39.9 s and t3 = 39.5 s
The least count of measuring instruments = 0.1 s ......(As measurements have only one decimal place)
Precision in the measurement = Least count of the measuring instrument = 0.1 s
The mean value of time for 20 oscillations is given by
t = `(t_1 + t_2 + t_3)/3`
= `(39.6 + 39.9 + 39.5)/5`
= 39.7 s
Absolute errors in the measurements
Δt1 = t – t1 = 39.7 – 39.6 = 0.1 s
Δt2 = t – t2 = 39.7 – 39.9 = – 0.2 s
Δt3 = t – t3 = 39.7 – 39.5 = 0.2 s
Mean absolute error = `(|Δt_1| + |Δt_2| + |Δt_3|)/3`
= `(0.1 + 0.2 + 0.2)/3`
= `0.5/3` = 0.17 ≈ 0.2 .....(Rounding off up to one decimal place)
∴ Accuracy of measurement = ± 0.2 s
APPEARS IN
संबंधित प्रश्न
The error in the measurement of the sides of a rectangle is 1%. The error in the measurement of its area is ______.
Define Mean absolute 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?
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.
If Q = `"X"^"n"/"Y"^"m"` and Δx is absolute error in the measurement of X, Δy is absolute error in the measurement of Y, then absolute error ΔQ in Q is ______.
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 ______.
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 dependence of g on geographical latitude at sea level is given by `g = g_0(1 + betasin^2Phi)` where Φ is the latitude angle and β is a dimensionless constant. If Δg is the error in the measurement of g then the error in measurement of latitude angle is ______.
A travelling microscope has 20 divisions per cm on the main scale while its Vernier scale has total 50 divisions and 25 Vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?
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?
Instrumental error can be minimised by ______.
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 ______.
