English

Define relative error. - Physics

Advertisements
Advertisements

Question

Define relative error.

Definition
Advertisements

Solution

The ratio of the mean absolute error in the measurement of a physical quantity to its arithmetic mean value is called relative error.

Relative error = `(triangle "a"_"mean")/"a"_"mean"`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Units and Measurements - Exercises [Page 14]

APPEARS IN

Balbharati Physics [English] Standard 11 Maharashtra State Board
Chapter 1 Units and Measurements
Exercises | Q 2. (iii) 3. | Page 14

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 percentage 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.


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.


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:


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 ______.


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 ______.


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.


The resistance R = `"V"/"I"`, where V = (50 ± 2) V and I = (20 ± 0.2)A. The percentage error in R is 'x' %. 

The value of x to the nearest integer is ______.


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.


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 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. 


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 ______.


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?


Which strategy would best reduce an instrumental error caused by a faulty weighing scale?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×