Question and solution on errors in physics plzz
Answers
Answer:
Q1: Define error.
Q1: Define error. Answer: The exact measurement of a physical quaintly not possible. This is known as Heisenberg uncertainly principle. Uncertainty in the measurements is called error. Numerically, the deviation of measured value from the actual value is called error. If X is the quantity measured, then ΔX is called error in X. i.e. Error = Actual value – Measured value.
Q2: What are different sources of errors?
Answer: An error can be of following types:
(a) systematic errors
(b) random errors.
(c) least count errors
(d) constant errors
(e) Errors due to external factors.
(a) Systematic error is the deviation caused due a single known source is called a systematic error. Following are the sources of systematic errors:
Instrumental errors: Imperfect design or calibration and/or Zero error.
Imperfection in experimental technique or procedure
Personal errors or Gross errors due to individual’s bias, lack of proper setting of the apparatus or individual’s carelessness in taking observations without observing proper precautions,
(b) Random Error: Error due to unknown reasons and that occurs while taking measurements.
(c) The least count error is the error associated with the resolution of the instrument.
(d) Constant Errors. Error in magnitude caused due to problems in calibration of scales. This error repeats itself in all measurements. Least Count error is also a type of constant error.
(e) External factors like air, temperature, pressure etc. can cause errors while taking measurements.
Q3: How can we minimize errors?
Answer: Using instruments of higher precision, improving experimental techniques, etc., we canr reduce the least count error.
Repeating the observations several times and taking the arithmetic mean of all the observations, the mean value would be very close to the true value of the measured quantity.
Gross errors can be minimized only if the observer is very careful in his observations and sincere in his approach.
Q4: What are the different ways of expressing an error?
Answer: different ways to express errors are:
Absolute Error
Relative Error
Percentage Error
Q5: What is Absolute Error?
Answer: The absolute error of measurement is the magnitude of the difference between the value of the quantity and the individual measurement value. Because we are not sure about the correct value of the quantity, correct or true value of quantity is taken as Arithmetic mean (Amean) of read values.
∴ If there are ‘n’ number of readings (A1, A2, A3… An), corresponding absolute errors can be represented as:
ΔA1 = Amean – A1
ΔA2 = Amean – A2
ΔA3 = Amean – A3
ΔAn = Amean – An
Final Absolute error is arithmetic mean of magnitudes of absolute errors i.e.
ΔAmean= ( |ΔA1|+ |ΔA2| + |ΔA3|+ … + |ΔAn|) / n
Q6: Define accuracy.
Answer: The accuracy of an instrument is a measure of how close the output reading of the instrument is to the correct value.
Q7: What is meant by precision? Can we say an instrument of high precision is accurate?
Answer: Precision describes an instrument’s degree of freedom from random errors. If a large number of readings are taken of the same quantity by a high precision instrument, then the spread of readings will be very small. It is not necessary an instrument of high precision is accurate.