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    Errors Of Measurements - Practice Questions & MCQ

    Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

    Quick Facts

    • Error in sum and Error in difference of two physical quantities, Error in product and Error in division of two physical quantities are considered the most difficult concepts.

    • Errors of measurements, Error in quantity raised to some power are considered the most asked concepts.

    • 47 Questions around this concept.

    Solve by difficulty

    For a measurement of the radius of a ball following readings are taken:

    3.26cm        3.28cm         3.31cm

    absolute error for the first reading is :

     

    In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows: \text{P}=\frac{a^{3}b^{2}}{cd} % error in P is:

    Concepts Covered - 4

    Errors of measurements

    It is the magnitude of the difference between the true value and the measured value of the quantity.

    It may be positive in certain cases and negative in certain other cases

    If   a_{1}, a_{2},a_{3}.........a_{n}   are a measured value

    then   a_{m}= \frac{a_{1}+a_{2}+......a_{n}}{n}

    where am  = true value

    then  

    1)Absolute Error for nth reading =\Delta a_n= a_{m}- a_{n}  = true value - measured value

    So \Delta a_{1}      =        a_{m}- a_{1}

         \Delta a_{2}     =         a_{m}- a_{2}

    2)  Mean absolute error

    \dpi{100} \Delta\bar{ a}= \frac{\left | \Delta a_{1} \right |+\left | \Delta a_{2} \right |+....\left | \Delta a_{n} \right |}{n}

    3) Relative error or Fractional error

    The ratio of mean absolute error to the mean value of the quantity measured.

    Relative \ \ error=\frac{\Delta\bar{ a}}{a_{m}}

    \Delta\bar{a} - mean\: absolute\: error

    a_{m}= mean \ \ value

    4) Percentage error

    Percentage \ \ error=\frac{\Delta\bar{ a}}{a_{m}}\times100 % 

    Error in sum and Error in difference of two physical quantities

    1)Error in sum (x=a+b)

    • Error in sum (x=a+b):-

    • absolute error in x=     \Delta x= \pm \left ( \Delta a+\Delta b \right )

             where 

               \Delta a= absolute error in measurement of a

               \Delta b= absolute error in measurement of b

               \Delta x= absolute error in measurement of x

    •          The percentage error in the value of x

                   =  \frac{\Delta x}{x}= \frac{\left ( \Delta a+\Delta b \right )}{a+b}\times 100%

          2) Error in difference (x=a-b)

    •        absolute error in x=\Delta x= \pm \left ( \Delta a+\Delta b \right )

    • Percentage error in the value of x= \frac{\Delta x}{x}= \frac{\left ( \Delta a+\Delta b \right )}{a-b}\times 100%

    Error in product and Error in division of two physical quantities

    1) Error in product x=a.b

    • maximum fractional error=\frac{\Delta x}{x}= \pm \left ( \frac{\Delta a}{a} +\frac{\Delta b}{b} \right )

             where 

               \Delta a= absolute error in measurement of a

               \Delta b= absolute error in measurement of b

               \Delta x= absolute error in measurement of x

    •   The percentage error in the value of x=

                      = =\dpi{100} \frac{\Delta x}{x}*100= \pm \left ( \frac{\Delta a}{a}*100+ \frac{\Delta b}{b}*100 \right )

                      =(% error in value of a + % error in value of b)

    2) Error in division x = a/b

    • maximum fractional error in  x

                  = \frac{\Delta x}{x}=\pm \left ( \frac{\Delta a}{a}+\frac{\Delta b}{b} \right )

    • The percentage error in the value of x=

                       =\dpi{100} \frac{\Delta x}{x}*100= \pm \left ( \frac{\Delta a}{a}*100+ \frac{\Delta b}{b}*100 \right )

                      =(% error in value of a + % error in value of b)

    Error in quantity raised to some power

    when  

    • The maximum fractional error in x is:- \frac{\Delta x}{x}=\pm \left ( n\frac{\Delta a}{a}+m\frac{\Delta b}{b} \right )
    • Percentage error in the value of x== \frac{\Delta x}{x}*100=\pm \left ( n\frac{\Delta a}{a}*100+m\frac{\Delta b}{b} *100\right )

    Study it with Videos

    Errors of measurements
    Error in sum and Error in difference of two physical quantities
    Error in product and Error in division of two physical quantities

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