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Errors Of Measurements MCQ - Practice Questions with Answers

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.

  • 48 Questions around this concept.

Solve by difficulty

The magnitude of difference between the true value and measured value of quantity is called

The value of absolute error of first measurement in a measured value a1,a2..............ais equal to 

[am is the true value]

 

The ratio of mean absolute error to the mean value of the quantity measured is called:

 

The unit of percentage error is :

 

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 :

 

For the measurement of the cylinder following readings are taken :

1.52cm         1.50cm         1.51cm        1.48cm

mean absolute error for the measurement is :

 

The value of the two resistor are R1=(6±0.3)KΩ and R2=(10±0.2)KΩ.The maximum absolute error in equivalent resistance when they are connected in series will be:

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Two roads of length (3.161±0.3)cm and (1.121±0.1)cm. What is the percentage error in the measurement of their difference :

If the length of the stick P is (28.7±0.5)cm and that of the stick Q is (19.6±0.3)cm. What will be the percentage error in R, if R=P+Q

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If the mass of box A is (3.25±0.01)kg and that of B is (4.19±0.01)kg, then box B is heavier than A by:

 

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 a1,a2,a3an are a measured value then

am=a1+a2+ann
 

where am  = true value

then  

1)Absolute Error for nth reading =Δan=aman= true value - measured value

S0Δa1=ama1Δa2=ama2

2) Mean absolute error

Δa¯=|Δa1|+|Δa2|+.|Δan|n
 

3) Relative error or Fractional error

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

Relative error =Δa¯am
Δa¯ mean absolute error
am= mean value
4) Percentage error

 Percentage error =Δa¯am×100%
 

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=Δx=±(Δa+Δb)
    where
    Δa= absolute error in measurement of a
    Δx= absolute error in measurement of ×

  •          The percentage error in the value of x

               = Δxx=(Δa+Δb)a+b×100

      2) Error in difference (x=a-b)

  • absolute error in x=Δx=±(Δa+Δb)

  • Percentage error in the value of x=Δxx=(Δa+Δb)ab×100%

Error in product and Error in division of two physical quantities

1) Error in product x=a.b

  •  maximum fractional error =Δxx=±(Δaa+Δbb)
    where
    Δa= absolute error in measurement of a
    Δb= absolute error in measurement of b
    Δx= absolute error in measurement of x

  •   The percentage error in the value of x=

                  =Δxx100=±(Δaa100+Δbb100)

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

2) Error in division x = a/b

  • maximum fractional error in  

              

=Δxx=±(Δaa+Δbb)

The percentage error in the value of x=

=Δxx100=±(Δaa100+Δbb100)

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

Error in quantity raised to some power

when (x=anbm)
- The maximum fractional error in × is:- Δxx=±(nΔaa+mΔbb)
- Percentage error in the value of x==Δxx100=±(nΔaa100+mΔbb100)

 

 

 

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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