Error In Physics And Types Of Error

Q.6: Define Error? What are different types of error?

Answer: ERROR:

An error is defined as, “The difference between the measured and the actual values”.

Types OF ERROR:

There are following types of errors as:

Personal Error:

Personal error can arise due to making a mistake in reading a scale. In order to record a reading from a scale you have to line up the object you are measuring with the scale and hold your eyes in one particular position for making a correct observation.

Systematic Error:

This error is due to a fault in the measuring instrument and is usually called zero error, which may be positive or negative.

Random Error:

This error is called accidental error. This arises due to the experimental conditions. E.g. changes in temperature, humidity, voltage etc. These are beyond the control of the person making measurement.

Q.7: How can we find the percentage error In?

  • Meter Rod
  • Temperature
  • Sphere
  • Box
  • Density

Answer: PERCENTAGE ERROR IN METER ROD:

During the measurement of a quantity the maximum possible error of an instrument is defined as half the distance between two consecutive divisions.

Examples:

Suppose a measurement rod is marked in millimeters. The likely error in the measurement on this scale would be 0.5mm at one end. If a rod to be measured is placed along the scale the likely error in the measurement will be 0.5mm + 0.5mm = 1mm or 0.5cm because at both ends the likely error is 0.5mm. This error may be positive or negative because in the measurement both possibilities are there. If the rod is measured 16.2cm in length the its numerical value should be written as (16.2 + 0.5) cm. it means that likely error in Measurement is 0.1cm. This error is usually expressed in percent, hence the relative possible error in the above

PERCENTAGE ERROR IN TEMPERATURE:

Consider another example of measurement in which a thermometer is used. It is calibrated in 0.2°C division. In an experiment initial and final temperature are recorded as 20.2°C and 25.4°C. At each reading the likely error is 0.1°C. Therefore the error in rise in temperature (25.4°C – 20.2°C = 5.2°C) would be (0.1°C + 0.1°C = 0.2°C). The percentage error will be:

02 00

52*}

PERCENTAGE ERROR IN THE VOLUME OF A SPHERE:

Usually in an experiment we use a formula to find the final result. If a formula contains one or more quantities raised to some power say volume of a sphere is given by formula V = 4/3 it rr’, where “r’ stand for the radius of the sphere then error in the result increases due to the quantity multiplied by the power to which the quantity is raised in the original formula.

Where “d” stand for diameter of sphere. Percentage error in V = 3x% error in d. since the diameter is raised to the power three.

PERCENTAGE ERROR IN THE Volume OF A Box:

If two or more quantities are measurement in an experiment then. The error in the final result will be the sum of error of individual quantity. For example the volume of a box is give as,

V = length x breadth x height

V =/bh

Then,

Percentage error in volume = % error in length + % error in breadth + % error in height.

V = % of l + % of b + % of h

PERCENTAGE ERROR IN DENSITY:

If quotient involved in formula say density of a material is given as,

Mass

P =      volume

Then percentage error in the result would again be the sum of percentage error in individual quantity. Thus % error in density = % of m + % of V,