Question

21. What do you mean by relative error? Give the name of different types of errors. What is the
speciality of least count error over the other types of errors? If percentage error in radius of a
sphere is 2%, then find the percentage error and relative error in its surface area.
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Answer 1

Answer:

Relative Error : The ratio of mean absolute error to the true value is called Relative error.

Relative Error = $\mathsf{\dfrac{\Delta{x}}{xm}}$

Types of Error :

• Systematic error
• Instrumental error
• Personal error
• Random error
• Absolute error
• Mean absolute error

We can find the dimension of smallest object like wire, with the help of least count.

Solution :

% error in radius of sphere = 2 %

Surface area of sphere = $\mathsf{4 {\pi{r} ^{2}}}$

Reltaive error in surface area = 2 ×$\mathsf{\dfrac{\Delta{r}}{r}* 100}$

Reltaive error in surface area = 2 × 2 %

Reltaive error in surface area = 4 %