Question

State the uses of dimensional analysis
using dimensions, show that 1 joule = ${10}^7$ erg
OR
Explain different types of errors in measurement.
An object was weighed by a physical balance and following readings were obtained $5.04g,5.06g,4.17g,5gm,4.93gm$
Find
1.) Mean absolute error
2.) percentage error

Answer 1

1. We have to prove that
1 joule = 10 erg
= (kg/gm) (m/cm) (s/s)
= (1000gm/1gm) (100cm/1cm) (1)
= (10) (10) (1)
(10) (10)
= (10)
= 10
Hence proved.
OR
Different type of error in measurement
a. Gross error
b. Blunders
c. measurement error - systematic error and random error
a. Gross error
ross errors are caused by mistake in using instruments or meters, calculating measurement and recording data results. The best example of these errors is a person or operator reading pressure gage 1.01N/m2 as 1.10N/m2. It may be due to the persons bad habit of not properly remembering data at the time of taking down reading, writing and calculating, and then presenting the wrong data at a later time. This may be the reason for gross errors in the reported data, and such errors may end up in calculation of the final results, thus deviating results.b. Blunders
Blunders are final source of errors and these errors are caused by faulty recording or due to a wrong value while recording a measurement, or misreading a scale or forgetting a digit while reading a scale. These blunders should stick out like sore thumbs if one person checks the work of another person. It should not be comprised in the analysis of data.c. Measurement error
The measurement error is the result of the variation of a measurement of the true value. Usually, Measurement error consists of a random error and systematic error. The best example of the measurement error is, if electronic scales are loaded with 1kg standard weight and the reading is 10002grams, then
The measurement error is = (1002grams-1000grams) =2grams
Measurement Errors are classified into two types: systematic error and random errors
Systematic Errors
The Systematic errors that occur due to fault in the measuring device are known as systematic errors. Usually they are called as Zero Error a positive or negative error. These errors can be detached by correcting the measurement device. These errors may be classified into different categories.
Instrumental Errors
Environmental Errors
Observational Errors
Theoritical