Case Study Questions Class 11 Physics Chapter 2 Units and Measurement
CBSE Class 11 Case Study Questions Physics Units and Measurement. Important Case Study Questions for Class 11 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Units and Measurement.
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CBSE Case Study Questions Class 11 Physics Units and Measurement
1.) In general, the errors in measurement can be broadly classified as (a) systematic errors and (b) random errors.
Systematic errors: The systematic errors are those errors that tend to be in one direction, either positive or negative. Some of the sources of systematic errors are:
(a) Instrumental errors that arise from the errors due to imperfect design or calibration of the measuring instrument, zero error in the instrument, etc. For example, the temperature graduations of a thermometer may be inadequately calibrated (it may read 104 °C at the boiling point of water at STP whereas it should read 100 °C); in a vernier calipers the zero mark of vernier scale may not coincide with the zero mark of the main scale, or simply an ordinary metre scale may be worn off at one end.
(b) Imperfection in experimental technique or procedure to determine the temperature of a human body, a thermometer placed under the armpit will always give a temperature lowers than the actual value of the body temperature.
(c) Personal errors that arise due to an individual’s bias, lack of proper setting of the apparatus or individual’s carelessness in taking observations without observing proper precautions, etc. For example, if you, by habit, always hold your head a bit too far to the right while reading the position of a needle on the scale, you will introduce an error due to parallax.Systematic errors can be minimized by improving experimental techniques, selecting better instruments and removing personal bias as far as possible. For a given set-up, these errors may be estimated to a certain extent and the necessary corrections may be applied to the readings.
Random errors:The random errors are those errors, which occur irregularly and hence are random with respect to sign and size. These can arise due to random and unpredictable fluctuations in experimental conditions (e.g. unpredictable fluctuations in temperature, voltage), personal (unbiased) errors by the observer taking readings, etc. For example, when the same person repeats the same observation, it is very likely that he may get different readings every time.
Least count error: The smallest value that can be measured by the measuring instrument is called its least count. All the readings or measured values are good only up to this value. The least count error is the error associated with the resolution of the instrument.
(1) The errors due to imperfect design or calibration of the measuring instrument
(a) Instrumental error
(b) Random error
(c) Least count error
(d) None of the above
(2) The errors which occur irregularly
(a) Instrumental error
(b) Personal error
(c) Random error
(d) None of these
(3) Write a note on least count error
(4) Write a note on random error
(5) Write a note on systematic error
Answer key-
(1) a
(2) c
(3) The least count is the smallest possible value which can be measured with the help of the measuring instrument. All the readings or measured values are read. only up to this value. The least count error is the error related to the resolution of the instrument.
(4) The random errors are irregular errors and comes in measurement randomly hence called as random errors. The causes are unpredictable fluctuations in experimental conditions like temperature, voltage, personal errors by the observer taking readings, etc.
(5) Systematic errors: The systematic errors are those errors that tend to be in one direction, either positive or negative. Some of the sources of systematic errors are:
(a) Instrumental errors that arise from the errors due to imperfect design or calibration of the measuring instrument, zero error in the instrument.
(b) Imperfection in experimental technique or procedure.
(c) Personal errors
Case 2
Every measurement involves errors. Thus, the result of measurement should be reported in a way that indicates the precision of measurement. Normally, the reported result of measurement
is a number that includes all digits in the number that are known reliably plus the first digit that is uncertain. The reliable digits plus the first uncertain digit are known as significant digits or significant figures. If we say the period of oscillation of a simple pendulum is 1.62 s, the digits 1 and 6 are reliable and certain, while the digit 2 is uncertain. Thus, the measured value has three significant figures.A choice of change of different units does not change the number of significant digits or figures in a measurement. This important remark makes most of the following observations clear,
- All the non-zero digits are significant.
- All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.
- If the number is less than 1, the zero(s) on the right of decimal point but to the left of the first non-zero digit are not significant.
- The terminal or trailing zero(s) in a number without a decimal point are not significant.[Thus 123 m = 12300 cm = 123000 mm has three significant figures, the trailing zero(s) being not significant.
- The trailing zero(s) in a number with a decimal point are significant. [The numbers 3.500 or 0.06900 have four significant figures each]
- For a number greater than 1, without any decimal, the trailing zero(s) are not significant.
- For a number with a decimal, the trailing zero(s) are significant
(b) The digit 0 conventionally put on the left of a decimal for a number less than 1 (like 0.1250) is never significant. However, the zeroes at the end of such number are significant in a measurement.
(c)The multiplying or dividing factors which are neither rounded numbers nor numbers representing measured values are exact and have infinite number of significant digits.
(d)In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal
places. For example, the sum of the numbers 436.32 g, 227.2 g and 0.301 g by mere arithmetic addition, is 663.821 g. But the least precise measurement (227.2 g) is correct to only one decimal place. The final result should, therefore, be rounded off to 663.8 g.
(1) Significant figures in 12300 cm are
(a) 5
(b) 4
(c) 3
(d) None of these
(2) All the non-zero digits are
(a) Significant
(b) Non significant
(c) None of these
(3) Give rules for significant figures
(4) Give rules for addition and subtraction operations with significant figure
(5) Give rules for multiplication and division operations with significant figure
Answer key-
(1) c
(2) a
(3) All the non-zero digits are significant.
- All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all.
- If the number is less than 1, the zero on the right of decimal point but to the left of the first non-zero digit are not significant.
- The terminal or trailing zero(s) in a number without a decimal point are not significant.
- The trailing zero(s) in a number with a decimal point are significant.
- For a number greater than 1, without any decimal, the trailing zero(s) are not significant.
- For a number with a decimal, the trailing zero(s) are significant.
- The digit 0 conventionally put on the left of a decimal for a number less than 1 (like 0.1250) is never significant. However, the zeroes at the end of such number are significant in a measurement.
(4) In addition or subtraction, the final result after the operation should have as many decimal places as are there in the number with the least decimal places.
(5) In multiplication or division, the final result after operation should have as many significant figures as are there in the original number with the least significant figures. if the speed of light is given as 3 × 108 m s-1 (one significant figure) and one year (1y = 365.25 d) has 3.1557 × 107 s (five significant figures), the light year is 9.47 × 1015 m (three significant figures
Case 3
The rules for determining the uncertainty or error in the measured quantity in arithmetic operations can be understood from the following examples.
a.) If the length and breadth of a thin rectangular sheet are measured, using a metre scale as 16.2 cm and, 10.1 cm respectively, there are three significant figures in each measurement. It means that the length L may be written as L = 16.2 ± 0.1 cm = 16.2 cm ± 0.6 %.
Similarly, the breadth b may be written as b = 10.1 ± 0.1 cm = 10.1 cm ± 1 %
Then, the error of the product of two (or more) experimental values, using the combination of errors rule, will be L*b = 163.62 cm2 + 1.6% = 163.62 + 2.6 cm2
This leads us to quote the final result as L*b = 164 + 3 cm2. Here 3 cm2 is the uncertainty or error in the estimation of area of rectangular sheet.
b.) If a set of experimental data is specified to n significant figures a result obtained by combining the data will also be valid to n significant figures.However, if data are subtracted, the number of significant figures can be reduced.For example, 12.9 g – 7.06 g, both specified to three significant figures, cannot properly be evaluated as 5.84 g but only as 5.8 g, as uncertainties in subtraction or addition combine in a different fashion (smallest number of decimal places rather than the number of significant figures in any of the number added or subtracted).
c.) The relative error of a value of number specified to significant figures depends not only on n but also on the number itself. For example, the accuracy in measurement of mass 1.02 g is ± 0.01 g whereas another measurement 9.89 g is also accurate to ± 0.01 g. The relative error in 1.02 g is
= (± 0.01/1.02) × 100 % = ± 1%
Similarly, the relative error in 9.89 g is = (± 0.01/9.89) × 100 % = ± 0.1 %
Finally, remember that intermediate results in a multi-step computation should be calculated to one more significant figure in every measurement than the number of digits in the least precise measurement.
d.) The nature of a physical quantity is described by its dimensions. All the physical quantities represented by derived units can be expressed in terms of some combination of seven fundamental or base quantities. We shall call these base quantities as the seven dimensions of the physical world, which are denoted with square brackets [ ]. Thus, length has the dimension [L], mass [M], time [T], electric current [A], thermodynamic temperature [K], luminous intensity [cd], and amount of substance [mol]. The dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity. Note that using the square brackets [ ] round a quantity means that we are dealing with ‘the dimensions of’ the quantity. In mechanics, all the physical quantities can be written in terms of the dimensions [L], [M] and [T]. For example, the volume occupied by an object is expressed as the product of length, breadth and height, or three lengths. Hence the dimensions of volume are [L] × [L] × [L] = [L3].
(1) Dimensions of area is
(a) [L2]
(b) [L3]
(c) [M2]
(d) None of these
(2) dimensions of volume are
(a) [L2]
(b) [L]
(c) [L3]
(d) None of these
(3) What is uncertainty in physics? Explain with one example
(4) define dimensions of a physical quantity
(5) Give list for 7 base quantities with dimensions
Answer key-
(1) a
(2) c
(3) Uncertainty means the range of possible values within which true values of the measurement lies. For example. If the length and breadth of a thin rectangular sheet are measured, using a metre scale as 16.2 cm and, 10.1 cm respectively, there are three significant figures in each measurement. It means that the length L may be written as L = 16.2 ± 0.1 cm = 16.2 cm ± 0.6 %.
Similarly, the breadth b may be written as b = 10.1 ± 0.1 cm = 10.1 cm ± 1 % Then, the error of the product of two (or more) experimental values, using the combination of errors rule, will be L*b = 163.62 cm2 + 1.6% = 163.62 + 2.6 cm2
This leads us to quote the final result as L*b = 164 + 3 cm2. Here 3 cm2 is the uncertainty or error in the estimation of area of rectangular sheet.
(3) The dimensions of a physical quantity are defined as the powers to which the base quantities must be raised to represent that quantity.
(4) All the physical quantities represented by derived units can be expressed in terms of some combination of seven fundamental or base quantities. These quantities are
(5) Length has the dimension [L]
Mass [M]
Time [T]
Electric current [A]
Thermodynamic temperature [K]
Luminous intensity [cd]
Amount of substance [mol].
Case Study Questions Class 11 Physics Units and Measurement
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