Units and Measurements Physics - Units and Measurements

In 4700m, significant digits are:

Which of the following statement is incorrect regarding mass?

If the unit of force is 100N, unit of length is 10m and unit of time is 100s. What is the unit of mass in this system of units?

Percentage errors in the measurement of mass and speed are 2% and 3%, respectively. The error in the estimation of kinetic energy obtained by measuring mass and speed will be:

If the length of a rectangle l = 10.5cm, breadth b= 2.1cm and minimum possible measurement by scale = 0.1cm, then the area is:

Fill in the blanks by suitable conversions:

G = 6.67 × 10^-11 Nm²kg^-2 = _______ cm²s^-2g^-1

Relation between astronomical unit and light year is ______.

The surface area of a solid cylinder of radius 2cm and height 10cm is equal to _________ (mm)².

Difference between the true value and the measured value of the quantity is known as ______.

1 fermi = _____ m. 

Which of the following is the most precise device for measuring length:
an optical instrument that can measure length to within a wavelength of light?

Fill in the blanks:
The surface area of a solid cylinder of radius 2.0cm and height 10.0cm is equal to ...(mm)²

Fill in the blanks:
The volume of a cube of side 1cm is equal to .....m³.

Which of the following is the most precise device for measuring length:
a screw gauge of pitch 1mm and 100 divisions on the circular scale.

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):
The wind speed during a storm.

It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02s. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1s?

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):
The number of strands of hair on your head.

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5mm. What is the estimate on the thickness of hair?

Answer the following:
You are given a thread and a metre scale. How will you estimate the diameter of the thread?

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding 107K, and its outer surface at a temperature of about 6000K. At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data : mass of the Sun = 2.0 × 1030kg, radius of the Sun = 7.0 × 108m.

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):
The number of air molecules in your classroom.

A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR, the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0s. What is the distance of the enemy submarine? (Speed of sound in water = 1450m s^–1).

Read the passage given below and answer the following questions from (i) to (v).
All engineering phenomena deal with definite and measured quantities and so depend on the making of the measurement. We must be
clear and precise in making these measurements. To make a measurement, magnitude of the physical quantity (unknown) is compared.
The record of a measurement consists of three parts, i.e. the dimension of the quantity, the unit which represents a standard quantity and a number which is the ratio of the measured quantity to the standard quantity.

1. A device which is used for measurement of length to an accuracy of about 10^-5m, is:

1. Screw gauge
2. Spherometer
3. Vernier callipers
4. Either (a) or (b)

2. Which of the technique is not used for measuring time intervals?

1. Electrical oscillator
2. Atomic clock
3. Spring oscillator
4. Decay of elementary particles

3. The mean length of an object is 5cm. Which of the following measurements is most accurate?

1. 4.9cm
2. 4.805cm
3. 5.25cm
4. 5.4cm

4. If the length of rectangle l = 10.5cm, breadth b = 2.1cm and minimum possible measurement by scale = 0.1cm, then the area is:

1. 22.0cm²
2. 21.0cm²
3. 22.5cm²
4. 21.5cm²

5. Age of the universe is about 10¹⁰ yr, whereas the mankind has existed for 10⁶ yr. For how many seconds would the man have existed, if age of universe were 1 day?

1. 9.2s
2. 10.2s
3. 8.6s
4. 10.5s

Read the passage given below and answer the following questions from  1 to 5.
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:

1. Instrumental error
2. Random error
3. Least count error
4. None of the above

2. The errors which occur irregularly

1. Instrumental error
2. Personal error
3. Random error
4. 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

Read the passage given below and answer the following questions from  1 to 5.
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 16.2cm 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 ± 0.1cm   = 16.2cm ± 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 = 163.62cm² + 1.6% = 163.62 + 2.6cm²
This leads us to quote the final result as L*b = 164 + 3cm². Here 3cm² 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, 12.9g – 7.06g, both specified to three significant figures, cannot properly be evaluated as 5.84g but only as 5.8g, 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 1.02g is ± 0.01g whereas another measurement 9.89g is also accurate to ± 0.01g. The relative error in 1.02g 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:

1. [L²]
2. [L³]
3. [M²]
4. None of these

2. dimensions of volume are:

1. [L²]
2. [L]
3. [L³]
4. 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:

Read the passage given below and answer the following questions from (i) to (v).
Measurement of Physical Quantity All engineering phenomena deal with definite and measured quantities and so depend on the making of the measurement. We must be clear and precise in making these measurements. To make a measurement, magnitude of the physical quantity (unknown) is compared. The record of a measurement consists of three parts, i.e. the dimension of the quantity, the unit which represents a standard quantity and a number which is the ratio of the measured quantity to the standard quantity. 

1. A device which is used for measurement of length to an accuracy of about 10”5m, is:

1. screw gauge
2. spherometer
3. vernier callipers
4. Either (a) or (b)

2. Which of the technique is not used for measuring time intervals?

1. Electrical oscillator
2. Atomic clock
3. Spring oscillator
4. Decay of elementary particles

3. The mean length of an object is 5cm. Which of the following measurements is most accurate?

4. 4.9cm
5. 4.805cm
6. 5.25 cm
7. 5.4 cm 63.

4. If the length of rectangle I = 105 cm, breadth b = 2.1 cm and minimum possible measurement by scale = 0.1 cm, then the area is

1. 22.0cm²
2. 21.0cm²
3. 22.5cm²
4. 21.5cm

5. Age of the universe is about 10¹⁰ yr, whereas the mankind has existed for 10⁶ yr. For how many seconds would the man have existed, if age of universe were 1day?

1. 9.2s
2. 10.2s
3. 8.6s
4. 10.5s

A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

It is a well known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the Sun. From this fact and from the information you can gather from examples 2.3 and 2.4, determine the approximate diameter of the moon.