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Q2.22(d):
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
Solution :
Step 1: Establishing the Geometric Model
To estimate the total number of hair strands on a human scalp ($N$), we model the scalp as a spherical cap (or a hemisphere) and treat the hair density as a uniform distribution per unit area. Let $A_{scalp}$ be the surface area of the scalp and $\rho$ be the number of hair follicles per unit area.
The total number of strands is given by the product: $N = A_{scalp} \times \rho$ [Per principles of area-based spatial distribution].
Step 2: Estimating Surface Area of the Scalp
Assuming the scalp is a hemisphere of radius $r$. For an average adult, the diameter of the head is approximately $18\text{ cm}$ to $20\text{ cm}$. Taking the radius $r \approx 9\text{ cm} = 0.09\text{ m}$.
The surface area of a hemisphere is $A = 2\pi r^2$.
$A = 2 \times 3.14 \times (0.09\text{ m})^2$
$A = 6.28 \times 0.0081\text{ m}^2 \approx 0.05\text{ m}^2$
Converting to square centimeters ($1\text{ m}^2 = 10,000\text{ cm}^2$):
$A \approx 500\text{ cm}^2$ [Geometric approximation].
Step 3: Estimating Hair Follicle Density ($\rho$)
Biological studies indicate that the average human scalp has a hair density ranging from $150$ to $300$ strands per square centimeter depending on hair color and genetic factors. We shall use a median value for a robust estimate:
$\rho \approx 200\text{ strands/cm}^2$ [Per common physiological data].
Step 4: Calculating the Total Estimate
Substitute the values into the primary equation:
$N = 500\text{ cm}^2 \times 200\text{ strands/cm}^2$
$N = 100,000\text{ strands}$
Step 5: Establishing Upper Bound
To ensure we satisfy the request for an upper bound, consider the maximum density observed in individuals with high hair density ($\rho_{max} \approx 300\text{ strands/cm}^2$):
$N_{upper} = 500\text{ cm}^2 \times 300\text{ strands/cm}^2 = 150,000\text{ strands}$.
| Variable | Estimated Value |
|---|---|
| Scalp Area ($A$) | $500\text{ cm}^2$ |
| Average Density ($\rho$) | $200\text{ strands/cm}^2$ |
| Total Count ($N$) | $10^5\text{ strands}$ |
Final Solution: The estimated number of hair strands on the human head is approximately $10^5$ (100,000), with an upper bound of approximately $1.5 \times 10^5$ (150,000) strands.
More Questions from Class 11 Physics Units and Measurements EXERCISES
- Q2.1(a): Fill in the blanks (a) The volume of a cube of side 1 cm is equal to .....m$^3$
- Q2.1(a): Fill in the blanks The volume of a cube of side 1 cm is equal to .....(m^{3})
- Q2.1(b): Fill in the blanks The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...(mm)^{2}
- Q2.1(b): Fill in the blanks (b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...(mm)$^2$
- Q2.1(c): Fill in the blanks (c) A vehicle moving with a speed of 18 km h$^{–1}$ covers....m in 1 s
- Q2.1(c): Fill in the blanks A vehicle moving with a speed of 18 km (h^{-1}) covers....m in 1 s
- Q2.1(d): Fill in the blanks (d) The relative density of lead is 11.3. Its density is ....g cm$^{–3}$ or ....kg m$^{–3}$.
- Q2.1(d): Fill in the blanks The relative density of lead is 11.3. Its density is ....(g cm^{-3}) or ....(kg m^{-3}).
- Q2.10(a): State the number of significant figures in the following : 0.007 (m^{2})
- Q2.10(a): State the number of significant figures in the following : (a) 0.007 m$^2$
- Q2.10(b): State the number of significant figures in the following : (2.64 \times 10^{24}) kg
- Q2.10(b): State the number of significant figures in the following : (b) $2.64 \times 10^{24}$ kg
- Q2.10(c): State the number of significant figures in the following : 0.2370 (g cm^{-3})
- Q2.10(c): State the number of significant figures in the following : (c) 0.2370 g cm$^{–3}$
- Q2.10(d): State the number of significant figures in the following : (d) 6.320 J
- Q2.10(d): State the number of significant figures in the following : 6.320 J
- Q2.10(e): State the number of significant figures in the following : (e) 6.032 N m$^{–2}$
- Q2.10(e): State the number of significant figures in the following : 6.032 (N m^{-2})
- Q2.10(f): State the number of significant figures in the following : (f) 0.0006032 m$^2$
- Q2.10(f): State the number of significant figures in the following : 0.0006032 (m^{2})
- Q2.11: The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.
- Q2.11: The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.
- Q2.12(a): The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is the total mass of the box?
- Q2.12(a): The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is (a) the total mass of the box,
- Q2.12(b): The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is the difference in the masses of the pieces to correct significant figures ?
- Q2.12(b): The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is (b) the difference in the masses of the pieces to correct significant figures ?
- Q2.13: A physical quantity (P) is related to four observables (a), (b), (c) and (d) as follows : (P = \frac{a^{3} b^{2}}{\sqrt{c} d}) The percentage errors of measurement in (a), (b), (c) and (d) are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity (P) ? If the value of (P) calculated using the above relation turns out to be 3.763, to what value should you round off the result ?
- Q2.13: A physical quantity P is related to four observables a, b, c and d as follows : $P = \frac{a^3 b^2}{\sqrt{c} d}$ The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?
- Q2.14(a): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (y = a \sin \frac{2\pi t}{T}) ((a) = maximum displacement of the particle, (v) = speed of the particle. (T) = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(a): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (a) $y = a \sin \frac{2\pi t}{T}$ (a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(b): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (y = a \sin vt) ((a) = maximum displacement of the particle, (v) = speed of the particle. (T) = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(b): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (b) $y = a \sin vt$ (a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(c): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (y = (\frac{a}{T}) \sin \frac{t}{a}) ((a) = maximum displacement of the particle, (v) = speed of the particle. (T) = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(c): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (c) $y = (\frac{a}{T}) \sin \frac{t}{a}$ (a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(d): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (d) $y = (\frac{a}{\sqrt{2}}) (\sin \frac{2\pi t}{T} + \cos \frac{2\pi t}{T})$ (a = maximum displacement of the particle, v = speed of the particle. T = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.14(d): A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion : (y = (\frac{a}{\sqrt{2}}) (\sin \frac{2\pi t}{T} + \cos \frac{2\pi t}{T})) ((a) = maximum displacement of the particle, (v) = speed of the particle. (T) = time-period of motion). Rule out the wrong formulas on dimensional grounds.
- Q2.15: A famous relation in physics relates ‘moving mass’ $m$ to the ‘rest mass’ $m_0$ of a particle in terms of its speed $v$ and the speed of light, $c$. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes : $m = \frac{m_0}{(1 - v^2)^{1/2}}$. Guess where to put the missing $c$.
- Q2.15: A famous relation in physics relates ‘moving mass’ (m) to the ‘rest mass’ (m_{0}) of a particle in terms of its speed (v) and the speed of light, (c). (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant (c). He writes : (m = \frac{m_{0}}{(1 - v^{2})^{1/2}}). Guess where to put the missing (c).
- Q2.16: The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å: 1 Å = $10^{–10}$ m. The size of a hydrogen atom is about 0.5 Å. What is the total atomic volume in m$^3$ of a mole of hydrogen atoms ?
- Q2.16: The unit of length convenient on the atomic scale is known as an angstrom and is denoted by (Å): (1 Å = 10^{-10} m). The size of a hydrogen atom is about 0.5 (Å). What is the total atomic volume in (m^{3}) of a mole of hydrogen atoms ?
- Q2.17: One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio so large ?
- Q2.17: One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen ? (Take the size of hydrogen molecule to be about 1 (Å)). Why is this ratio so large ?
- Q2.18: Explain this common observation clearly : If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train’s motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. (In fact, since you are aware that you are moving, these distant objects seem to move with you).
- Q2.18: Explain this common observation clearly : If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train’s motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. (In fact, since you are aware that you are moving, these distant objects seem to move with you).
- Q2.19: The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit (\approx 3 \times 10^{11}m). However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second of arc) from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres ?
- Q2.19: The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit $\approx 3 \times 10^{11}$m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of $1''$ (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of $1''$ (second of arc) from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of metres ?
- Q2.2(a): Fill in the blanks by suitable conversion of units 1 (kg m^{2} s^{-2}) = ....(g cm^{2} s^{-2})
- Q2.2(a): Fill in the blanks by suitable conversion of units (a) 1 kg m$^2$ s$^{–2}$ = ....g cm$^2$ s$^{–2}$
- Q2.2(b): Fill in the blanks by suitable conversion of units (b) 1 m = ..... ly
- Q2.2(b): Fill in the blanks by suitable conversion of units 1 m = ..... ly
- Q2.2(c): Fill in the blanks by suitable conversion of units 3.0 (m s^{-2}) = .... (km h^{-2})
- Q2.2(c): Fill in the blanks by suitable conversion of units (c) 3.0 m s$^{–2}$ = .... km h$^{–2}$
- Q2.2(d): Fill in the blanks by suitable conversion of units (G = 6.67 \times 10^{-11} N m^{2} (kg)^{-2} = .... (cm)^{3} s^{-2} g^{-1}).
- Q2.2(d): Fill in the blanks by suitable conversion of units (d) G = $6.67 \times 10^{–11}$ N m$^2$ (kg)$^{–2}$ = .... (cm)$^3$ s$^{–2}$ g$^{–1}$.
- Q2.20: The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?
- Q2.20: The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?
- Q2.21: Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.
- Q2.21: Precise measurements of physical quantities are a need of science. For example, to ascertain the speed of an aircraft, one must have an accurate method to find its positions at closely separated instants of time. This was the actual motivation behind the discovery of radar in World War II. Think of different examples in modern science where precise measurements of length, time, mass etc. are needed. Also, wherever you can, give a quantitative idea of the precision needed.
- Q2.22(a): 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 total mass of rain-bearing clouds over India during the Monsoon
- Q2.22(a): 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) : (a) the total mass of rain-bearing clouds over India during the Monsoon
- Q2.22(b): 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) : (b) the mass of an elephant
- Q2.22(b): 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 mass of an elephant
- Q2.22(c): 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) : (c) the wind speed during a storm
- Q2.22(c): 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
- Q2.22(d): 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) : (d) the number of strands of hair on your head
- Q2.22(e): 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) : (e) the number of air molecules in your classroom.
- Q2.22(e): 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.
- Q2.23: The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding $10^7$ K, and its outer surface at a temperature of about 6000 K. 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 = $2.0 \times 10^{30}$ kg, radius of the Sun = $7.0 \times 10^8$ m.
- Q2.23: The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding (10^{7}) K, and its outer surface at a temperature of about 6000 K. 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 \times 10^{30}) kg, radius of the Sun = (7.0 \times 10^{8}) m.
- Q2.24: When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be $35.72''$ of arc. Calculate the diameter of Jupiter.
- Q2.24: When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72" of arc. Calculate the diameter of Jupiter.
- Q2.3: A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J = 1 kg m$^2$ s$^{–2}$. Suppose we employ a system of units in which the unit of mass equals $\alpha$ kg, the unit of length equals $\beta$ m, the unit of time is $\gamma$ s. Show that a calorie has a magnitude 4.2 $\alpha^{–1} \beta^{–2} \gamma^2$ in terms of the new units.
- Q2.3: A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where (1J = 1 kg m^{2} s^{-2}). Suppose we employ a system of units in which the unit of mass equals (\alpha) kg, the unit of length equals (\beta) m, the unit of time is (\gamma) s. Show that a calorie has a magnitude (4.2 \alpha^{-1} \beta^{-2} \gamma^{2}) in terms of the new units.
- Q2.4(a): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : (a) atoms are very small objects
- Q2.4(a): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : atoms are very small objects
- Q2.4(b): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : (b) a jet plane moves with great speed
- Q2.4(b): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : a jet plane moves with great speed
- Q2.4(c): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : (c) the mass of Jupiter is very large
- Q2.4(c): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : the mass of Jupiter is very large
- Q2.4(d): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : (d) the air inside this room contains a large number of molecules
- Q2.4(d): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : the air inside this room contains a large number of molecules
- Q2.4(e): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : (e) a proton is much more massive than an electron
- Q2.4(e): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : a proton is much more massive than an electron
- Q2.4(f): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : (f) the speed of sound is much smaller than the speed of light.
- Q2.4(f): Explain this statement clearly : “To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a standard for comparison”. In view of this, reframe the following statements wherever necessary : the speed of sound is much smaller than the speed of light.
- Q2.5: A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance ?
- Q2.5: A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the Sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance ?
- Q2.6: Which of the following is the most precise device for measuring length :
- Q2.6: Which of the following is the most precise device for measuring length :
- Q2.7: 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 3.5 mm. What is the estimate on the thickness of hair ?
- Q2.7: 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 3.5 mm. What is the estimate on the thickness of hair ?
- Q2.8(a): Answer the following : You are given a thread and a metre scale. How will you estimate the diameter of the thread ?
- Q2.8(a): Answer the following : (a)You are given a thread and a metre scale. How will you estimate the diameter of the thread ?
- Q2.8(b): Answer the following : A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale ?
- Q2.8(b): Answer the following : (b)A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale ?
- Q2.8(c): Answer the following : The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only ?
- Q2.8(c): Answer the following : (c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only ?
- Q2.9: The photograph of a house occupies an area of 1.75 (cm^{2}) on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 (m^{2}). What is the linear magnification of the projector-screen arrangement.
- Q2.9: The photograph of a house occupies an area of 1.75 cm$^2$ on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 m$^2$. What is the linear magnification of the projector-screen arrangement.
CBSE Solutions for Class 11 Physics Units and Measurements
Chapters in CBSE - Class 11 Physics
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(78)
Super Tutor
New Friends Colony, Delhi
10 yrs of
Exp
30 students
4691 hrs of classes completed
500
per hour
IB & IGCSE Maths Tutor | Application, Problem Solving & Exam Preparation | 10+ Years
Online Classes
I help students in Classes 11–12 develop strong conceptual understanding, advanced problem-solving skills, and confidence for school, board, and competitive-level examinations. My classes cover: Algebra – equations, sequences & series, permutations & combinations, binomial theorem, complex numbers, etc. Trigonometry – identities, equations and applications Coordinate Geometry – straight lines, circles and conic sections Calculus – limits, continuity, differentiation, applications of derivatives, integration and related concepts Probability & Statistics Vectors & 3D Geometry Matrices & Determinants Application-based and higher-order problems Regular practice, tests, and detailed error analysis Exam-oriented preparation with focus on accuracy, speed, and time management My Teaching Approach Instead of simply teaching formulas, I focus on helping students understand why a concept works, when to apply it, and how to approach unfamiliar questions. Concept → Understand → Practise → Apply → Solve → Analyse → Improve Classes are personalised according to the student's current level, curriculum, learning gaps, and academic goals, with structured practice and continuous feedback. Suitable for: CBSE, ICSE, IB, IGCSE, GCSE, Cambridge, and other international curricula.
Naman Gupta
The teacher explained concepts with simple examples and experiments, which made learning easy and interesting I understood the topic better and improved my performance .
Skills:
Mathematics
Also teaches:
Class 12 Tuition, Class 10 Tuition
and more
(22)
Top Tutor
Choolissery, Thrissur
20 yrs of
Exp
1 student
446 hrs of classes completed
600
per hour
professional teacher with more than 20 years of experience. I have MSc and B. Ed in mathematics.
Online Classes
Very simple and easy to learn
Skills:
Mathematics
,
Statistics
Also teaches:
Class 8 Tuition, Class 9 Tuition
and more
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