CBSE Class 11 Physics Physical World And Measurement Notes Set A

MAIN POINTS

√  Physics deals with the study of the basic laws of nature and their manifestation in different phenomena. The basic laws of physics are universal and apply in widely different contexts and conditions.

√  The scope of physics is wide, covering a tremendous range of magnitude of physical quantities.

√  Physics and technology are related to each other. Sometimes technology gives raise to new physics at other times physics generates new technology. Both have direct impact on society.

√  There are four fundamental forces in nature that govern the diverse phenomena of the macroscopic and the microscopic world. These are the ‘gravitational force ‘, the electromagnetic force’, ‘the strong nuclear force’, and the weak nuclear force’

√  The physical quantities that remain unchanged in a process are called conserved quantities. Some of the general conservation laws in nature include the law of conservation of mass, energy, linear momentum, angular momentum, charge, parity, etc. 

√  Conservation laws have a deep connection with symmetries of nature .symmetries of space and time, and other types of symmetries play a central role in modern theories of fundamental forces in nature.

√  Gravitational force is the force of mutual attraction between any two objects by virtue of their masses. It is always attractive

√  Electromagnetic Force is the force between charged particles .It acts over large distances and does not need any intervening medium. Enormously strong compared to gravity.It can be attractive or repulsive. 

√  Strong nuclear force is the force that binds the nucleons together.It is the strongest of all the fundamental forces. It is charge independent. And very short range.

√  Weak nuclear force appears only in certain nuclear processes such as β-decay. Weak nuclear force is not as weak as the gravitational force.

√  In a chemical reaction if the total binding energy of the reacting molecules is less than that of the product molecules the difference appears as heat and the reaction is exothermic

√  In a chemical reaction if the total binding energy of the reacting molecules is more than that of the product molecules the difference amount of energy is absorbed and the reaction is endothermic.

√  In a nuclear process mass gets converted into energy. This is the energy which gets released in a nuclear power generation and nuclear explosions.

There are four fundamental forces which govern both macroscopic and microscopic phenomena. There are

(i) Gravitational force             (iii) Electromagnetic force

(ii) Nuclear force                   (iv) Weak force

The relative strengths of these forces are

                        Fg :Fw:Fe:Fs=1:1025:1036:1038 .

All those quantities which can be measured directly or indirectly and in terms of which the laws of physics can be expressed are called physical quantities.

(a) Fundamental quantities            (b) Derived quantities.

The units of the fundamental quantities called fundamental units , and the units of derived quantities called derived units.

System of units:-

(a) MKS                (b) CGS                  (c) FPS           (d) SI

• The dimensions of a physical quantity are the powers to which the fundamental quantities are raised to represent that physical quantity.

• The equation which expresses a physical quantity in terms of the fundamental units of mass, length and time, is called dimensional equation.

• According to this principle of homogeneity a physical equation will be dimensionally correct if the dimensions of all the terms in the all the terms occurring on both sides of the equation are the same.

• If any equation is dimensionally correct it is not necessary that must be mathematically correct too.

 There are three main uses of the dimensional analysis-

(a) To convert a unit of given physical quantities from one system of units to another system for which we use

n2 = n1[M1/M2]a[L1/L2]b[T1/T2]c

(b) To check the correctness of a given physical relation.

(c) To derive a relationship between different physical quantities.

• Significant figures: - The significant figures are normally those digits in a measured quantity which are known reliably plus one additional digit that is uncertain.

For counting of the significant figure rule are as:

(i) All non- zero digits are significant figure.

(ii) All zero between two non-zero digits are significant figure.

(iii) All zeros to the right of a non-zero digit but to the left of an understood decimal point are not significant. But such zeros are significant if they come from a measurement.

(iv) All zeros to the right of a non-zero digit but to the left of a decimal point are significant.

(v) All zeros to the right of a decimal point are significant.

(vi) All zeros to the right of a decimal point but to the left of a non-zero digit are not significant. Single zero conventionally placed to the left of the decimal point is not significant.

(vii) The number of significant figures does not depend on the system of units.

• In addition or subtraction, the result should be reported to the same number of decimal places as that of the number with minimum number of decimal places.

• In multiplication or division, the result should be reported to the same number of significant figures as that of the number with minimum of significant figures.
• Accuracy refers to the closeness of a measurement to the true value of the physical quantity and precision refers to the resolution or the limit to which the quantity is measured.
• Difference between measured value and true value of a quantity represents error of measurement.
It gives an indication of the limits within which the true value may lie.
Mean of n measurements
amean = a1 + a2 + a3 +....+ an / n

Absolute error ( Δa ) = amean - ai Where ai = measured value It may be - positive, negative or zero.
(i) Mean absolute error
(ii) Relative error - it is the ratio of the mean absolute error to the true value.
δa = I Δa I/ amean
(iii) The relative error expressed in percent is called percentage error.

The error is communicated in different mathematical operations as detailed below:
(i) For x = (a ± b),                       Δx = ± ( Δa + Δb)
(ii) For x = a x b ,                        Δx/x = ± ( Δa/a + Δb/b)
(iii) For x = a/b ,                          Δx/x = ± ( Δa/a + Δb/b)
(iv) For x= anbm /cp                     Δx/x = ± ( nΔa/a +m Δb/b + pΔc/c

Comprehension Based

Paragraph –I

In simple pendulum experiment a student measures length of string 75.5 cm with meter scale having lest count 0.1 cm. He measures diameter of bob with Vernier calliper having 10 divisions in 1 cm on min scale and 20 divisions of vernier scale coinciding with 18 divisions of man scale. With jaws closed the zero of vernier scale lies on left of zero of main scale and 5th division of vernier scale concides with same main scale division. With bob placed between the jaws the zero of vernier scale crosses 42 divisions of main scale and 7th division concides with any of main scale division. With above observations answer the following question if time measured for 20 vibrations is 40.2 sec with stop watch of least count 0.1 s:

Question. The diameter of bob measured is recorded as:
a. (4.27 ± 0.01) cm
b. (4.22 ± 0.01) cm
c. (4.32± 0.01) cm
d. (4.18± 0.01)cm
Answer : C

Question. Which is more accurate measurement and which is more precise measurement?
a. Length is more accurate, diameter is more precise
b. Length is more precise, diameter is more accurate
c. Length is more accurate as well as more precise
d. Diameter is more accurate as well as more precise
Answer : A

Question. Percentage error in measurement of value of g with this pendulum is:
a. 0.5 %
b. 0.64 %
c. 0.56 %
d. 0.52 %
Answer : B

Paragraph –II

Method of dimensional analysis was devised to derive certain unknown physical relations. But this method has certain limitation due to which it does not give correct information about the relations derived. With knowledge of the limitation answer the following question:

Question. Distance moved by a particle having uniform acceleration a starting with initial velocity u in nth second is mentioned a s = u + a(2n −1) This relation is:
a. dimensionally correct numerically wrong
b. both dimensionally and numerically wrong
c. both numerically and dimensionally correct
d. neither dimensionally nor numerically correct
Answer : A

Question. Out of the given pair one pair has same dimensional formula:
a. gravitational8 potential and torque
b. velocity gradient and angular velocity
c. tension and surface tension
d. force constant and elastic constant
Answer : B

Question. Out of the given pairs one is not similar to others:
a. angular momentum and Planck’s constant
b. impulse and momentum
c. Rydberg constant and wave propagation constant
d. gravitational potential energy and surface energy
Answer : D

Paragraph –III

Standard gas equation was derived based on kinetic theory of gases which was valid only for ideal gases. However, real gases are no: ideal gases. van der Waals’ derived equation which was valid for real gases considering the size of molecules and intermolecular forces between them. He introduced correction in the form of constant a and b and arrived at the following relation (P+ a/V²) (V - b) = RT where P,V,T are pressure volume and temperature of gas and R is universal gas constant. In this relation:

Question. The dimensional formula for ab is that of:
a. work
b. force
c. pressure
d. momentum
Answer : A

Question. The dimension of “a” mass, length and time as:
a. [1, 2, –2]
b. [1, 5, –2]
c. [1, –2, 2]
d. [1, 3, –2]
Answer : B

Question. Dimensional formula for R is:
a. [M L² T⁻³ ]
b. [M¹ L² T⁻¹ ]
c. [M¹ L² T⁻² K⁻¹ ]
d. [M¹ L³T⁻³ K⁻¹ ]
Answer : C

Paragraph –IV

A student is given a calorimeter made of copper sheet. He is given a Vernier calliper and screw gauge. The Vernier calliper used by him has 20 division in a centimeter on main scale and 25 divisions of vernier scale coincide with 24 divisions of main scale. Screw gauge also has 20 division in a centimeter on linear scale and 100 division an circular scale. Check the following measurement made by him:

Question. Least founts of Vernier callipers and screw gauge are:
a. 0.01 mm, 0.01 mm
b. 0.02 mm, 0.05 mm
c. 0.02 mm, 0.005 mm
d. 0.02 mm, 0.005 cm
Answer : C

Question. He measures depth by Vernier callipers as 5.250 cm and diameter as 2.500 cm. The thickness of sheet used is measured by Screw gauge as 250 mm. The area of sheet used to make calorimeter with correct significant figures is:
a. 27.500 cm²
b. 27.5 cm²
c. 27.50 cm²
d. 0.275 cm²
Answer : C

Question. Volume of cylinder with % error is:
a. 25.8 ± 0.20%
b. 25.78 ± 2%
c. 25.781 ± 0.2%
d. 25.8 ± 2.0%
Answer : C

Match the Column

Question. Match the statement of Column with those in Column II:
      Column I                                           Column II
(A) Fundamental quantity is                  1. Charge
(B) Derived quantity is                           2. Wm–2
(C) Fundamental unit is                         3. Current
(D) Derived unit of intensity of light is    4. Candela
a. A → 3, B → 1, C → 4, D → 2
b. A → 2, B → 4, C → 3, D → 1
c. A → 1, B → 3, C → 2, D → 4
d. A → 4, B → 1, C → 3, D → 2
Answer : A

Question. Match the statement of Column with those in Column II:
      Column I                            Column II
(A) Angular velocity            1. Velocity gradient
(B) Gravitation intensity      2. Acceleration
(C) Stress                           3. Energy density
(D) Angle                            4. Strain
a. A → 4, B → 3, C → 2, D → 1
b. A → 3, B → 2, C → 1, D → 4
c. A → 2, B → 1, C → 4, D → 3
d. A → 1, B → 2, C → 3, D → 4
Answer : D

Question. Match the statement of Column with those in Column II:
      Column I                            Column II
(A) Magnetic flux                     1. A m²
(B) Magnetic induction            2. Nm A⁻¹
(C) Magnetic dipole moment  3. N A⁻¹
(D) Magnetic permeability      4. N m⁻¹ A⁻¹
a. A → 1, B → 2, C → 3, D → 4
b. A → 4, B → 3, C → 2, D → 1
c. A → 3, B → 2, C → 1, D → 4
d. A → 2, B → 4, C → 1, D → 3
Answer : D

Question. Match the statement of Column with those in Column II:
      Column I                         Column II
(A) Velocity gradient        1. [M⁻³ L² T⁴ Q⁻⁴ ]
(B) Planck’s constant      2. [M¹ L² T⁻¹ ]
(C) Gravitational field      3. [M⁰ L¹ T⁻² ]
(D) Angular velocity         4. [M¹L¹T⁻¹]
a. A → 1, B → 2, C → 3, D → 4
b. A → 4, B → 3, C → 2, D → 1
c. A → 3, B → 1, C → 4, D → 2
d. A → 4, B → 1, C → 2, D → 2
Answer : A

Integer

Question. The correct number of significant figures in 0.0005083 is:
Answer : 4

Question. Light from the sun reaches the earth approximately in x×10² sec, where x is:
Answer : R

Question. If units of measurement of two systems are in the ratio 2 : 1, then the ratio of units of angular momentum in the two systems will be:
Answer : 4

Question. The least count of a watch is 0.2 s. The time for 25 oscillations of a pendulum is measured to be 20 sec. The percentage error in this time measurement is:
Answer : 1

Question. Heat generated in a circuit is given by H = I² Rt. If error in measuring current I, resistance R and time t are 2%, 1% and 3% respectively, then percentage error in calculating heat is:
Answer : 8

Question. A wire has a mass 0.3 ± 0.003 g , radius 0.5 ±0.005mm and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is:
Answer : 4

Question. The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with vernier calipers having least count 0.01 cm. Given that length is 5.0 cm. and radius is 2.0 cm. The percentage error in the calculated value of the volume will be:
Answer : 3

Question. The number of significant figures in all the given numbers 25.12, 2009, 4.156 and 1.217 x 10⁻⁴ is:
Answer : 4

_{Very short answer type questions, (1 mark question)}

<sub>Q1. State one law that holds good in all natural processes.
Ans. One such laws is the Newton’s gravitation law, According to this law everybody in this nature are attracts with other body with a force of attraction which is directly proportional to the product of their masses and inversely proportionally To the square of the distance between them.

Q2: Among which type of elementary particles does the electromagnetic force act?
Ans : Electromagnetic force acts between on all electrically charged particles.

Q3. Name the forces having the longest and shortest range of operation.
Ans : longest range force is gravitational force and nuclear force is shortest range force.

Q4. If ‘slap’ times speed equals power, what will be the dimensional equation for ‘slap’?
Ans . Slap x speed = power
Or slap = power/speed = [MLT-2]

Q5. If the units of force and length each are doubled, then how many times the unit of energy would be affected?
Ans : Energy = Work done = Force x length
So when the units are doubled, then the unit of energy will increase four times.

Q6. Can a quantity has dimensions but still has no units?
Ans : No, a quantity having dimension must have some units of its measurement.
Q7. Justify L +L = L and L – L =L.</sub>