LECTURE - 2 : CLASS VIII : SCIENCE : CHAPTER 12 : FRICTION

CLASS VIII   |    SCIENCE    |    CHAPTER 12

      Notes prepared by Subhankar Karmakar

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• FACTORS AFFECTING FRICTION:

It has been found that the friction between two surfaces depends on two factors:

(i) the nature of the two surfaces (smoothness or roughness of the two surfaces)

(ii) the force with which two surfaces are pressed together.

• 1. Dependence of friction on the nature of two surfaces:

Friction depends on the smoothness or roughness of the two surfaces which are in contact with each other. When the two surfaces in contact are smooth, then the friction between them will be small. As the degree of roughness of the two surfaces in contact increases, the friction also increases. 

• 2. Dependence of friction on the forces with which two surfaces are placed together.

The friction between two surfaces depends on the force with which the two surfaces are pressed together. Greater the weight of an object which moves over another surface, more is the force with which the two surfaces are pressed together and greater will be the friction between them. 

• Types of friction:

There are three types of friction. 

• 1. Static friction
• 2. Sliding friction and
• 3. Rolling friction

• 1. Static friction: 

The maximum frictional force present between two any two objects when one object just tends to move or slip over the surface of the other object, is called static friction. In the case of static friction, the object is actually not moving or sliding over the other object, it only takes to move or slide. It is the maximum frictional force. 

• 2. Sliding friction:

the frictional force present when one object moves slowly or slides over the surface of another object is known as sliding friction. Is the sliding friction is smaller than the static friction, it is easier to keep an object moving which is already in motion than to move the same object from rest or stationary position. Sliding friction is smaller than the static friction. 

• Why does sliding friction is smaller than the static friction?

When an object has already started moving or sliding the irregularities on its surface do not get enough time to lock into the irregularities on the surface of the other object completely. Since the interlocking of the two surfaces is less when an object has already started moving, therefore, the sliding friction is smaller than the static friction. 

• 3. Rolling friction:

when an object like a wheel rolls over the surface of another object the resistance to its motion is called rolling friction. Therefore it is always easier to roll than to slide an object over another object. Show rolling friction is much less than the sliding friction. Rolling reduces friction.

heavy machines can be easily move from one place to another by placing round logs of wood under them and then pushing with the force of hands. 

• Maximum Friction : Static Friction 
• Minimum Friction : Rolling Friction

Static friction > sliding friction > rolling friction.

Lecture-4 : CLASS-X: SCIENCE : Chapter: Electricity

CLASS X  |    SCIENCE    |    ELECTRICITY

      notes prepared by subhankar Karmakar

                                                                         

Ohm's Law: 

According to Ohm's Law, at constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends. 

If Ｉis the current flowing through a conductor and V is the potential difference (voltage) across its ends, then according to Ohm's Law:

Ｉ ∝ V  (at constant temperature)

This can also be written as:  V ∝ Ｉ

or V = RＩ

where R is a constant called "resistance" of the conductor. The value of this constant depends on the nature, length, area of cross section and temperature of the conductor. 

V/Ｉ = R

The ratio of potential difference applied between the ends of a conductor and the current flowing through it is a constant quantity called resistance.

Therefore, 

(i) The current is directly proportional to potential difference, and

(ii) The current is inversely proportional to resistance. 

a. "Current is proportional to the potential difference" - it means if the potential difference across the ends of o conductor is doubled, the current flowing through it also gets doubled, and if the the potential difference is halved the current also gets halved.

b. "The current is inversely proportional to resistance" - it means if the resistance is doubled, the current gets halved, and if the resistance is halved the current gets doubled.

Resistance of a conductor:

The property of a conductor due to which it opposes the flow of current through it is called resistance.

The resistance of a conductor depends on length, thickness, nature of material and temperature of the conductor. 

SI unit of resistance:

The SI unit of resistance is ohm. It is generated by the symbol Omega, Ω. The unit of resistance can be defined as following. "1 ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends a current of 1 ampere flows through the conductor". 

Numericals on Ohm's law:

1. Potential difference between two points of a wire carrying a 0.4 ampere current is 0.6 volt. Calculate the resistance between these points.

Soln: From Ohm's law we know that resistance of a conductor is equal to the ratio of the potential difference applied across the conductor and the current flowing through it. Therefore, R = V/Ｉ

or, resistance, R = 0.6/0.4 = 3/2 = 1.5 Ω

2. A simple electric circuit has a a 12 volt battery and a resistor of 60 ohms. What will be the current in the circuit? The resistance of the connecting wires is negligible. 

Soln. From Ohm's law we know that current flowing through the circuit, Ｉ is equal to the ratio of the potential difference across the ends of the conductor V and the resistance R attached to it. 

Therefore, Ｉ = V/R = 12/60 = 0.2 A (ampere).

3. An electric appliance draws a current of 2.2 ampere from a 220 volt supply line. What current will this electric iron draw when connected to 110 volt supply line?

Soln. From Ohm's law we know that resistance of a conductor is equal to the ratio of the potential difference applied across the conductor and the current flowing through it. As the resistance of the appliance is same.

R = V₁/Ｉ₁ = V₂/Ｉ₂

V₁ = 220 V, Ｉ₁ = 2.2 A,  V₂= 110 V, Ｉ₂ = ?

Ｉ₂ =  V₂Ｉ₁/V₁ = 110x2.2 /220 = 1.1 A

4. If 20 C of charge pass a point in a circuit in two second, what is the current flowing?

Soln. Charge passing through a conductor per unit time is called current. Therefore, current, Ｉ = q/t, q = charges passing through the conductor, t = time. 

Ｉ = q/t = 20 /2 = 10 A

5. If a potential difference of 20 volt causes a current of 1 ampere to flow for 2 minute how much energy is transferred?

Soln. Q = Heat generated, Ｉ= Current = 1 A;

          R = Resistance = V/Ｉ , t = time = 120 s

Q = Ｉ²Rt = ＩVt = 1 x 20 x 120 = 2400 Joules.

LECTURE - 1 : CLASS VIII : SCIENCE : CHAPTER 12 : FRICTION

CLASS VIII   |    SCIENCE    |    CHAPTER 12

      Notes prepared by Subhankar Karmakar

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• FRICTION : 

The force which always opposes the motion of one object over another object in contact with it, is called friction. 

• friction occurs between the two surfaces which are in contact with each other. 

• friction is a force which occurs when the two objects tend to slide over each other and even when there are actually sliding over each other. 

• Direction of force of friction:

The force of friction always opposes the motion of one object over another object. The force of friction acts in a direction opposite to the direction in which an object moves. Therefore, the force of friction acts in a direction opposite to the direction of motion of an object.

• Cause of friction:

Friction is caused by the interlocking of irregularities in the surfaces of the two objects which are in contact with each other. 

When we try to move an object over the other, we have to apply a force to overcome interlocking of the irregularities in the their surfaces. More the roughness of a surface, larger is the number of irregularities on its surface and hence greater will be the friction. Thus, the force of friction is greater if very rough surfaces are involved. Friction will be less if the surface is smooth and polished. 

• Spring balance:

The spring balance is a device which is used for measuring force acting on an object. With the help of a spring balance we can measure the frictional force. 

The spring balance contains a coiled spring which gets stretched when a force is applied to its free end having a hook. The extent by which the spring gets structured is a measure of the force applied. Larger the stretching of spring, greater will be the magnitude of the force applied. the stretching of spring or magnitude of force is indicated by a pointer attached to the spring which moves on a graduated scale. The reading on the scale of spring balance give us the magnitude of force. When the spring balance is held vertically, it is used to measure the weight of an object hung from its hook. and when spring balance is held horizontally it can be used to measure the force being applied to pull the object on a horizontal surface.

• Factors affecting friction:

It has been found by experiment that friction between two surfaces depends on two factors.

• The nature of the two surfaces (smoothness or roughness of the two surfaces).
• The force with which two surfaces are pressed together.

The force of friction does not depend on the amount of surface area of the two objects which is in contact with each other. 

Dependence of friction on the nature of two surfaces:

• Friction depends on the smoothness or roughness of the two surfaces which are in contact with each other. 
• If the two contact surfaces are smooth, then the frictional force is less where as when the two contact surfaces are rough, frictional forces are more. 

LECTURE 3 : CLASS XII: PHYSICS : ELECTRIC FIELD

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

(the physical quantity written in bold letters are vectors )

ELECTRIC FIELD: 

The electric field or electric intensity or the electric field strength E at a point is defined as the force experienced by a unit positive test charge placed at that point, without disturbing the position of source charge. 

• Electric field E is a vector quantity. 

• SI unit of electric field is N/C. 

• Dimension of electric field is

 [E] = force/charge = [MLT⁻²]/[AT] = [MLT⁻³A⁻¹]

Electric field is an example of vector field:

As the value of electric field E is different at different point, so we can say each point having a position vector r , therefore, the vector E is a function of position vector of a point. Hence, we can say electric field is an example of vector field. 

Principle of superposition of electric fields:

It says the electric field at any point due to a group of charges is equal to the the vector sum of the electric field produced by the each charge individually at that point, when all other charges are assume to be absent. 

LECTURE 1 : CLASS XII: PHYSICS : ALTERNATING CURRENT (AC)

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

Alternating current:

An alternating current is that current whose magnitude changes continuously with time and direction reverses periodically. 

When a coil is rotated in a magnetic field, an alternating EMF is induced in it which is given by the relation

ℰ = ℰₒ sin (ⲱt) ---------------------------- (i)

When applied to a circuit of resistance R, it will produce a current Ｉ such that

Ｉ = ℰ/R = (ℰₒ/R) sin (ⲱt) = Ｉₒ sin (ⲱt)--------(ii)

Therefore, the current in the circuit varies sinusoidally with time and it is called alternating current. 

Ｉ = Instantaneous Current

Ｉₒ = ℰₒ/R = Maximum or peak value of current. It is also called current amplitude. 

Amplitude: The maximum value attained by an alternating current in either direction is called its amplitude or peak value and is denoted by Ｉₒ. 

Time Period: The time taken by an alternating current to complete one cycle of its variations is called its time period and is denoted by T.

This time is equal to the time taken by the coil to complete one rotation in the magnetic field. 

T = 2π/ⲱ ; where ⲱ = angular velocity of the coil. 

Frequency: The number of cycles completed per second by an alternating current is called its frequency and is denoted by f. It is equal to the frequency of rotation of the coil in the magnetic field. 

f = 1/T = ⲱ/(2π)

∴ Ｉ = Ｉₒ sin (ⲱt) = Ｉₒ sin (2πft) = Ｉₒ sin (2πt/T) -------- (iii)

• In India AC supply has a frequency of 50 Hz

Mean / Average Value of AC over a half cycle:

Average value of AC : It is defined as that value of direct current which sends the same charge in a circuit in the same time as is sent by the given alternating current in its half time period. It is denoted by Ｉₘ or Ｉₐᵥ.

LECTURE 2 : CLASS XII: PHYSICS : ELECTRIC CHARGE & FIELD NUMERICALS

CLASS XII   |    PHYSICS    |    CHAPTER 1

      notes prepared by subhankar Karmakar

Numericals on quantization of charge:

1. Which is bigger 1 coulomb or a charge on an electron? How many electronic charges form one coulomb of charge?

2. If a body gives out 10⁹ electrons every second, how much time is required to get a total charge of 1 coulomb from it?

3. How much positive and negative charge is there in a cup of water? (Take the mass of water contained in a cup is 250 g).

4. Calculate the charge carried by 12.5 x 10⁸ electrons. 

5. Estimate the total number of electrons present in hundred gram of water. How much is the total negative charge carried by these electrons? (Take Avogadro number = 6.02 x 10²³ and molecular mass of water = 18).

Numericals on Coulomb's law of electrostatics:

6. Two particles, each having a mass of 5 gram and charge 0.1 microcoulomb , stay in limiting equilibrium on a horizontal table with a separation of 10 centimetre between them. The coefficient of friction between each particle and the table is same. Find the coefficient of friction.

7. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. What is the mutual force of electrostatic repulsion if the charge on each is 6.5 x 10⁻⁷ C ? The radii of A and B are negligible compared to the distance of separation. What will be the force of repulsion if the two spheres are placed in water?

8. Two insulated charged copper spheres A and B have their centres separated by a distance of 50 cm. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally remove from both. What is the new force of repulsion between A and B?

9. Two similarly equally charged identical metal spheres A and B repel each other with a force of 2.0 x 10⁻⁵ N. A third identical unchaged sphere C is touched to A, then placed at the mid point between A and B. Calculate the net electrostatic force on C. 

10. Two identical charges, Q each, are kept at a distance r from each other. A third charge q is placed on the line joining the above two charges such that all the three charges are in equilibrium. What is the magnitude, sign and position of the charge q?

Numericals on the superposition principle:

11. Consider three charges q₁, q₂, q₃ each equal to q at the verices of an equilateral triangle of side l. What is the force on a charge Q placed at the centroid of the triangle?

12. Consider the charges +q, +q and -q placed at the vertices of an equilateral triangle. What is the force on a charge?

13. Four equal point charges each 16 μC are placed on the four corners of a square of side 0.2 m. Calculate the force on any one of the charges. 

1 mark questions:

1. Two identical metallic spheres of exactly equal masses are taken. One is given a positive charge q and other an equal negative charge. Are their masses after charging equal?

2. Can two like charges attract each other? If yes, how?

3. Electrostatic experiments do not work well on humid days.  give reasons. 

4. A comb runs through one's dry hair attract small bits of paper. Why? What happens if the hair is wet or if it is a rainy day?

5. Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting. Why is this necessary?

6. Vehicles carrying inflammable materials is usually have metallic ropes touching the ground during motion. Why?

7. An inflated balloon is charged by rubbing with fur. Will it stick readily to a conducting wall or to an insulating wall? Give reason.

8. What does q₁ + q₂ = 0 signify in electrostatics?

9. Can a body have a charge of 2.4 x 10⁻¹⁹ C? Justify your answer by comment?

10. If the distance between two equal point charges is doubled and their individual charges are also doubled, what would happen to the force between them?

MOVING COIL GALVANOMETER

Galvanometer: 

A galvanometer is a device to detect current in a circuit. 

Principle: 

A current carrying coil placed in a magnetic field experiences a current dependent torque, which tends to rotate the coil and produces angular deflection. 

Construction:

A galvanometer consists f a rectangular coil of fine insulated copper wire wound on a light non magnetic metallic frame. The two ends of the axle of this frame are pivoted between two bearings. The motion of the coil is controlled by a pair of hair springs of phosphor bronze. The inner ends of the springs are soldered to the two ends of the coil and the outer ends are connected to the the binding screws. The springs provide the restoring torque and serve as current leads. A light aluminium pointer attached to the coil measures its deflection on a suitable scale. 

The coil is symmetrically placed between the cylindrical pole pieces of strong permanent horseshoe magnet. 

Theory and Working:

Let Ｉ = current flowing through the coil PQRS

     a, b = sides of the coil PQRS

       A  = ab = area of the coil

       θ = angle between the direction of B and normal to the plane of the coil.

       N = number of turns in the coil

Since the field is radial, the plane of the coil always remains parallel to the field B. Magnetic forces on the sides QR and SP are equal, opposite and collinear, so their resultant is zero. According to Fleming's left hand rule, the side PQ experiences a normal inward force equal to NＩbB why is the side QR experiences an equal normal out what force. The two forces on sides PQ and RS are equal and opposite. They form a couple and exert a torque given by 

τ = one of the force x perpendicular distance between them 

τ = F a sin θ = ＩbBa sin θ = ＩBA sin θ

[ ∵ ab = A]

If the rectangular loop has N turns, the torque increases N times ie.,

τ = NＩBA sin 90° = NＩBA

Here, θ = 90°, because the normal to the plane of coil remains perpendicular to the field B in all positions. 

The torque τ deflects the coil through an angle α. A restoring torque is set up in the coil due to elasticity of the springs such that

      τᵣ ∝ α   or   τᵣ = kα 

Where K is is the the torsion constant of the springs. 

Restoring Torque = Deflecting Torque

kα = NＩBA

Or  α = (NBA/k)Ｉ

Or      α ∝ Ｉ

Thus the deflection produced in the galvanometer coil is proportional to the current flowing through it. Consequently, the instrument can be provided with a scale with equal divisions along a circular scale to indicate equal steps in current. Such a scale is called linear scale.

Ｉ = (k/NBA) α = Ｉ = Gα

G = (k/NBA) is constant for a galvanometer and is called galvanometer constant for current reduction factor of the galvanometer.

TORQUE EXPERIENCED BY A CURRENT LOOP IN A UNIFORM MAGNETIC FIELD

Torque on a current loop in a uniform magnetic field:

A rectangular coil PQRS suspended in a uniform magnetic field B. The axis of the rectangular coil is perpendicular to the field. 

Let Ｉ = current flowing through the coil PQRS

     a, b = sides of the coil PQRS

       A  = ab = area of the coil

       θ = angle between the direction of B and normal to the plane of the coil.

 

Direction of the area and B makes an angle θ

all the forces acting on the sides of the rectangular coil PQRS

According to Fleming's left hand rule, 

i) the magnetic force on the side QR is F₁

 and it is acting upward.

F₁ = Ｉ(a xB) = ＩaB

ii) the magnetic force on the side SP is F'₁ and it is acting downward. 

F'₁ = Ｉ(a xB) = ＩaB

So, net force along vertical direction is zero as 

F₁ and F'₁ are equal and opposite as both are acting along the axis of the coil.

iii) the magnetic force on the side SR is F and it is coming out of the board.

F = Ｉ(b xB) = ＩbB

iv) the magnetic force on the side QP is F' and it is going into the board.

F' = Ｉ(b xB) = ＩbB

coil as seen from the top : m is the direction of the magnetic moment as well as coil area (perpendicular to the plane of the coil).

Therefore F and F' will produce a torque τ

We know, 

τ = one of the force x perpendicular distance between them 

τ = F a sin θ = ＩbBa sin θ = ＩBA sin θ

[ ∵ ab = A]

If the rectangular loop has N turns, the torque increases N times ie.,

τ = NＩBA sin θ

But there is one physical quantity called "magnetic moment" or m = NＩA

τ = m B sin θ = m x B

The direction of the torque τ is such that it rotates the loop clockwise about the axis of the loop. 

The torque will be zero when θ = 0 ie., When the plane of the loop is perpendicular to the magnetic field. 

The torque will be maximum when θ = π/2 and τ = NＩBA ie., when the plane of the loop is parallel to the magnetic field. 

Lecture- 5 : CLASS-X: SCIENCE : Chapter: REFLECTION OF LIGHT & NUMERICALS

CLASS X   |    SCIENCE    |    LIGHT

      notes prepared by subhankar Karmakar

                                                                         

Numericals on concave mirror:

Q1. What is the nature of a mirror having a focal length of, + 4 cm?

1. Ans. As the focal length is positive, the mirror is convex mirror. 

Q2. What kind of mirror can have a focal length of, - 6 cm?

2. Ans. As the focal length is negative, the mirror is a concave mirror. 

Q3. If the radius of curvature of a mirror is - 20 cm, what will be its focal length? What type of mirror it is? 

3. Ans. As the focal length is half of the the radius of curvature, so, f = -10 cm. As the  focal length is negative it is a concave mirror. 

Q4. Focal length of a small concave mirror is 2.5 cm. In order to use this concave mirror as a dentist's mirror, what must be the distance of tooth from the mirror?

4. Ans. As a dentist's mirror needs a real and magnified image of the tooth, the tooth must be placed in between pole and focus. Therefore, the distance of the tooth must be less than focal length of 2.5 cm. 

Q5. We wish to obtain an erect image of an object using a concave mirror of focal length 15 cm. 

a. What should be the range of distance of the object from the mirror?

b. What is the nature of the image?

c. Draw a ray diagram to show the image formation in this case. 

5. Ans. a. In order to obtain an erect image of an object with a concave mirror, the object should be at a distance less than its focal length. Therefore, here, the object must be placed at a distance less than 15 cm. 

        b. The nature of the image will be virtual. The image will be larger than the object

Q6. The image formed by a concave mirror is seen to be virtual, erect and larger than the object. Where should we place the object?

6. Ans. We should place the object in between pole and focus of the mirror. 

Q7. A concave mirror has a focal length of 20 cm. Where should an object be placed in front of this Concave mirror so as to obtain an image which is real, inverted and same size of the object?

7. Ans. When the object is placed at the centre of curvature, it produces an image, which is real, inverted and same size of the object. The distance of the centre of curvature from the pole is called radius of curvature and it is equal to twice of the focal length. 

Hence, the object must be placed at a distance (2x20 = 40 cm) 40 cm from the pole in front of the concave mirror. 

Q8. An object is placed in front of a concave mirror focal length 10 cm. Find the object distance if it produces a magnified real image?

8. Ans. If the object is placed in between focus and the centre of curvature,  then the image produce is real and inverted and magnified. Therefore, the object must be in between focus (f) and centre of curvature (2f). 

So, the object must be placed in between 10 cm to 20 cm from the pole in front of the mirror. 

Q9. An object is placed in front of a concave mirror focal length 5 cm. Find the object distance if it produces a diminished real image?

9. Ans. When the object is beyond the centre of curvature of the concave mirror it produces a diminished real image. Therefore the object must be at least more than 2f = 2x5 cm = 10 cm from the pole in front of the mirror.

Q10. An object is 20 mm in front of a concave mirror which produces an upright image or erect image. The radius of the curvature of the mirror is

a. Less than 20 mm       b. Exactly 40 mm

c. In between 20 mm and 40 mm

d. More than 40 mm. 

10. Ans. As for an erect image, object must be placed in between pole and focus, then focal length in this case is more than 20 mm. Therefore, the centre of curvature must be more than 2 x 20 mm = 40 mm. 

d. is the correct answer. 

Q11. Find the size, nature and position of image formed when an object of size 2 cm is placed at a distance of 9 cm from a concave mirror of focal length 6 cm. 

11. Ans. Focal length, f = - 6 cm and object distance, u = - 9 cm. Height of the object, h₁ = 2 cm. 

We know, mirror formula, 1/u + 1/v = 1/f

⟹ 1/v = 1/f - 1/u

⟹ 1/v = (u - f)/fu

⟹ v= fu/(u - f)

⟹ v = (-6)(-9)/( - 9 + 6) = (6x9)/(-3) 

∴ v = - 18 cm (position)

Magnification, 

m = (h₂/h₁) = (- v/u) = 18/(-9) = - 2

h₂ = m x h₁ = - 2 x 2 = - 4 cm (inverted)

Position: The image is 18 cm in front of the mirror. 

Nature: The image is real, inverted and magnified.

Size: The image is 4 cm high, inverted and twice magnified and below the principal axis.

Q12. An object 1 cm high is placed at a distance of 10 cm from a concave mirror which produces a real image 2 cm high. (i) what is the focal length of the mirror? (ii) find the position of the image.

Q13. A concave mirror produces three times magnified real image of an object placed at 8 cm in front of it. Where is the image located? What is the focal length of the mirror?

Q14. What is the nature of the image formed by a concave mirror if the magnification produced by the mirror is (i) +2 (ii) - 0.50 ?

Q15. An object is placed at a distance 8 cm from a concave mirror of focal length 12 cm. 

a. Draw a ray diagram for the formation of image.

b. Calculate the image distance.

c. State two characteristics of the image formed. 

Q16. At what distance from a concave mirror of focal length 12 cm should an object 1 cm long be placed in order to get an erect image 4 cm tall?

Q17. When an object is placed at a distance of 4 cm from a concave mirror, its image is formed at 6 cm behind the mirror. Calculate the focal length of the mirror. 

Q18. An object is placed in between principal focus and centre of curvature in front of a concave mirror. Draw a ray diagram to show how the image is formed, and describe its size, position and nature.

Lecture 1: CLASS XI : PHYSICS : CHAPTER - 5 : LAWS OF MOTION

FORCE: 

Force may be defined as an agency (a push or a pull) which changes or tends to change the state of rest or of uniform motion or the direction of motion of a body.

Effects produced by a force:

1. Force can change speed of an object.

When force is applied on a body the body starts to move. Again, when a force exerted by the brakes slows or stops moving train.

2. Force can change the direction of motion of an object.

Force exerted by a bat to a ball, changes the direction of the ball. 

3. Force can change the shape of an object. 

If we apply a force on a rubber ball, round shape of a rubber ball gets distorted.

Galileo's Laws of inertia:

A body moving with certain speed along a straight path will continue to move with same speed along the same straight path in the absence of external forces. 

INERTIA: 

The inherent property of a material body by virtue of which it cannot change, by itself, its state of rest or of uniform motion in a straight line is called inertia. 

Different types of inertia:

a. Inertia of rest: The tendency of a body to remain in its position of rest is called inertia of rest. 

Example: A person standing in a bus falls backward when the bus suddenly starts moving forward. 

b. Inertia of motion: The tendency of a body to remain in its state of uniform motion in a straight line is called inertia of motion. 

Example: When a moving bus suddenly stops, a person sitting in it falls forward. 

c. Inertia of direction: The inability of a body to change by itself its direction of motion is called inertia of direction.

Example: When a bus takes a sharp turn, a person sitting in the bus experiences a force acting away from the centre of the curved path. It is due to inertia of direction. 

Measurement of inertia of a body:

Mass of a body is the measure of its inertia. If a body has more mass, it has more inertia, it means it is more difficult to change its state of rest or of uniform motion. 

Linear momentum (p):

Momentum of a body is the quantity of motion possessed by the body. It is equal to the product of Mass and velocity of the body.

Momentum = mass x velocity 

Momentum is a vector quantity because the velocity v is a vector and mass m is a scalar. Its direction is same as the direction of the velocity of the body. Its magnitude is given by

p = mv

SI unit of momentum = kg m/s

CGS unit of momentum = g cm/s

The dimensional formula of momentum = [MLT⁻¹]

Q1. Two objects, each of mass m and velocities v₁ and v₂. If v₁> v₂, which one has more momentum?

Ans: p₁ = mv₁ and p₂ = mv₂

∴ (p₁/p₂) = (mv₁/mv₂) = (v₁/v₂)

As v₁> v₂ , so p₁> p₂

Q2. Two objects having mass m₁ and m₂ such that m₁> m₂ , and same velocity v. Which one has more momentum?

Ans: p₁ = m₁v and p₂ = m₂v

∴ (p₁/p₂) = (m₁v/m₂v) = (m₁/m₂)

As m₁> m₂ , so p₁> p₂

Q3. Two objects having same momenta (p₁ = p₂), if m₁> m₂, which one has more velocity?

Ans. p₁ = m₁v₁ and p₂ = m₂v₂

As p₁ = p₂

∴ m₁v₁ = m₂v₂ 

or  (v₂/v₁) = (m₁/m₂)

As m₁> m₂ , so v₁< v₂

Velocities of bodies having equal linear momenta are inversely proportional to their masses. 

So, when two objects have equal linear momentum, the lighter object will move faster than the heavier one. 

    

Lecture- 6 : CLASS-X: SCIENCE : Chapter: REFLECTION OF LIGHT & SIGN CONVENTIONS

CLASS X   |    SCIENCE    |    LIGHT

      Notes prepared by Subhankar Karmakar

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SCIENCE: CLASS X: CBSE (CLASS NOTES)

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SIGN CONVENTION FOR SPHERICAL MIRRORS:

According to the new cartesian sign convention:

1. All the distances are measured from pole of the mirror as origin. 

2. Distances measured in the same direction as that of incident light are taken as positive.

3. Distances measured against the direction of incident light are taken as negative.

4. Distances measured upward and perpendicular to the principal axis are taken as positive.

5. Distances measured downward and perpendicular to the principal axis are taken as negative. 

 

KEY POINTS TO REMEMBER

• The object is always placed on the left side of the mirror. 

• All the distances measured from the pole (P) of mirror to the right side will be considered positive and to the left side will be negative. 

• The object distance (u) is always negative.

• If an image is formed behind a concave mirror or to the right side of the mirror, the image distance (v) is positive, if the images formed in front of the mirror or to the left side of the mirror, then the image distance will be negative. 

• The image distance (v) for a convex mirror will be always positive.

• The focal length of a concave mirror is always negative

• The focal length of a convex mirror is always positive

• The height of an object is always positive

• If an image is formed above the principal axis its height is positive

• If an image is formed below the principal axis its height is negative

• The height of all the virtual and erect images is positive

• The height of all the real and inverted images is negative.

MIRROR FORMULA:

A formula which gives the relationship between image distance (v), object distance (u) and focal length (f) of a spherical mirror is known as the mirror formula. It is given as

1/v + 1/u = 1/f

Linear magnification produced by mirrors:

The ratio of the height of image to the height of object is known as linear magnification. It is also equal to the ratio of the image distance to the object distance, with a minus sign. 

∴  magnification = height of image/height of object

⟹ m = h₂ / h₁ = - v/u

h₁ = height of object

h₂ = height of image

• if the magnification has a plus sign, then the image is virtual and erect. 

• if the magnification has a negative sign, then the image is real and inverted. 

Position of the image means image distance.

Nature of image means whether  the image is "real and inverted" or "virtual and erect".

Size of image means value of magnification.

Lecture- 5 : CLASS-X: SCIENCE : Chapter: Reflection of light & concave mirror

CLASS X   |    SCIENCE    |    LIGHT

      Notes prepared by Subhankar Karmakar

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SCIENCE: CLASS X: CBSE (CLASS NOTES)

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 • Rules for obtaining images formed by Concave Mirror:

The image will be formed at the point where atleast two reflected rays intersect or appear to intersect. 

1. A ray of light which is is parallel to the principal axis of a concave mirror, passes through its focus after reflection from the mirror. 

2. A ray of light passing through the centre of curvature of a concave mirror is reflected back along the same path. Arrow pointing from left to right indicates the direction of incident ray and the arrow pointing from right to left indicates the direction of reflected ray.

3. A ray of light passing through the focus of a concave mirror becomes parallel to the principal axis after reflection.

4. A ray of light which is incident at the pole of a concave mirror is reflected back making the same angle with the principal axis. 

• If a ray of light is incident on a concave mirror along its principal axis, then it is reflected back along the same path. 

• FORMATION OF DIFFERENT TYPES OF IMAGES BY A CONCAVE MIRROR

The type of image formed by a concave mirror depends on the position of object in front of the mirror. At different places, an object produces different types of images. 

a. When the object is in between Pole (P) and focus (F):

When an object is placed between the pole (P) and focus (F) of a concave mirror, the image formed is:

i. Behind the mirror

ii. Virtual and erect, and

iii. Larger than the object or magnified.

Uses of concave mirror using this type of images:

1. A concave mirror can be used to magnify objects. Therefore, it will be used as a magnifying glass.

2. A concave mirror can be used as a makeup mirror. It magnifies a part of the face.

3. Dentist's mirror is a small concave mirror fitted in a frame with a long handle. It gives magnified image of tooth.

b. When the object is placed at the focus (F) of a concave mirror:

When an object is placed at the focus of a concave mirror, the image formed is:

i. At infinity, 

ii. Real and inverted, and

iii. Highly magnified.

Uses of concave mirror using this type of images:

1. When a light bulb is placed at the focus of a concave mirror reflector, the diverging light rays off the bulb are collected by the concave reflector and then reflected to produce a strong, parallel beam of light. 

c. When the object is placed between focus (F) and centre of curvature (C):

When an object is placed between the focus (F) and the centre of curvature (C) of a concave mirror, the image formed is:

i. Beyond the centre of curvature

ii. Real and inverted, and

iii. Larger than object or magnified.

d. When the object is placed at the centre of curvature (C) of a concave mirror:

When an object is placed at the centre of curvature (C) of a concave mirror, the image formed is:

i. At the centre of curvature (C),

ii. Real and inverted, and

iii. Same size as the object.

e. When the object is is beyond the centre of curvature (C) of the concave mirror:

When an object is placed beyond the centre of curvature (C) a concave mirror, the image formed is:

i. Between the focus (F) and the centre of curvature (C),

ii. Real and inverted, and

iii. Smaller than the object or diminished.

f. When the object is at infinity:

When an object is at infinity from a concave mirror, the image found is:

i. At the focus (F), 

ii. Real and inverted, and

iii. Much smaller than the object or highly diminished. 

"This means that a concave mirror can concentrate all The parallel rays of light to its focus."

Uses of concave mirror using this type of images:

1. A concave mirror is used as a "head mirror" by the doctors to concentrate light coming from a lamp onto the body part of a patient like ear, nose, throat etc. to be examined. 

2. The concave "metal dishes" are used in dish antenna of televisions to receive TV signals from the very distant communication satellite which are high up in the sky. 

USES OF CONCAVE MIRRORS:

1. A concave mirror can be used to magnify objects. Therefore, it will be used as a magnifying glass.

2. A concave mirror can be used as a makeup mirror. It magnifies a part of the face.

3. Dentist's mirror is a small concave mirror fitted in a frame with a long handle. It gives magnified image of tooth.

4. When a light bulb is placed at the focus of a concave mirror reflector, the diverging light rays off the bulb are collected by the concave reflector and then reflected to produce a strong, parallel beam of light. 

5. A concave mirror is used as a "head mirror" by the doctors to concentrate light coming from a lamp onto the body part of a patient like ear, nose, throat etc. to be examined. 

6. The concave "metal dishes" are used in dish antenna of televisions to receive TV signals from the very distant communication satellite which are high up in the sky. 

LECTURE -2 : CLASS VIII : SCIENCE : CHAPTER 4 : MATERIALS : METALS & NON-METALS

CLASS VIII   |    SCIENCE    |    CHAPTER 4

     Notes prepared by Subhankar Karmakar 

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CHEMICAL PROPERTIES OF METALS & NON METALS:

REACTION OF METALS:

 a. Reactions of metal with Oxygen (O₂):

 Metal reacts with oxygen to form metal oxides. Metal oxides are basic in nature. 

The basic metal oxides turn red litmus to blue. 

*(Metals and R & B)

∴ Metal + Oxygen (from air) = Metal Oxide (basic oxide) 

Magnesium burning in air: 

I. When Magnesium (Mg) burns in air, it combines with the oxygen (O₂) of air to form magnesium oxide. 

• Mg + O₂ = MgO (a basic oxide)

II. Magnesium oxide dissolves partially in water to form magnesium hydroxide Mg(OH)₂  solution:

• MgO + H₂O = Mg(OH)₂ (a base)

Sodium (Na) reacts with Oxygen in air and produces Sodium Oxide (Na₂O)

• Na + O₂ = Na₂O (a basic oxide) 

Water solution of Sodium Oxide forms Sodium Hydroxide (NaOH)

• Na₂O +  H₂O  = NaOH

 Reaction of iron with oxygen of air:

During the rusting of iron, iron (Fe) metal combines slowly with the oxygen (O₂) of air in the presence of water or moisture to form a compound called iron oxide (Fe₂O₃). This iron oxide is called rust. Damp air contains Oxygen (O₂) + water (H₂O). 

• Iron (Fe) + Oxygen (O₂) + water (H₂O) ⟹ Iron Oxide or rust (Fe₂O₃) (basic oxide)

• Reaction of copper metal with moist air:

When a copper object is exposed to moist air for a long time, then copper (Cu) reacts with water (H₂O), carbon dioxide (CO₂) and oxygen (O₂) present in moist air to form a green coating on the copper object. The green coating is a mixture of copper hydroxide [Cu(OH)₂] and copper carbonate (CuCO₃) which is formed by the action of moist air on copper object.

• 2Cu + H₂O + CO₂ + O₂ = Cu(OH)₂ + CuCO₃ 

• Corrosion of copper: The formation of green coating of basic copper carbonate on the surface of copper objects on exposure to moist air is called corrosion of copper. 

 

b. Reactions of metal with water:

 When a metal reacts with water, then a metal hydroxide and hydrogen gas are formed. 

Metal + water = Metal hydroxide + Hydrogen

Not all metals react with water. Some of the metals reacts with cold water, whereas some metals reacts with hot water and steam. It depends upon reactivity of metals.

Sodium and potassium very quickly reacts with cold water. 

·        Magnesium reacts slowly with cold water and quickly with hot water and zinc and iron slowly react with steam. 

·        Sodium (Na) + water (H₂O) → Sodium Hydroxide (NaOH) + Hydrogen (H₂)

·       Sodium (Na) is a very reactive metal. It reacts with moisture, oxygen and other gases present in air. So, if sodium metal is kept exposed to air, it will react with the various components of air and get spoiled. In order to prevent its reaction with the moisture and other gases of air, sodium metal is always told under kerosene. Potassium metal is also very reactive and also kept in kerosene. 

c. Reactions of metals with acids:

Most of the metals react with dilute acids to form salts and hydrogen gas. 

Metal + Acid → Salt + Hydrogen gas.

Only less reactive metals like Copper, silver and gold do not react with dilute acids. 

• Magnesium reacts with dilute hydrochloric acid to form magnesium chloride (salt) and hydrogen gas.

Magnesium + hydrochloric acid → magnesium chloride + hydrogen gas

Mg + HCl → MgCl₂ + H₂

 When foodstuffs containing acids like orange juice, pickles, and curds are kept in iron, aluminium or copper containers, the acids present in them react with the metal of the container slowly to form toxic salts. That's why acidic foodstuffs should not be kept in metal containers.

d. Reactions of metal with bases:

Only some metals react with bases to form salts and hydrogen gas. Like aluminium is a metal and Sodium hydroxide is a base. When aluminium is heated with sodium hydroxide solution, then sodium aluminate which is a salt and hydrogen gas is formed. 

Sodium hydroxide + aluminium → sodium aluminate + hydrogen

NaOH + Al → NaAlO₂ + H₂

Zinc also reacts with bases like sodium hydroxide to produce hydrogen gas. 

REACTION OF NON METALS:

a. Reaction of nonmetals with oxygen:

 Non metals react with oxygen to form non metal oxides. Non metal oxides are acidic in nature. Non metal oxides water solution turn blue litmus into red. 

Non metal + oxygen → non metal oxide

 1. When sulphur burns in air, it combines with the oxygen of air to form sulphur dioxide. Sulphur dioxide is a acidic oxide. 

Sulphur + oxygen → sulphur dioxide

S + O₂ → SO₂

Sulphur dioxide dissolves in water to form sulphurous acid solution

SO₂ + H₂O → H₂SO₃

b. Reactions of nonmetals with water:

 Non metals do not react with water. Therefore, highly reactive nonmetals like phosphorus cannot be kept open in the air as it reacts with oxygen of air and catches fire. So, in order to protect phosphorus from atmospheric air, it is stored in a bottle containing water.

 c. Reactions of nonmetals with acids:

 Non metals do not react with dilute acids. 

 d. Reactions of nonmetals with bases:

 Some of the nonmetals react with bases but no hydrogen gas is produced.

 Difference between metal oxides and non metal oxides:

 Metal oxides are basic in nature and turn red litmus to blue. 

Non metal oxides are acidic in nature and turn blue litmus to red. 

 REACTIVITY SERIES OF METALS:

The arrangement of metals in a vertical column in the order of decreasing reactivities is called the reactivity series of metals.  

In reactivity series, the most reactive metal is placed at the top whereas the least reactive metal is placed at the bottom.

Potassium is the most reactive metal, so it has been placed at the top of the reactivity series. Gold is the least reactive metal so it has been placed at the bottom of the reactivity series.

 

Potassium (K) (most reactive)

Sodium (Na)

Calcium (Ca)

Magnesium (Mg)

Aluminium (Al)

Zinc (Zn)

Iron (Fe)

Lead (Pb)

Copper (Cu)

Silver (Ag)

Gold (Au) (least reactive)

Reactivity of the metals decreases as we go down in the above series.