Physics - Class X - Chapter No.9 - Questions And Answers

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SIMPLE MACHINES

IMPORTANT QUESTIONS OF PAST PAPERS:

1. Define lever, principle of lever and derive formula for M.A of lever. (2013, 2016)
2. Draw the figure of Wheel and Axle and calculate its M.A. (2015)
3. Define the following inclined plane and pulley. (2013)
4. Define machine and write down the names of four simple machines. (2011, 2009)
5. What is inclined plane? Calculate its M.A. (2014, 2017, 2009)
6. The two bodies of different masses are attached with a string which passes over a friction less pulley such that the bodies are moving vertical derive the formula. (2017)
7. Write down the kinds of lever. (2016)
8. Define input and output. (2010, 2014)

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IMPORTANT SYMBOLS:
• Effort applied = P
• load = W
• height = h
• Pitch of the screw = h
• Efficiency = η
• mass = m
• weight = W
• length = L
• Distance moved by load = h
• Distance moved by effort = d
• Length of Tommy bar = r
• Pitch of the screw = h
• length of the handle of screw jack = r
• Mechanical Advantage ( M.A ) = ^𝒘 / _𝒑

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IMPORTANT FORMULA’S:
For pulley
•Mechanical advantages = ^𝒘eight / _efforts
•Input = Effort × Effort Arm
•Out put = Load × Load Arm
•Efficiency = ^output / _Input
•Input = Output
Tommy bar and screw jack
•M.A = ^{𝟐л 𝐫} / _h
Inclined plane
•M.A = ^l / _h

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Force = Effort  Weight = Load

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Questions/ Answer

Q.1: Define Machine and write down the names of four simple machines. Also write down the various purpose of machine.
Ans: MACHINE: A device which performs the work in convenient (useful) manner is called Machine.

       NAMES OF SIMPLE MACHINES:
•Lever
•Screw
•Wedge
•Inclined plane
•Screw jack
•Wheel and Axle

VARIOUS PURPOSE OF MACHINE:
• To lift the heavy load. (Screw jack)
• To change the direction of force. (pulley)
• To transfer energy from one point to another point. ( lever)

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Q.2: Define Effort, Load, Input, Output, Mechanical Advantage and Efficiency.
Ans: EFFORT:(P) The force directly applied on the machine is called Effort. It is denoted by “p”.

LOAD: (W) The weight lifted by machine is called Load. It is denoted by “W”.

INPUT: The work done on a machine is called Input.
Formula:

Input = Effort × Effort Arm
Input = P × d

OUTPUT: The work done by a machine is called Output.
Formula:

Output = Load × Load Arm
Output = W × h

MECHANICAL ADVANTAGE: The ratio of Load and Effort is called Mechanical advantage. It is denoted by M.A.
Unit: Since M.A is ratio between two forces, it has no unit. It is expressed in numbers.
Formula:

EFFICIENCY: The ratio of output and input is called Efficiency.
Formula:

The efficiency of a real machine is always less than 1, Ideal machine 100% efficiency or 1.

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Q.3: Define lever; describe working of lever, the terms used in liver, and principle of Lever and Mechanical Advantage of lever.
Ans:LEVER: A simplest machine, a strong metallic bar, which can be rotate about a fixed point, is called Lever.
WORKING OF LEVER: By applying a force on one end a bar, weight can be lifted at the other end.

Fulcrum: A fixed point around which lever is rotated, is called Fulcrum.
Effort Arm: The perpendicular distance between Effort and Fulcrum is called Effort Arm.
Moment of Effort: The product of Effort and Effort Arm is called Moment of Effort.
Load Arm: The perpendicular distance between Weight and Fulcrum is called Load Arm.
Moment of Load: The product of Load and Load Arm is called Moment of Load.

PRINCIPLE OF WORKING: The moment of effort is always equal to moment of load.

Moment of Effort = Moment of Load

Effort × Effort Arm = Load × Load Arm

P × d = W × h

This equation is called principle of lever.

MECHANICAL ADVANTAGES OF LEVER:
According to principle of lever:

P × d = W × h

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Q. 4: Write down the kinds of lever.
Ans:KINDS OF LEVER: There are three kinds of lever.


➤FIRST KIND OF LEVER: If fulcrum F is in between Effort E and Weight (load) W, is called first kind of lever.
Example:
• A pair of scissors
• See-saw
• A common balance



➤SECOND KIND OF LEVER: If Load W is in between fulcrum F and Effort F is called second kind of lever.

Example:
• A door
• A punching machine
• A nut cracker


➤THIRD KIND OF LEVER: If Effort P is in between fulcrum F and load W, is called third kind of lever.

Example:
• Human arm
• Upper and lower jaws in the mouth
• A pair of forceps
• A fire tongs

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Q.5: Define Screw Jack. Find its Mechanical advantage.
Ans:SCREW JACK: A Screw jack is a machine which is commonly used to lift heavy load.
MECHANICAL ADVANTAGE:
When the handle is turned through one complete revolution in a circle of radius r, the effort moves through a distance 2 л r and the load is raised through a height h in this case,

Input = effort × distance moved by effort
Input = p × 2 л r Tommy bar
Output = Load × distance moved by load
Output = W × h

For an ideal Machine,

Input = Output
P × 2 л r = W× h

The pitch of the screw is very small as compare to Tommy bar so the M.A of screw jack is very large.

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Q.6: What is inclined plane? Calculate its Mechanical Advantage.

Ans:INCLINED PLANE: A surface whose one end is higher than the other end is called an Inclined plane.

MECHANICAL ADVANTAGES:
Consider a smooth plane surface AB with make an angle ϴ with the horizontal. A load “W” is placed on inclined plane. Now effort “P” is applying on it through a distance l and weight W is raised to height.

Input = work done by effort
Input = Effort × distance
Input = P × l

Similarly,

Out put = work done in raising the ways
Out put = weight × height
Output = W × h

For a Smooth, friction less ideal inclined plane

Output = Input
W × h = P × l

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Q.7: Define pulley. Find the M.A of Fixed Pulley and Movable Pulley.

OR

The two bodies of different masses are attached with a string which passes over a friction less pulley such that the bodies are moving vertical derive the formula.
Ans:PULLEY: A pulley is grooved wheel supported in a frame called block such that wheel can turn about an axle in the block. The pulley can be suspended from a fixed beam by means of a hook.
FIXED PULLEY: A pulley whose block is fixed to a strong beam or ceiling and cannot move up and down is called Fixed pulley.

MECHANICAL ADVANTAGE: The Load W is tied to one end of the rope and effort P is applied at the other end. If we neglect the weight of the rope and friction then,

Input = Output
P × OA = W × OB

FIXED PULLEY: A pulley whose block is not fixed to a beam or ceiling is called movable pulley.

MECHANICAL ADVANTAGE: The load or weight W to be lifted is hung from the hook of the block. At every point in the rope, the tension is equal to the applied effort P. As both ends of the rope are pulling the weight W upwards so the effort P acting on the weight in the upward direction will be 2P. If we neglect the weight of the rope and friction then,

W = 2P
W / P = 2
M.A = 2

The M.A advantage of pulley is 2. It means double load can be lifted with the help of a simple movable pulley as compare to effort.

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Q. 8: Draw the figure of Wheel and Axle and calculate its M.A.
Ans:WHEEL AND AXLE: A Wheel with larger radius “R” and another with smaller radius “r” are fixed on the same shaft are called Wheel and Axle.
MECHANICAL ADVANTAGE: The effort “P” is applied at the rim of the wheel of radius “R” while the load “W” is lifted by a string wound around the axle. For one complete rotation, the effort moves through a distance 2 л R while the load raised through a distance 2 л r
If friction is neglect,

Output = Input
W × 2 л r = P × 2 л R

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Prepared By: Sir Waseem

Physics - Class X - Chapter No.8 - Questions And Answe

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WORK, ENERGY AND POWER

IMPORTANT QUESTIONS OF PAST PAPERS:

1.Define elasticity, work and energy. (2008)
2.Define kinetic energy and potential energy and write difference between them. (2009), (2013), (2007)
3.Define work and write down its formula. (2011)
4.Define work and energy state law of conservation of energy. (2008), (2013)
5.Define kinetic energy and potential energy derive the equation K.E = ^𝟏/₂mv² (2012), (2014), (2009).
6.Define power and derive equation P=FV. ( 2014), (2016)
7.Define interconversion of kinetic energy and potential energy. (2015)

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IMPORTANT SYMBOLS:
• Applied force = F
• Angle = ɵ
• Distance = d
• Weight = W
• Speed = V
• Work = w
• Mass = m
• Power = p
• Height = h
• Kinetic energy = K.E
• Gravity = g
• Potential energy = P.E

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IMPORTANT FORMULA’S:

• W= f×d
• W= fdcosɵ
• K.E = ^𝟏/₂ mv²
• P = w/ t
• P = FV
• W =F= mg
• P.E = mgh
• Gain in K.E = Loss in P.E
^𝟏/₂mv² = mgh

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Questions/ Answer

Q.1: Define Work, Power, Energy and Elasticity with formula and units also.
Ans:WORK: When a force acts on a body and body cover some displacement along the direction of force, then work is said to be done.

Work depend upon two physical quantities Force and displacement therefore work can be define as,

“The product of force and displacement is equal to work.”

Formula: Work = Force × Displacement
W = F × d
Unit: In S.I system the unit of work is joule and it is denoted by j.
•If ɵ = 0° when work is positive
•If ɵ = 180° when work is negative
•If ɵ = 90° when work is zero.

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POWER:“The work done by a body in unit time is called power.”

OR
“The rate of doing work is called work.”

Formula:

Unit: The unit of power is ^j / _s .

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ENERGY: The capability of doing work is called energy. Energy is an agent which is responsible to do work.
Unit: its unit is joule.

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ELASTICITY: It is ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.

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Q.2: Define kinetic energy and potential energy.
Ans:KINETIC ENERGY:& The energy possess by body by virtue of its motion is called kinetic energy. It value increases with velocity.
Formula: It can be calculated by K.E =& ^𝟏/₂ mv²
POTENTIAL ENERGY: The energy possessed by a body by virtue of position is called potential energy. It value increases with increase in altitude.
Formula: It can be calculate P.E= mgh.

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Q.3: Define power and derive equation P=FV.
Ans:POWER: “The work done by a body in unit time is called power.”
Suppose a constant force “F” acts on a body and displaces it through distance “d” in the direction of force in time “t”, the work is done,

W = Fd

Average power is developed,

Put the value of ^d / _tin equation (ii)

P = FV

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Q.4: Define potential energy and also derive P.E = mgh.
Ans: POTENTIAL ENERGY: The energy possessed by a body by virtue of position is called potential energy.
Mathematically: Consider a body of mass “m” on the ground. If it is lifted up with a vertical height “h” the force required to raise the body is just equal and opposite to its weight

W = mg. 

thus work done on it against gravitational field is store in its gravitational work,

W = F.d
But, F = W = mg
W = mg.d (d = h)
W = mgh (W = P.E)
P.E = mgh

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Q.5: Prove that Elastic potential energy = ^𝟏/₂ kx²
Ans:ELASTIC POTENTIAL ENERGY: The energy stored in a stretched or compressed elastic material like (spring or rubber band) is called Elastic potential energy.
Derivation: Consider an object is attached with a spring having mass “m” placed on a smooth and horizontal surface. A force f pushes a spring to compress it from its equilibrium position to another position.
According to Hooks Law, the applied force is directly proportional to the extension produce in the spring of distance “x”, so mathematically.

F œ x
F=Kx

Where “K” is constant (spring constant) its value depends on the stiffness of the spring, since the compression is zero at “O” and Kx at x, the average force needed to compress the spring from position “O” to x is

This work causes the elastic potential energy, therefore elastic potential energy = ^𝟏/₂ kx²

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Q.6: What do you mean by conservation of energy? State law of conservation of energy.

Ans: CONSERVATION OF ENERGY: Conservation of energy means that the amount of energy in the universe is fixed. Although energy can change forms or we can say that one kind of energy can change into another kind of energy. However the amount of energy in the universe remains the same.

LAW OF CONSERVATION OF ENERGY: Energy can neither be created nor be destroyed but it can be changed from one form to another form.

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Q.7: What happens to the potential energy of a body when dropped from certain height?
Ans: When a body is dropped from a certain height, it starts losing it P.E due to downward motion. By the time it reaches the ground the whole P.E is stores as energy.

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Q.8: Define kinetic energy derive the equationK.E = ^𝟏/₂mv²?
Ans: KINETIC ENERGY:
The energy possess by body by virtue of its motion is called kinetic energy.

MATHEMATICALLY: Consider a body mass “m” is initially at rest (V_i = 0). Now force F is applied on the body and body acquire velocity V (V_f = V).
If body covers some displacement “S” then work done is given by,

W = F.S……………………………… (i)

If force “F” produces acceleration “a” then according to Newton’s law

F = ma ……………………………..… (ii)

In order to find the value S we use third equation of motion,

2as= V_f² – V_i²
2as = V² – 0

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Q. 9: Define interconversion of kinetic energy and potential energy.
Ans: INTERCONVERSION OF K.E AND P.E: Interconversion of K.E can be converted into P.E and P.E can be converted into K.E.
EXPLANATION: Consider a body of mass “m” lying at height “h” from the ground this position it has P.E = mgh and K.E = 0. Now the body is allowed to fall under the action of gravity.
As the body move downward closer to the ground its P.E keeps on decreasing and its K.E keep on increasing. It is due to the fact that h is decreasing while v is increasing. When the body just hits the surface of the ground its P.E is zero and K.E is maximum,

Gain in K.E = Loss in P.E P.E= mgh
¹ / ₂ mv² = mgh
¹ / ₂ v² = gh
V² = 2gh
V =  √2gh

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Prepared by: Sir Waseem

Physics - Class X - Chapter No.7 - Questions And Answers

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CIRCULAR MOTION AND GRAVITATION

IMPORTANT QUESTIONS OF PAST PAPERS:

1. Define centripetal force and what are the factors depends on which it depends? Write down the formula of centripetal force. (2009)
2. State Newton law of gravitation derives the formula of mass of earth with its help. (2013)
3.States Newton’s law of gravitation and prove that F= G ^m₁m₂/_r² . (2009, 2013)
4. Define orbital velocity and derive the formula V= √ g R_e. (2016)

IMPORTANT SYMBOLS:

• Centripetal Force = F_c
• Centripetal acceleration = a_c
• Mass of Earth = Me
• Gravitation constant = G
• Centripetal acceleration = a_c
• Orbital velocity = V
• Distance & radius = r
• gravity = g

IMPORTANT FORMULA’S:

Questions/ Answer

Q. 1: Define the following terms with formulas and unit.
i.Circular motion
ii. Centripetal force
iii. Centripetal acceleration
iv. Centrifugal force
Ans:
i. CIRCULAR MOTION: When an object revolves in a circular orbit its motion is said to be Circular Motion.

OR

The force which acts towards the center along the radius of a circular path on which the body is moving with a uniform velocity is called Centripetal Force.

ii. CENTRIPETAL FORCE: The force which is responsible for the motion of a body in circular orbit is called Centripetal Force.
Formula:

Unit: unit of Centripetal Force is Newton N.

iii. CENTRIPETAL ACCELERATION: The change of the velocity on the circumference of the circle is called Centripetal Acceleration.
Formula:

Unit: Unit of Centripetal Acceleration is msec^-2 or m/sec²

iv. CENTRIFUGAL FORCE: The force which is directed away from the centre of circle is called Centrifugal Force. It is an opposite and equal reaction of centripetal force.

OR

The force which is reaction of the Centripetal Force is called centrifugal force.
Formula:

Unit: Unit of Centripetal Acceleration is msec^-2 or m/sec²

Q.2: What are the factors which depend on centripetal force?
Ans: There are three factors are as follow,
i. The mass of the Object increases.
ii. The speed of the Object increases.
iii. The radius of the circle in which it is travelling decreases.


Q.3: Show that Mathematically
 .
Ans: CENTRIPETAL FORCE: The force which is responsible for the motion of a body in circular orbit is called Centripetal Force.
MATHEMATICAL EXPRESSION:
If a body of mass m is moving in a circular path the magnitude of centripetal force F_c is given by the equation

F_c = ma_c

a_c is the centripetal acceleration, if r is the radius of the circle and V is the velocity then magnitude of centripetal acceleration is given by

Putting the value of a_c



Q. 4: States Newton’s law of gravitation and prove that F= G 𝐦_𝟏 𝐦_𝟐  / 𝐫^𝟐
Ans: NEWTON LAW OF GRAVITATION:

“Everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square root of the distance between their centers”.

MATHEMATICALLY:
Consider two spherical bodies A and B having the masses 𝐦_𝟏 and 𝐦_𝟐 respectively. The distance between their centers is r.

Q.5: State Newton’s law of gravitation derives the formula of mass of earth with its help.
Ans:NEWTON’S LAW OF GRAVITATION: 
The mass of earth can be determined with the help of Newton’s law of gravitation.
Consider a body of mass “m” placed on the surface of earth. If “M_e” be the mass of the earth and “R_e” its radius than the force with which the earth attracts the body towards its center is given by equation:

Q.6: Explain how the value of “g” decreases with a change in the altitude.
Ans: VARIATION OF “g” ALTITUDE: Consider a body of mass “m” on the surface of the earth, the gravitational force of attraction between the body and earth is equal to the m weight of the body.




Since “G” and “M_e” are constant the acceleration due to gravity “g” decreases increasing distances R from the center of the earth. Therefore,

Q.7: Define orbital velocity and derive the formula V= √gR_e.
Ans:ORBITAL VELOCITY: The velocity of an artificial satellite or a natural satellite which moves round the earth at a specific height is called orbital velocity.
MATHEMATICALLY:
Let a satellite having mass “m” be moving in an orbit of radius with velocity “V”. the gravitational force of attraction between the satellite and the earth provides the necessary centripetal force of the satellite.

Combining equation (i) and (ii)

V² = gR

If the satellite is revolving close to the surface of the earth then,

V= √gR_e

From above formula, the orbital velocity has been calculated as,

V= 7290 Kms^-2

Q.8: What is satellite? What are natural and artificial satellites?
Ans:SATELLITE: An object revolve around a planet in a fixed orbit is called satellite.
➤ NATURAL SATELLITE: Satellite which naturally exists in the universe and are revolving around a planet is called as Natural Satellite.
 For example moon.

➤ ARTIFICIAL SATELLITE: The Satellite sent by the Scientists which moves round the earth are called Artificial Satellite.
For example telecommunication and space research etc.

Q.9: What is banking of road? What are advantages of it?
Ans: BANKING OF ROAD: The outer edge of the curved roads is made higher than inner edges. This is called banking of road.

ADVANTAGES OF BANKING ROAD: When the vehicle exceeds a certain limits, turning a corner the centripetal force is unable to keep the vehicle moving in a circle and the vehicle tends to skit away from the center. The banker road keeps the vehicle moving safely around the curve. The speed limits are mentioned around the curves on the roads for safe driving.

Q.10: Write down the difference between “G” and “g”.
Ans:

G	g
• It represents gravitational constant.	• It represents acceleration due to gravity.
• It is a scalar quantity.	• It is a vector quantity.
• It remains constant.	• It varies place to place.
• Its value 6.67×10-11 Nm2/kg2.	• Its value 9.8 m/sec2.

Prepared By: Sir Waseem

Physics - Class X - Chapter No.6 - Questions And Answers

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EQUILIBRIUM

IMPORTANT QUESTIONS OF PAST PAPERS

1. Write down three states of equilibrium. (2009)
2. Prove that moments of couple is equal to the force and arm of couple. (2015)
3. Describe two condition of equilibrium. (2015)
4. Define moment arm. (2015)
5. Define torque. (2016)

IMPORTANT SYMBOLS: 

• Force = F
• Moment Arm (distance from one point to another point) = d & r
• Mass = m
• torque = ɽ

IMPORTANT FORMULA’S:

Torque = force × moment arm
τ = F × d

Questions/ Answer

Q.1: Define equilibrium and write down the types of equilibrium.
Ans:EQUILIBRIUM: A body said to be in equilibrium if the forces acting on it must be cancel the effect of each other.

“OR”

When two or more forces act on a body, such that their resultant effect on the body is zero and the body retains its state of rest or of uniform motion then the body is said to be in equilibrium.
Example: A book lying on the table. All forces which are acting are zero.

TYPES OF EQUILIBRIUM: There are two types of equilibrium.
1- Static Equilibrium: A body remains at rest under the influence of different forces it is called static equilibrium.
For example: book lying on the table.

2- Dynamic Equilibrium: If the body is moving with uniform velocity under the influence of different forces it is called dynamic equilibrium.
For example paratrooper falls down with uniform velocity.

Q.2: Define center of gravity.
Ans: CENTER OF GRAVITY: The point inside and outside the body where the whole weight of the body appears to act is called the center of the gravity.

Q.3: Write down the states of equilibrium with suitable example.
Ans: There are three states of equilibrium.
1- Stable Equilibrium: A body is said to be in stable equilibrium if it returns to its original position when it is slightly disturbed. The centre of gravity is raised and then comes to its original position.
Example: A cone is standing on its base.




  2- Unstable Equilibrium: A body is said to be in unstable equilibrium if it does not return to its original position when it is slightly disturbed. The centre of gravity is lowered and then does not come to its original position.
Example: A cone balanced on its top is unstable equilibrium.




3- Neutral state of Equilibrium: In equilibrium the centre of gravity of the body neither raised nor lowered when it is disturbed. Every time the centre of the gravity of body changed due to the new position of the body.
Example: If a ball is rolled on the surface of earth. The centre of the gravity of ball neither raised lowered when the ball is disturbed.

Q.4: Define Moment Arm.

Ans:  MOMENT ARM: It is the perpendicular distance between the axis of rotation and the line of the action of the forces.


Q.5: Define torque and write down its formula and unit.
Ans:TORQUE: The turning effect of a force on a body is called torque.

“OR”

&The product of force and moment arm is called torque.

Formula:

Torque = force × moment arm

τ = F × d

Unit: The unit of torque is Nm

Q. 6. Write down first condition and second condition of equilibrium.
Ans:FIRST CONDITION OF EQUILIBRIUM: The sum of all the forces acting along X- axis is zero the sum of all forces acting along Y-axis is zero.
On X-aix: If the sum of all forces acting on the body along x-axis.

∑F = 0
F_1x+ F_2x = F_3x+ F_4x
∑Fx = 0

On Y-axis: If the sum of all forces acting on the body along y-axis.

∑F = 0
F_1y+ F_2y = F_3y+ F_4y
∑Fy = 0

SECOND CONDITION OF EQUILIBRIUM: The sum of all torque acting on a body is always equal to zero.

Clockwise = anticlockwise
τ₁ + τ₂ = τ₃ + τ₄
∑ τ = 0

Q.7: Define parallel forces, like parallel forces and unlike parallel forces.
Ans:PARALLEL FORCES: When the number of forces acts on a body and if there are parallel they are called parallel forces.
LIKE PARALLEL FORCES: If two parallel forces have same direction is called like parallel force.
UNLIKE PARALLEL FORCES: If two forces have opposite direction is called unlike parallel forces.

Q.8: Prove that moments of couple is equal to the force and arm of couple.
Ans:COUPLE: A pair of equal, parallel and unlike forces having different lines of actions is called couple.
Calculation of Moment of Couple: Consider two equal unlike parallel forces, each of magnitude F, acting at A and B. The torques of moment of two forces is given by;

The moment of the force at A= F × OA

The moment of the force at B= F× OB

Both these moments have same direction i.e. counter clockwise, so the total moment of the two forces is equal to the sum of the two moments.

Moment of the Couple = F × OA + F× OB
Moment of the Couple = F (OA × OB)
Moment of the Couple = F × AB

Moment of the couple is equal to the product of one of the forces and the perpendicular distance between the lines of action of two forces this perpendicular distance between the two forces is called the arm of the couple.

Prepared by: Sir Waseem

Physics - Class X - Chapter No.5 - Questions And Answers

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VECTORS

IMPORTANT QUESTIONS OF PAST PAPERS
1. With the help of diagram define negative vector and resultant vector. ( 2017)
2. With the help of rectangular components of a derive vector equation for the resultant vector. (2016)
3. With the help of graphical method add two vector A and B. (2015)
4. Define resolution of vector and resolve of vector into its components. (2014)
5. Define vector and scalar quantities with two examples each. ( 2012)
6. Define resolution of vector and write down two formulas of rectangular components. (2011)
7. If Fx and Fy are the horizontal and vertical components of vector F, write down the formulas for F, show Fx and Fy by a diagram. (2010)
8. Define resolution of vector how is vector resolve into its components vectors. (2009)

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IMPORTANT SYMBOLS:
• Force= F
• Angle= 𝜽
• Horizontal Component= Fx
• Vertical Component= Fy

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IMPORTANT FORMULA’S:
1. F_x= F cos 𝜽
2. F_y=F Sin 𝜽

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Questions / Answers

Q.1: Define vector and scalar quantities with two examples each.
Ans:Scalar quantity: Physical quantities, which are completely specified by their magnitude only, are called scalar quantities. It is denoted by — .
Example: Time, Mass, Distance, Work, Energy, Temperature, Momentum etc.

Vector quantity: Physical quantities, which are completely specified by their magnitude and direction both, are called vector quantities. It is denoted by →.
Example: Displacement, Velocity, Acceleration, Force, Weight, Torque etc.

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Q.2: With the help of diagram define negative vector and resultant vector.
Ans: NEGATIVE VECTOR: A vector having the same magnitude as that of a given but opposite in direction is called negative of vector.
Diagram:

A    ↑ ↓  -A

2cm             2cm

RESULTANT VECTOR:  A vector which joins the tail of first vector to the head of the last vector is called the Resultant Vector.

➡️  ➡️  ➡️

R =A + B

Diagram:

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Q.3: With the help of graphical method add two vectors A and B. Describe the addition of vector by Head-To-Method.
Ans:   ADDITION OF TWO VECTOR GRAPHICALLY:

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Q. 4:  Describe subtraction of vectors.
Ans:SUBTRACTION OF VECTORS: 

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Q.5:  Define multiple of a vector with an example.
Ans:MULTIPLICATION OF VECTOR:

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Q. 6:  Define resolution of vector and resolve of vector into its components.
> Ans: RESOLUTION OF VECTORS: T
The process of splitting of a vector into parts (components) is called resolution of vector.
Explanation:   Consider a vector F, which make an angle ɵ  with x-axis represented by the line OB. From point B draw a perpendicular BA on x-axis. In this way we get two components of OA and OB. The component OA which is long x-axis is called horizontal component of vector F and denoted by F_x. the component AB which is parallel to y-axis is called vertical component of vector F and denoted by F_y.

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Q.7:   Describe addition of rectangular component of a vector and derive the expression for magnitude and direction of resultant vector?
Ans:Addition of Rectangular Components of Vector:
Rectangular components of vector (components that are perpendicular to each other) can be joining together to form resultant or original vector.

Consider right angle triangle ABC

F_x = AB = base

F_y = BC = perpendicular
F = AC = hypotenuse

FOR MAGNITUDE OF RESULTANT VECTOR:

For magnitude of vector by using Pythagoras
(H)² = (B)² + (P)²

(AC)² = (AB)² + (BC)²
 F² = (F_x)² + (F_y)²

F = F_x²+ F_y²

F = √ (F_x)² + (F_y)²
DIRECTION OF RESULTANT VECTOR:

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Prepared by: Sir  Waseem