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Download Think and Learn | Std. 4 & 5 APK Full | myboat044 boatplans NCERT Solutions for Class 10 Maths Chapter 2; NCERT Solutions for Class 10 Maths Chapter 3 If the rational number is represented by the ratio p/q, then q must be a non-zero integer. every integer is a rational number. In rational numbers class 8 covers all the concepts and the arithmetic operations and properties involved on rational. NCERT Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities. NCERT Solutions for Class 8 CBSE Maths Chapter 9, explains basic concepts like terms, factors, coefficients, like and unlike terms, addition and subtraction of algebraic expressions, and multiplication of two or . Access Answers of Maths NCERT Class 10 Chapter 8 � Introduction to Trigonometry Exercise 1. Evaluate the following: (i) sin 60� cos 30� + sin 30� cos 60� (ii) 2 tan 2 45� + cos 2 30� � sin 2 Solution: (i) sin 60� cos 30� + sin 30� cos 60� First, find the values of the given trigonometric ratios. sin 30� = 1/2. cos 30� = v3/2. sin 60� = 3/2.
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What does the slope of this line indicate? Answer The graph represents the motion with uniform acceleration, and the slope gives the acceleration of the moving body. How will the equation of motion for an object moving with a uniform velocity changes? Answer Uniform velocity means acceleration is zero.

A body moves in a circle of radius 2R. What is the distance covered and displacement of the body after 2 complete rounds? An athlete runs along a circular track of radius 2R. What is his displacement after covering half a round? Find its average velocity. Give S. What remains constant in a uniform circular motion? Answer The speed of the body remains constant. Which quantity is given by the area under velocity time-graph?

Answer It gives the displacement of the object in the given time interval. Why is uniform circular motion called accelerated motion? Answer Uniform circular motion is called accelerated motion because of its velocity changes at every point of motion due to change in its direction. Can a body be at rest and in motion, at the same time? Answer Yes, a body can be at rest with respect to one reference point and at motion with respect to some other reference point.

There are three solids made up of aluminium, steel and wood of the same shape and same volume. Which of them would have the highest inertia and why?

Answer The density of steel is more than that aluminium and wood. So, its mass is greater than the solids made of aluminium and wood. Inertia depends on the mass of the object. Hence, steel has a higher inertia. What do you mean by momentum? Write its S. Answer The momentum of a body is equal to the vector product of mass m and the velocity v of the body.

Which physical quantity corresponds to the rate of change of momentum? Answer A rate of change of momentum is directly proportional to force. So, it corresponds to the force. A horse continuously to apply force in order to move a cart, with a constant velocity. Answer The cart will move with a constant velocity if and only if no external force acts on it.

When the horse applies the force, the frictional force also acts between the wheels of the cart and road to oppose the motion. The cart will move with constant velocity, only if the force applied by the horse is equal to the frictional force. What is a net force acting on a body moving with a constant velocity? Answer As there is no acceleration, the net force on it is zero. Answer As we know that it is very difficult to change the state of rest or of uniform motion of a heavier body than that of a lighter one.

So, mass is a measure of inertia. A body is acted upon by two forces, but it does not move. Answer a The two forces must be equal in magnitude and in opposite direction. So, they balance each other. As there is no unbalanced force, the body does not move. Under what condition a body moves with uniform velocity?

Answer When forces acting on the body are balanced and no unbalanced force acts on it. Why do action and reaction not cancel each other? Answer Action and reaction do not cancel each other, because they act on different bodies. Name the principle on which a rocket works. Answer Law of conservation of momentum.

Calculate the mass of the body, when a force of N produces an acceleration of 3. State action and reaction in the case, when a bullet is fired from the gun. Answer Action � Force exerted on the bullet. Reaction � Force exerted on the gun. Why do we slip on a rainy day? Answer During rainy days, the wet ground becomes very smooth. The friction between our feet and the ground is reduced to the maximum. Thus, we slip.

Answer First Law of Motion: Its states that a body at rest will remain at rest and a body in motion will continue in motion in a straight line with uniform speed unless it is compelled by some external force to change its state of rest or of uniform motion.

Example: When a bus starts moving all of a sudden, the head of the passenger sitting in the bus strikes the back of his seat. This can be explained on the Byjus Class 9 Maths Notes Zero basis of the first law of motion. The lower part of the body of the passenger remains in contact with the body of the bus, but the upper part is free. Similarly, we can explain the jerking of passengers in the forward direction of a bus, when the moving bus stops all of a sudden.

Answer Third law of motion: It states that to every action, there is an equal and opposite reaction. Action and reaction always operate on different bodies. Example: When a man jumps from a boat on to the bank of a river, then he pushes the boat behind with his leg action and the boat pushes reaction the man in the opposite direction.

Because of this, the man move towards the bank of the river and the boat moves away from the bank in the opposite direction.

Why does a gun give a jerk to shoulder of the gunman, on firing a bullet from the gun? Answer When a bullet is fired from a gun, the force sending the bullet forward action is equal to the force sending the gun backward reaction. But the mass of the gun is more than the mass of a bullet, so it moves only a little distance backwards and gives a backward jerk on the shoulder of the gunman.

Why does a man slip when his footfalls on a banana skin, lying on road? Answer A man walks easily on the road because there is friction between foot and the ground. A man slips when his footfalls on a banana skin lying on the road due to the absence of friction. Why is it advised to tie luggage kept on the roof of a bus with a rope? Luggage on the top of the bus is not a compact part of the bus.

When a moving bus takes a sharp turn or suddenly applies brakes to stop, the luggage placed loosely on the roof of the bus continues moving forward inertia of motion and is likely to fall off the bus. Conversely, if a stationary bus accelerates suddenly, the luggage tends to remain in the same state inertia of rest and hence slides backward To avoid falling of luggage off the bus, it is advised to tie it with a rope. Why does a gun recoil when a bullet is fired? Calculate the velocity of recoil of the gun.

Or When the bullet is fired from a gun, the gun gives a kick in the backward direction. Answer When the bullet is fired from a gun the gun gives a kick in the backward direction. The reason behind is the force exerted on the bullet, known as a reaction.

Since the mass of gun is large than the mass of a bullet, so the gun recoil with a velocity much lesser than the velocity with which the bullet moves forward.

A bullet shot with high velocity pierces through a window pane, whereas, the pane is shattered by a pebble thrown at it. Answer A bullet moving with high velocity has a large momentum.

When it strikes the window pane, the velocity decreases and momentum reduces to a very small value. This sudden change in momentum exerts a large impulsive force enough to pierce through the window pane, making a hole. On the other hand, the velocity of a pebble thrown at it is not very high, its momentum is less.

Discuss the factors on which buoyant force depends. Explain the law of floatation of bodies in a liquid. Answer a The upward force exerted by a liquid on the body, immersed in the liquid is known as the upthrust or buoyant force. Buoyant force acting on a body depends on the volume of the body submerged in the liquid and the density of the liquid in which the body is immersed. According to him, when a body is wholly or partially immersed in a liquid at rest, it experiences an upthrust, equal to the weight of the liquid displaced by the body.

Give a reason for the following: a The cork floats while the nail sinks when both are placed on the surface of the water. Answer a The density of cork is less than that of water, whereas the density of a nail is greater than that of water. A substance whose density is less than a liquid will float on the surface of that liquid.

Thus, a cork floats in water. On the other hand, a substance whose density is greater than that of a liquid will sink in that liquid. Thus, a nail sinks in water. Due to greater pressure, the sand under pencil-heeled shoe sinks in greater depth and therefore, it is difficult to walk with a pencil- heeled shoe on the sand. On the other hand, flat shoes exert less pressure and do not sink down in the sand.

Answer Uniform motion-If an object travels an equal distance in equal intervals of time, then the motion of the object is said to be uniform motion. Draw two lines OX and OY at right angles. Show the above data on the graph. We get a straight line OP which represents uniform motion.

Non-uniform Motion: If an object travels unequal distance in equal time intervals, then the motion of the object is said to be non-uniform motion. For Example, A car is in motion with unequal speed, then the distances covered per second will be unequal. The distances travelled by car per second are as follows:. If a graph is drawn between distance and time, then we get a curved line graph. The graph shows a non-uniform motion. If the slope increases, then it shows increasing speed.

If the slope decreases, then it shows decreasing speed. State the law of action and reaction. Explain with a suitable and necessary diagram that. Answer When a force acts on a body, then it is called the action. The force produced as a result of action acts on another object but in opposite direction is called reaction.

According to this law, for every action, there is an equal and opposite reaction. Action and reaction always operate on different objects but in opposite directions. Experiment: Take an oil funnel and fill half of it with water and fix it on a small boat, as shown in the figure. The funnel is heated at the bottom with the help of a lamp. When steam begins to come out from the jet fastly, the boat experiences a force in a backward direction, and it begins to move in a direction opposite to the direction of the outgoing steam the body.

It can also be stated as: The rate of change of momentum is equal to the force applied to the body and the change in momentum always takes place in the direction of the force. From this experiment, it is clear that the force action due to the outgoing steam acts in a forward direction and force of reactions acts, i. This proves that action and reaction act on two different objects. If a displacement of 1m is produced by a force of 1N acting in the direction of displacement then the work done by the force is 1J.

For example, when you push a wall with a force F, then the displacement of the wall is zero. Therefore, the work done by force F on the wall is zero. When you sit on a chair and prepare a lesson in two hours, you may feel tired. But according to physics, no work is done. Therefore, work done by you on the briefcase is zero. Let us consider a body A lying on a smooth horizontal surface. A constant force F acts at an angle q to the horizontal.

The body is displaced through distance in the horizontal direction. Here the complete force F is not responsible to displace the body. A part of the force acting in the direction of displacement Byjus Class 9 Maths Icse Zero is responsible for displacing the body. This horizontal part is F cos q. Work done in this case is defined as 'work done by a constant force acting at an angle to the displacement is the product of component of force in the direction of displacement and the displacement of the body'.

Work done is maximum when force acts in the direction of displacement. Case-1 : Work done is positive when q is acute. This happens when force acts in the direction of displacement. Therefore, work done by centripetal force is zero. When a coolie moves on a horizontal surface, he applies a force on the load kept on his head in vertically upward direction.

Therefore, work done by the force applied by coolie is zero. Work done by the centripetal force which is the gravitational pull of sun on earth acting on earth is zero. Because centripetal force is perpendicular to the displacement. A block A is pushed by the force F and displaced through s. Work done by applied force,. When a car runs, the engine of the car generates a force which displaces the car. In other words, work is done by the car.

This work is done on the expense of fuel. Fuel provides the energy needed to run the car. Had the petrol tank been empty, car could not be run. The conclusion is that, if there is no source of energy, no work will be done.

Let us take another example. Suppose a lift takes some persons from ground floor to second floor. Then the lift performs work. If you enquire, you will find that the lift is operated by an electrical motor. Thus, electrical energy does the work. If there is no electricity the lift will not operate. Again if there is no source of energy, no work will be done. The above statement is not just true for the above two examples, but is true for all processes. Therefore, energy is defined as the capacity to do work.

The S. Nature has been very kind to us in providing us energy in various forms. These forms of energy are as follows. Solar energy. The energy radiated by the Sun is called solar energy. Plants collect and store this energy to make food through photosynthesis. Heat energy. It is the energy released when coal, oil, gas or wood burn and it produces in us the sensation of warmth.

Light energy. It is the form of energy which produces in us the sensation of light. Sun is the natural source of light. Chemical energy. It is the energy possessed by fossil fuels coal; petroleum and natural gas and is also called the fuel energy. The food that we eat has chemical energy Byjus Maths Class 7 Chapter 8 Zero stored in it. Hydro energy. The energy possessed by water flowing in rivers and streams is called hydro energy. This energy is used to generate electricity in hydroelectric power plants.

Wind energy. The energy possessed by moving air is called wind energy. Ocean thermal energy OTE. Solar energy stored in the oceans in the form of heat is called ocean thermal energy. Geothermal energy. It is the heat energy of the Earth and is found within rock formations and the fluids held within those formations.

Biomass energy. It is the energy obtained from biomass i. Tidal energy. It is the energy derived from the rising and falling ocean tides. Sound energy. It is the energy possessed by vibrating objects and it produces in us the sensation of hearing. Mechanical energy. It is the energy possessed by a body due to its position or configuration or motion. The energy possessed due to position or configuration is called potential energy and that due to motion is called kinetic energy.

The sum of these two energies is called the mechanical energy. Electric energy. The energy possessed by charges either at rest or in motion is called electric energy. Magnetic energy. It is the energy possessed by magnetised bodies e. Electromagnetic energy. It is the general name for electric and magnetic energies.

Nuclear energy. The energy produced in the processes of fission and fusion is called nuclear energy. A moving object is capable of doing work because of it" motion. Hence, we say that the object has kinetic energy.

Hence, kinetic energy means energy due to motion. The energy is stored in the object when work is done to change its velocity from a lower value to a higher value, or from rest to certain velocity. Kinetic energy of an object is defined as the energy which it possesses by virtue of its motion, and is measured by the amount of work that the object can do against an opposing force before it comes to rest.

Kinetic energy of an object moving with a certain velocity is equal to the work done on it to enable it to acquire that velocity. A ball rolling on a surface because it can set another ball into motion by striking it. A bullet fired from a gun as it is able to penetrate some distance into a target which it strikes. A tarpedo in motion as it can do work by penetrating into the side' of a ship. A fast wind as it can set a boat in motion when striking against its sail.

A moving hammer as it drives a nail into a wall against the resistance offered to it by the wall. What is the total number of workers having daily income less than ? What is the total number of workers having daily income more than ? What is the total number of workers having daily income between ? Cards marked with numbers 1 to 25 are placed in the box and mixed thoroughly.

One card is drawn at random from the box. Answer the following questions Q11 � Q20 :. What is the probability of getting number 5? What is the probability of getting number less than 11? What is the probability of getting number greater than 25?

What is the probability of getting a multiple of 5? What is the probability of getting an even number? What is the probability of getting an odd number? What is the probability of getting a prime number? What is the probability of getting a number divisible by 3? What is the probability of getting a number divisible by 4? What is the probability of getting a number divisible by 7?

The information collected in terms of number is called �������. Data available in an unorganized form is called �������� data.




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