Physics numericals

 (i) Asteroids Asteroids are small heavenly bodies which orbit round the Sun between the orbits of Mars and Jupiter. They are the pieces of much larger planet which broke up due to the gravitational effect of Jupiter. About 1600 asteroids are revolving around the Sun. The largest among them has a diameter of about 700 km is called Ceres. It circles the Sun once in every 4½ years. (ii) Comets A comet consists of a small mass of rock−like material surrounded by large masses of substances such as water, ammonia and methane. These substances are easily vapourised. Comets move round the Sun in highly elliptical orbits and most of the time they keep far away from the Sun. As the comet approaches the Sun, it is heated by the Sun’s radiant energy and vapourises and forms a head of about 10000 km in diameter. The comet also develops a tail pointing away from the Sun. Some comets are seen at a fixed regular intervals of time. Halley’s comet is a periodic comet which made its appearance in...

The ratio of the amount of solar energy reflected by the planet to that incident on it is known as albedo. From the knowledge of albedo, we get information about the existence of atmosphere in the planets. The albedo of Venus is 0.85. It reflects 85% of the incident light, the highest among the nine planets. It is supposed to be covered with thick layer of atmosphere. The planets Earth, Jupiter, Saturn, Uranus and Neptune have high albedoes, which indicate that they possess atmosphere. The planet Mercury and the moon reflect only 6% of the sunlight. It indicates that they have no atmosphere, which is also confirmed by recent space probes. There are two factors which determine whether the planets have atmosphere or not. They are (i) acceleration due to gravity on its surface and (ii) the surface temperature of the planet. The value of g for moon is very small (¼th of the Earth). Consequently the escape speed for moon is very small. As the average velocity of the atmospheric air molecul...

Television pictures and photographs show astronauts and objects floating in satellites orbiting the Earth. This apparent weightlessness is sometimes explained wrongly as zero–gravity condition. Then, what should be the reason? Consider the astronaut standing on the ground. He exerts a force (his weight) on the ground. At the same time, the ground exerts an equal and opposite force of reaction on the astronaut. Due to this force of reaction, he has a feeling of weight. When the astronaut is in an orbiting satellite, both the satellite and astronaut have the same acceleration towards the centre of the Earth. Hence, the astronaut does not exert any force on the floor of the satellite. So, the floor of the satellite also does not exert any force of reaction on the astronaut. As there is no reaction, the astronaut has a feeling of weightlessness.

(i) Satellite communication Communication satellites are used to send radio, television and telephone signals over long distances. These satellites are fitted with devices which can receive signals from an Earth – station and transmit them in different directions. (ii) Weather monitoring Weather satellites are used to photograph clouds from space and measure the amount of heat reradiated from the Earth. With this information scientists can make better forecasts about weather. Youmight have seen the aerial picture of our country taken by the satellites, which is shown daily in the news bulletin on the television and in the news papers. (iii) Remote sensing Collecting of information about an object without physical contact with the object is known as remote sensing. Data collected by the remote sensing satellities can be used in agriculture, forestry, drought assessment, estimation of crop yields, detection of potential fishing zones, mapping and surveying. (iv) Navigat...

Galileo was the first to make a systematic study of the motion of a body under the gravity of the Earth. He dropped various objects from the leaning tower of Pisa and made analysis of their motion under gravity. He came to the conclusion that “in the absence of air, all bodies will fall at the same rate”. It is the air resistance that slows down a piece of paper or a parachute falling under gravity. If a heavy stone and a parachute are dropped where there is no air, both will fall together at the same rate. Experiments showed that the velocity of a freely falling body undergravity increases at a constant rate. (i.e) with a constant acceleration. The acceleration produced in a body on account of the force of gravity is called acceleration due to gravity. It is denoted by g. At a given place, the value of g is the same for all bodies irrespective of their masses. It differs from place to place on the surface of the Earth. It also varies with altitude and depth. The value of g at sea−lev...

According to Newton’s third law of motion, for every action there is an equal and opposite reaction. The equal and opposite reaction to the centripetal force is called centrifugal reaction, because it tends to take the body away from the centre. In fact, the centrifugal reaction is a pseudo or apparent force, acts or assumed to act because of the acceleration of the rotating body. In the case of a stone tied to the end of the string is whirled in a circular path, not only the stone is acted upon by a force (centripetal force) along the string towards the centre, but the stone also exerts an equal and opposite force on the hand (centrifugal force) away from the centre, along the string. On releasing the string, the tension disappears and the stone flies off tangentially to the circular path along a straight line as enuciated by Newton’s first law of motion. When a car is turning round a corner, the person sitting inside the car experiences an outward force. It is because of the fac...

Newton’s first law of motion deals with the behaviour of objects on which all existing forces are balanced. Also, it is clear from the first law of motion that a body in motion needs a force to change the direction of motion or the magnitude of velocity or both. This implies that force is such a physical quantity that causes or tends to cause an acceleration. Newton’s second law of motion deals with the behaviour of objects on which all existing forces are not balanced. According to this law, the rate of change of momentum of a body is directly proportional to the external force applied on it and the change in momentum takes place in the direction of the force. The force acting on a body is measured by the product of mass of the body and acceleration produced by the force acting on the body. The second law of motion gives us a measure of the force. The acceleration produced in the body depends upon the inertia of the body (i.e) greater the inertia, lesser the acceleration. One newton...

Various philosophers studied the basic ideas of cause of motion. According to Aristotle, a constant external force must be applied continuously to an object in order to keep it moving with uniform velocity. Later this idea was discarded and Galileo gave another idea on the basis of the experiments on an inclined plane. According to him, no force is required to keep an object moving with constant velocity. It is the presence of frictional force that tends to stop moving object, the smaller the frictional force between the object and the surface on which it is moving, the larger the distance it will travel before coming to rest. After Galileo, it was Newton who made a systematic study of motion and extended the ideas of Galileo. Newton formulated the laws concerning the motion of the object. There are three laws of motion. A deep analysis of these laws lead us to the conclusion that these laws completely define the force. The first law gives the fundamental definition of force; the seco...

A body thrown with some initial velocity and then allowed to move under the action of gravity alone, is known as a projectile. If we observe the path of the projectile, we find that the projectile moves in a path, which can be considered as a part of parabola. Such a motion is known as projectile motion. A few examples of projectiles are (i) a bomb thrown from an aeroplane (ii) a javelin or a shot-put thrown by an athlete (iii) motion of a ball hit by a cricket bat etc. (i) It can be projected horizontally from a certain height. (ii) It can be thrown from the ground in a direction inclined to it. The projectiles undergo a vertical motion as well as horizontal motion. The two components of the projectile motion are (i) vertical component and (ii) horizontal component. These two perpendicular components of motion are independent of each other. A body projected with an initial velocity making an angle with the horizontal direction possess uniform horizontal velocity and variable vertic...

A study of motion will involve the introduction of a variety of quantities, which are used to describe the physical world. Examples of such quantities are distance, displacement, speed, velocity, acceleration, mass, momentum, energy, work, power etc. All these quantities can be divided into two categories – scalars and vectors. The scalar quantities have magnitude only. It is denoted by a number and unit. Examples : length, mass, time, speed, work, energy,temperature etc. Scalars of the same kind can be added, subtracted, multiplied or divided by ordinary laws. The vector quantities have both magnitude and direction. Examples: displacement, velocity, acceleration, force, weight, momentum, etc.

Mechanics is one of the oldest branches of physics. It deals with the study of particles or bodies when they are at rest or in motion. Modern research and development in the spacecraft design, its automatic control, engine performance, electrical machines are highly dependent upon the basic principles of mechanics. Mechanics can be divided into statics and dynamics. Statics is the study of objects at rest; this requires the idea of forces in equilibrium. Dynamics is the study of moving objects. It comes from the Greek word dynamis which means power. Dynamics is further subdivided into kinematics and kinetics. Kinematics is the study of the relationship between displacement, velocity, acceleration and time of a given motion, without considering the forces that cause the motion. Kinetics deals with the relationship between the motion of bodies and forces acting on them. We shall now discuss the various fundamental definitions in kinematics. Particle A particle is ideally just a piece ...

The uncertainity in the measurement of a physical quantity is called error. It is the difference between the true value and the measured value of the physical quantity. Errors may be classified into many categories. (i) Constant errors It is the same error repeated every time in a series of observations. Constant error is due to faulty calibration of the scale in the measuring instrument. In order to minimise constant error, measurements are made by different possible methods and the mean value so obtained is regarded as the true value. (ii) Systematic errors These are errors which occur due to a certain pattern or system. These errors can be minimised by identifying the source of error. Instrumental errors, personal errors due to individual traits and errors due to external sources are some of the systematic errors. (iii) Gross errors Gross errors arise due to one or more than one of the following reasons. (1) Improper setting of the instrument. (2) Wrong recordin...

 The digits which tell us the number of units we are reasonably sure of having counted in making a measurement are called significant figures. Or in other words, the number of meaningful digits in a number is called the number of significant figures. A choice of change of different units does not change the number of significant digits or figures in a measurement. For example, 2.868 cm has four significant figures. But in different units, the same can be written as 0.02868 m or 28.68 mm or 28680 µm. All these numbers have the same four significant figures. From the above example, we have the following rules. i) All the non−zero digits in a number are significant. ii) All the zeroes between two non−zeroes digits are significant, irrespective of the decimal point. iii) If the number is less than 1, the zeroes on the right of decimal point but to the left of the first non−zero digit are not significant. (In 0.02868 the underlined zeroes are not significant). iv) The zeroes at the en...

All measurements are made with the help of instruments. The accuracy to which a measurement is made depends on several factors. For example, if length is measured using a metre scale which has graduations at 1 mm interval then all readings are good only upto this value. The error in the use of any instrument is normally taken to be half of the smallest division on the scale of the instrument. Such an error is called instrumental error. In the case of a metre scale, this error is about 0.5 mm. Physical quantities obtained from experimental observation always have some uncertainity. Measurements can never be made with absolute precision. Precision of a number is often indicated by following it with ± symbol and a second number indicating the maximum error likely. For example, if the length of a steel rod = 56.47 ± 3 mm then the true length is unlikely to be less than 56.44 mm or greater than 56.50 mm. If the error in the measured value is expressed in fraction, it is called fractional e...

. The units named after scientists are not written with a capital initial letter. For example : newton, henry, watt 2. The symbols of the units named after scientist should be written by a capital letter. For example : N for newton, H for henry, W for watt 3. Small letters are used as symbols for units not derived from a proper name. For example : m for metre, kg for kilogram 4. No full stop or other punctuation marks should be used within or at the end of symbols. For example : 50 m and not as 50 m. 5. The symbols of the units do not take plural form. For example : 10 kg not as 10 kgs 6. When temperature is expressed in kelvin, the degree sign is omitted. For example : 273 K not as 273o K (If expressed in Celsius scale, degree sign is to be included. For example 100o C and not 100 C) 7. Use of solidus is recommended only for indicating a division of one letter unit symbol by another unit symbol. Not more than one solidus is used. For example : m s−1 or m / s, J / K mol or J K–1 mol–1...

Physics can also be defined as the branch of science dealing with the study of properties of materials. To understand the properties of materials, measurement of physical quantities such as length, mass, time etc., are involved. The uniqueness of physics lies in the measurement of these physical quantities.  Fundamental quantities and derived quantities Physical quantities can be classified into two namely, fundamental quantities and derived quantities. Fundamental quantities are quantities which cannot be expressed in terms of any other physical quantity. For example, quantities like length, mass, time, temperature are fundamental quantities. Quantities that can be expressed in terms of fundamental quantities are called derived quantities. Area, volume, density etc. are examples for derived quantities. To measure a quantity, we always compare it with some reference standard. To say that a rope is 10 metres long is to say that it is 10 times as long as an object whose len...

Sir Issac Newton was the first one to give an exact definition for force. “Force is the external agency applied on a body to change its state of rest and motion”. There are four basic forces in nature. They are gravitational force, electromagnetic force, strong nuclear force and weak nuclear force. Gravitational force It is the force between any two objects in the universe. It is an attractive force by virtue of their masses. By Newton’s law of gravitation, the gravitational force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. Gravitational force is the weakest force among the fundamental forces of nature but has the greatest large−scale impact on the universe. Unlike the other forces, gravity works universally on all matter and energy, and is universally attractive. Electromagnetic force It is the force between charged particles such as the force between two electrons, or the force between ...

Technology is the application of the doctrines in physics for practical purposes. The invention of steam engine had a great impact on human civilization. Till 1933, Rutherford did not believe that energy could be tapped from atoms. But in 1938, Hann and Meitner discovered neutron-induced fission reaction of uranium. This is the basis of nuclear weapons and nuclear reactors. The contribution of physics in the development of alternative resources of energy is significant. We are consuming the fossil fuels at such a very fast rate that there is an urgent need to discover new sources of energy which are cheap. Production of electricity from solar energy and geothermal energy is a reality now, but we have a long way to go. Another example of physics giving rise to technology is the integrated chip, popularly called as IC. The development of newer ICs and faster processors made the computer industry to grow leaps and bounds in the last two decades. Computers have become affordable now due t...

The word science comes from a Latin word “scientia” which means ‘to know’. Science is nothing but the knowledge gained through the systematic observations and experiments. Scientific methods include the systematic observations, reasoning, modelling and theoretical prediction. Science has many disciplines, physics being one of them. The word physics has its origin in a Greek word meaning ‘nature’. Physics is the most basic science, which deals with the study of nature and natural phenomena. Understanding science begins with understanding physics. With every passing day, physics has brought to us deeper levels of understanding of nature. Physics is an empirical study. Everything we know about physical world and about the principles that govern its behaviour has been learned through observations of the phenomena of nature. The ultimate test of any physical theory is its agreement with observations and measurements of physical phenomena. Thus physics is inherently a science of measurement...