2d shapes

DeviationA ray of light of a single colour incident on an equilateral glass prism is refracted towards the normal N| and travels through the glass at reduced speed. When it emerges into the air it is refracted away from the normal N2 and speeds up again. The ray has been deviated from its original direction; the angle of deviation D is the angle between the original and final directions, as shown in Fig. 17.1. The three prisms in Fig. 17.2(a) have been placed so that they 'deviate' three parallel rays to a single point F. A converging (convex) lens can be thought to consist of a set of differently shaped prisms. In Fig. 17.2(b) rays of light from a point O are deviated by the different sections of the lens to form a real image at 1. This is covered in greater detail in Chapter 18, p.221.

elasticity formula

One Mark Questions With Answers1. What is a rigid body ?A body which experiences a small deformation when a sufficiently large force is applied is considered to be rigid.2. When is a body said to be perfectly elastic ?A body is said to be perfectly elastic if it tends to resist deformation. It recovers completely from the deformation once the deforming force is removed.3. When is a body said to be perfectly plastic ?If a body does not recover its original state when the external force is removed but retains its altered state, it is said to be perfectly plastic.4. Define stress.When an external force F is applied uniformly over a surface of area A then the force per unit area is called stress. (Stress = F/A)5. Define strain.The fractional change in the dimension of a body produced by the external force acting on itis known as strain.6. What is the SL unit of stress ?SI unit of stress is Nm~2.7. What is the dimensional formula for stress ?[stress] = [M'L-'r2]8. What is the SI unit of strain ?Strain has no unit.9. State Hooke's law.The law states that, provided the strain is small stress is directly proportional to strain.10. Define coefficient of elasticity.It is the ratio of stress to strain.11. Define Young's modulus.It is the ratio of stress to longitudinal strain.12. What is the SI unit of Young's modulus ?SI unit of Young's modulus is Nm~2.13. What is the dimensional formula for Young's modulus.[Young's modulus] = [M1 L_1T~2]14. Define Rigidity modulus.Rigidity modulus is defined as the ratio of tangential stress to shearing strain.15. What is the SI unit of* Rigidity modulus ?SI unit of rigidity modulus is Nnr2.16. Define Bulk modulus.It is the ratio of stress to volume strain.17. What is the SI unit of bulk modulus.SI unit of bulk modulus is Mm"2.18. What is the dimensional formula of Bulk modulus.[Bulk modulus] = [MW2] Two Marks Questions1. What is elasticity ?2. Distinguish between elastic and plastic materials.3. State and explain Hooke's law.4. Define stress and strain.5. Explain why a rubber tube is longer when suspended vertically than when placed horizontally on a table.6. If the stress to which a wire is subjected is equal to the Young's modulus of its material, find the relation between the initial and final lengths of the wire.Five Marks Questions1. State and explain Hooke's law. Explain the terms elastic limit, yield point and breaking stress.2. Define the three moduli of elasticity. What is the SI unit of the modulus of elasticity ?3. Explain the terms stress and strain.

discovery of oxygen

Q. 8. How Thomson discovered 'isotopes' from the analysis of positive rays ? How did it clear the anomaly of fractional atomic masses? (1996, 98)Or How are the isotopes discovered with the help of analysis of the properties of positive rays? (2001,02)Ans. Isotopes : The atoms having different masses but possessing same atomic numbers (or same chemical properties) are called isotopes.Discovery of Isotopes : When Thomson was studying the mass spectrograph of neon gas, he found two parabolas. He explained this fact by saying that the neon gas contains two kinds of atoms which can not be separated chemically, meaning that, they possess same chemical properties or same atomic number but thier ions have different values of e/M. That means they have different masses. For the first time he used the word 'isotopes' for these atoms having same atomic number but different masses. In this way, the study of positive rays lead to the discovery of isotopes.Thomson also measured the intensities of two parabolas and stated that, the two isotopes of neon having atomic masses 20 and 22 are present in the neon in the ratio of 9:1. Therefore, average atomic mass of neon is given by9x20 + 1x22 =2Qi 2 9 + 1Thus discovery of isotopes in neon also cleared the anomaly of fractional atomic mass of neon. Later on Aston confirmed the existence of isotopes in chlorine also.

define pitch

The following are associated with musical notes: A amplitude B intensity C pitchD timbre (quality) E speed.Which of the above Q1 is determinedby the fundamental frequency of the note?Q2 is determined by the presence of overtones? Q3 is constant for all sounds produced by an orchestra? Q4 can be used to distinguish between different musical instruments? (L). Questions 5-8The diagrams which follow show the waveforms of five musical notes displayed successively on a cathode ray oscilloscope without adjusting its controls.Which waveform shows Q5 the note with the greatest number of overtones? Q6 the note of largest amplitude? Q7 the note with the highest pitch? Q8 the note with the lowest frequency? (L)Q9 (a) Define the terms wavelength, frequency and velocity as applied to. a wave. State a relalionship between them.(b) Describe, in detail, an experiment you would carry out to measure the speed of sound in air. Explain how the result would be calculated from your measurements,(c) State two differences between an electromagnetic wave and a sound wave, both of wavelength 1 metre.(d)Name two types of electromagnetic wave with wavelengths less than 1 metre. (C)Q10 Which one of the following is not an example of a transverse wave? A a sound wave B a light waveC a wave on the surface of the bathwater D a wave on a skipping rope which is shaken E a ripple in a flag on a windy day (NEA)Qll A man sees 'steam' start to come from a factory whistle and 3 seconds later he hears the sound. The velocity of sound in air is 360 m s"1. The distance from the'man to the whistle (in metre) isA 120. B 780. C 960. D 1080 E 2160. Q12 A sonar signal (a high frequency sound wave) sent vertically downwards from a J hip is reflected from the ocean floor and detected by a microphone on the keel 0.4 s after transmission. If speed of sound in water is 1500 ms-1, what is the depth, in m, of the ocean? A 150 B 300 C 600 D 3000 E 6000 (AEB) Q13 (a) Explain the meaning of the terms amplitude and frequency <A a vibration.Describe the effect of changing these two quantifies with respect to(i) the light emitted by a lamp,(ii) the sound emitted by a source of sound.The diagram shows a vibrating tuning fork. The timeitaken for a prong to go from A to B Is s.ouuWhat is the frequency of the vibration? If the velocity of sound in air is 330 m s"1 what is the wavelength of the note emitted by the fork? (AEB}Q14 Explain the difference between longitudinal and transverse waves. Give one example of each kind of wave.Explain how waves transfer energy from one place to another.Ripples are sent across a pond and a small floating object goes up and down six times in 15 seconds. If the wave crests are 40 cm apart, calculate the speed of the waves across the pond. (WjQ15 State three similarities and three differences between the water waves on a ripple tank and sound waves in air.A set of plane waves on a ripple tank reaches a portion of the tank where the water is shallower. The boundary of _ the shallow water is at an angle of approximately 45 ° to the wave fronts. Explain, with the aid of a diagram, what happens to the waves as they enter the area of shallow water.Name two types of electromagnetic waves and explain three ways in which they differ from each other. (JMB) Q16 Describe how you would find the speed with which sound travels in air, by experiment,A radio station broadcasts on a frequency of 200 000 Hz and the wavelength of its signal is 1500 m. Calculate(a) the speed of radio waves in m s"1,(b) the wavelength of the signal of another station that broadcasts on a frequency of 1250 000 Hz.State, and explain, two differences between sound waves and light waves. (C)Q17 (a) A flexible metal strip presses lightly against the teeth of a cog wheel as it rotates uniformly at 600 revolutions per minute. If the wheel has 50 teeth find (i) the frequency, and (ii) the wavelength of the note which it emits in air, given that the speed of sound in air is 340 m s"1.If the wheel is now rotated at 300 revolutions per minute, explain whether the time taken for the sound to reach a distant observer will be charged.What will be the effect, if any, on the pitch of the note emitted if the temperature of the surrounding air now increases by several degrees, all other factors remaining unchanged? Explain your answer, (b) Explain the meaning of (i) echo, and (ii) resonance. Describe in detail how one of these two phenomena can be used to determine the speed of sound in air. (L) Q18 A wheel has 50 spokes and rotates at 10 revolutions per second. Calculate the frequency of the note obtained by holding a card lightly against the spokes as they rotate. What would you expect to observe if a source of sound of frequency 502 Hz was placed near the card?Describe briefly how you would use a stroboscope to check the rate of rotation of the wheel. (S)

binary number converter

26. What is an ideal gas ?A gas which obeys Boyle's law and Charle's law at all temperatures and pressures is called an ideal gas or a perfect gas.27. Write down the perfect gas equation.PV = RT for 1 mole of a gasPV = nRT for n moles of a gas where R is the universal gas constant.28. Give the SI unit of R. It is J moP1 K"1.29. Why gas laws are generally expressed with reference to absolute scale of temperature ?This is because of simplicity in their mathematical forms.30. Give the relation connecting gas constant(/?), Avogadro's number (A^) and the Boltzmann constant (fc)R = KNa)31. A sample of an ideal gas occupies a volume V at a pressure P and absolute temperature 7*. The mass of each molecule is m. If k be the Boltzmann constant then what is the expression for the density p of the gas ?32. Give the dimensional formula of gas constant R.[R] = [ML2T"V2]33. What is an isothermal process ?An isothermal process is origin which the changes in pressure and volume of a given mass of gas take place at constant temperature.34. Which gas law holds good for an isothermal change ? Boyle's law35. What is an adiabatic process ?An adiabatic process is one in which the changes in volume and pressure of a given mass of gas take place such that heat is neither allowed to enter nor leave the gas.36. Will temperature remain constant in an adiabatic change ? \ No. Temperature of the gas undergoes a change. \37. Give an equation which represents an adiabatic change. \ PVy = constant where y = C /C . ■' \' p V \38. What is an isothermal ?A graph of pressure (P) versus Volume (V) for an isothermal process is called an isothermal.39. What is an adiabatic curve ?A graph of pressure (P) versus Volume (V) for an adiabatic process is called an adiabatic curve.40. Isothermals at two different temperatures Tl and T2 of an ideal gas are as shown in the figure. What is the relation between Ty and T2 ?T > T2 V(v Temperature of the isothermal farthest from the origin will be maximum.)41. If an isothermal and an adiabatic curve are drawn on the same scale for the same initial state of a gas, which curve will have a greater slope ?The adiabatic curve is steeper than the isothermal curve. That is, adiabatic curve will have a greater slope.42. Write the equation of state for an ideal gas. PV = nRT for n mole of an ideal gas.43. Write Vander Waal's equation of state applicable for a real gas.P +-^r\(V-b) = nRT where a and b are constants.I V2 J44. What is the effect on the pressure of a gas if it is compressed at constant temperature ?The pressure of the gas increases according to Boyle's law.45. A gas contained in a sealed container is heated up. What is the effect on pressure ? The pressure of the gas increases according to Charle's law.46. When an automobile travels for a long distance the air pressure in the tyres increases. Give reasons.When an automobile travels along a road work is done against the frictional force between the tyres and the surface of the road. The work done is converted into heat which rises the temperature of air inside. Hence air pressure in the tyres increases.47. What is the value of molar gas constant R 1 R = 8.315 J mor'K-*.48. What is the physical significance of molar gas constant R ?It represents the work done or energy supplied in increasing the temperature of 1 mole of a gas through 1 K.49. What happens when a gas is compressed adiabatically ?In the adiabatic compression of a gas, volume decreases while pressure and temperature increase.50. What is the ratio of slope of an adiabatic curve to the slope of an isothermal curve ?Slope of isothermal curve = m, = P Slope of adiabatic curve - m2 = yP•'• m2/mi=Y Two Mark Questions1. Define volume co-efficient and pressure co-efficient of a gas.2. State and explain Boyle's law.3. State and explain Charle's law.4. Explain Kelvin scale of temperature on the basis of Charle's law.5. Why real gases deviate from ideal gases ?6. Evaluate molar gas constant R using perfect gas equation ?7. Give any two characteristics of an isothermal change.8. Give any two characteristics of an adiabatic change.9. Obtain the dimensional formula of R.10. Explain briefly Vander Waal's equation of state. Five Marks Questions1. Explain the two co-efficients of expansion of a gas.2. State Boyle's law and Charle's law. Deduce the perfect gas equation.3. Explain Charle's law and Gay Lussac's law.4. Distinguish between isothermal and adiabatic changes.

integration by parts examples

All problems given as worked examples and exercises are designed to test the understanding, application and computation skills of the students. However, the following problems are included from the point of view of a student who appears for competitive examinations like IIT, etc.

specific heat water

The standard enthalpy of formation or heat of formation of a compound is the enthalpy change accompanying the formation of one mole of a compound from its elements, all substances being in their standard states. It is denoted by ΔHof. The standard state of any substance is taken as in its natural state at 25oC under one atmospheric pressure.