Christopher Cabellon

F.Sc. Physics (Part-II) 1|Page Solved Numerical Problems Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 12: ELECTROSTATICS 12.1 Compare magnitudes of electrical and gravitational forces exerted on an object (mass = 10.0 g, charge = 20.0 µC) by an identical object that is placed 10.0 cm from the first. Given Data: Masses , Charges , Distance To Determine: ( Calculations: ) ( ( ) ) 12.2 Calculate vectorially the net electrostatic force on q as shown in the figure. Given Data: Charges , , To Determine: Total Force on ( ) Calculations: From Fig. Force Exerted by Charge on : Force Exerted by Charge on : Now And √ √ Magnitude of Resultant Force ( Direction of Resultant Force Resultant Force ⃗ ) (Resultant is along x-axis) ̂ 12.3 A point charge origin on the z-axis. is placed at the origin. Calculate electric field at a point 2.0 m from the Given Data: Charge , Direction: z-axis ̂ , Distance ̂ To Determine: Electric Field ̂ Calculations: ⃗ ( ) ̂ ( ̂) F.Sc. Physics, (1st Year), Complete Physics Notes CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-complete-physicsnotes.html 2|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 12.4 Determine the electric field at the position placed at origin. ̂ Given Data: Position Vector ̂ ̂ ̂ caused by a point charge , Charge To Determine: Electric Field ⃗ Calculations: ⃗ | | ̂ √ ̂ ̂ ̂ | | Equation (1) becomes: ⃗ ̂ ̂ 12.5 Two point charges, and justify the zero-field location. ̂ ̂ and Given Data: Charges , ̂ ̂ ̂ , are separated by a distance of 3.0 m. Find , Let Distance between Charges To Determine: Zero Field Location Calculations: Let P is zero field location, then at point P (distant x from Electric Field due to Let Distance of P from | ): Electric Field due to | | and Distance of P from | Now consider So the correct answer is 12.6 Find the electric field strength required to hold suspended a particle of mass between two plates 10.0 cm apart. Given Data: Mass , Charge and charge , Distance between Plates To Determine: Electric Field Strength Calculations: For present case: 12.7 A particle having a charge of 20 electrons on it falls through a potential difference of 100 volts. Calculate the energy acquired by it in electron volts (eV). Given Data: Charge , Potential Difference To Determine: Energy Acquired Calculations: Energy Acquired 3|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 12.8 In Millikan’s experiment, oil droplets are introduced into the space between two flat horizontal plates, 5.00 mm apart. The plate voltage is adjusted to exactly 780 V so that the droplet is held stationary. The plate voltage is switched off and the selected droplet is observed to fall a measured distance of 1.50 mm in 11.2 s. Given that the density of the oil used is 900 kg m-3, and the viscosity of air at laboratory temperature is , -2 calculate: a) The mass, and b) The charge on the droplet (Assuming g=9.8ms ) Given Data: Distance between Plates , Potential Difference Distance Covered , Time , Density , Viscosity To Determine: Mass of Droplet , Charge on Droplet Calculations: (a) Mass of Droplet Terminal Velocity For a body moving with terminal velocity: √ √ Equation (1) becomes: (b) Charge 12.9 A proton placed in a uniform electric field of 5000 NC-1 directed to right is allowed to go a distance of 10.0 cm from A to B. Calculate (a) (b) (c) (d) (e) Potential difference between the two points Work done by the field The change in P.E. of proton The change in K.E. of the proton Its velocity (mass of proton is ) Given Data: Electric Field , Distance covered Charge on proton , Mass of proton To Determine: (a) Potential Difference (d) Change in K.E. , , (b) Work Done , (c) Change in P.E. , (e) Velocity Calculations: (a) As (b) As (c) (d) By work-energy principle: √ (e) As √ √ 12.10 Using zero reference point at infinity, determine the amount by which a point charge of the electric potential at a point 1.2 m away, when (a) Charge is positive (b) Charge is negative Given Data: Charge alters , Distance To Determine: (a) Electric Potential when charge is positive (b) Electric Potential when charge is negative , , Calculations: (a) ( (b) 4|Page ) Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 12.11 In Bohr's atomic model of hydrogen atom, the electron is in an orbit around the nuclear proton at a distance of with a speed of . ( , mass of electron = ). Find (a) The electric potential that a proton exerts at this distance (b) Total energy of the atom in eV (c) The ionization energy for the atom in eV Given Data: Distance , Speed Charge of Electron , , Mass of Electron = To Determine: (a) Electric Potential due to proton , (b) Total Energy of atom (c) Ionization Energy of the atom Calculations: (a) (b) From theory of atomic spectra, the energy of electron in nth orbit: For present case , so equation (1) takes the form: ( ) (c) As electron possess 13.6 eV energy in the ground state of a H-atom. So, if we want to ionize such Hatom, we must supply 13.6 eV. Hence, the ionization energy of H-atom in ground state is 13.6 eV 12.12 The electronic flash attachment for a camera contains a capacitor for storing the energy used to produce the flash. In one such unit, the potential difference between the plates of a 750 µF capacitor is 330 V. Determine the energy that is used to produce the flash. Given Data: Potential Difference , Capacitance To Determine: Energy Calculations: As 12.13 A capacitor has a capacitance of . In the charging process, electrons are removed from one plate and placed on the other one. When the potential difference between the plates is 450 V, how many electrons have been transferred?( ) Given Data: Capacitance , Potential Difference , Charge To Determine: Total Number of Electrons Transferred Calculations: For a capacitor , From Quantization of Charges Comparing (1) and (2): F.Sc. Physics, (1st Year), Multiple Choice Questions (MCQs) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-1st-year-multiplechoice.html 5|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 13: CURRENT ELECTRICY 13.1 How many electrons pass through an electric bulb in one minute if the 300 mA current is passing through it? Given Data: Current , Time To Determine: No. of Electrons Calculations: As Current 13.2 A charge of 90 C passes through a wire in 1 hour and 15 minutes. What is the current in the wire? Given Data: Charge , Time To Determine: Current Calculations: Current 13.3 Find the equivalent resistance of the circuit (Fig.), total current drawn from the source and the current through each resistor. Given Data: emf , Resistances To Determine: (a) Equivalent Resistance (c) Current Through Calculations: (a) (a) Let As and (b) Total Current Drawn from Source , (d) Current Through is Equivalent resistance of , (e) Current Through and , , , then are connected in series, therefore: (b) Total Current Drawn from Source (c) Potential Difference across Current Through (d) Current Through (e) Current Through 13.4 A rectangular bar of iron is 2.0 cm by 2.0 cm in cross section and 40 cm long. Calculate its resistance if the resistivity of iron is 11 x 10-8 Ωm. Given Data: Cross-Sectional Area Length , , Resistivity To Determine: Resistance Calculations: As 6|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 13.5 The resistance of an iron wire at 0 C is 1x10 Ω. What is the resistance at 500 oC if the temperature coefficient of resistance of iron is 5.2 x 10-3 K-1? o 4 Given Data: Resistance at 0 , Temperature Temperature Coefficient of Resistance ̅ To Determine: Resistance of Iron at 500 oC Calculations: From definition of Temperature Coefficient of Resistance ̅ ̅ ̅ 13.6 Calculate terminal potential difference of each of cells in circuit of Fig. Given Data: emf of 1st battery nd , Internal Resistance of 1st Battery nd emf of 2 battery , Internal Resistance of 2 Battery st To Determine: (a) Terminal Potential Difference of 1 Battery , , External Resistance , nd (b) Terminal Potential Difference of 2 Battery Calculations: As , and are in series: Equivalent Resistance Effective emf Current in Circuit (a) (b) 13.7 Find the current which flows in all the resistances of the circuit of Fig. Given Data: emf of 1st battery Resistances , To Determine: (a) Current Through Calculations: Let , emf of 2nd battery and , (b) Current Through are the current through Loop-1 and Loop-2 respectively Applying KVR for Loop-1: Applying KVR for Loop-2: Putting value of from equation (1) in equation (2), we get: Putting value of in equation (1): (a) Current Through (b) Current Through 7|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 13.8 Find the current and power dissipated in each resistance of the circuit shown in the Fig. Given Data: emf of 1st battery Resistances , emf of 2nd battery , , , To Determine: (a) Current Through Resistances, (b) Power Dissipation in Resistances Calculations: Let and are the current through Loop-1 and Loop-2 respectively Applying KVR for Loop-1: Applying KVR for Loop-2: Putting value of from equation (1) in equation (2), we get: Putting this value in equation (1), we get: (a) Current Through : Current Through : Current Through : Current Through : Current Through : Current Through : (b) Power Dissipation in : Power Dissipation in : Power Dissipation in : Power Dissipation in : Power Dissipation in : Power Dissipation in : F.Sc. Physics, (1st Year), Exercise Short Questions CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/exercise-short-questions-fscphysics.html F.Sc. Physics, (2nd Year), Exercise Short Questions CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/exercise-short-questions-fscphysics_10.html 8|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 14: ELECTROMAGNETISM 14.1 Find the value of the magnetic field that will cause a maximum force of wire carrying a current of 10.0 A. Given Data: Maximum Magnetic Force on a 20.0 cm straight , Length , Current To Determine: Magnetic Field Strength Calculations: For maximum magnetic force: 14.2 How fast must a proton move in a magnetic field of weight? Given Data: Magnetic Field such that the magnetic force is equal to its , Charge of Proton , Mass of Proton To Determine: Speed of Proton Calculations: For present case: 14.3 A velocity selector has a magnetic field of 0.30 T. If a perpendicular electric field of 10,000 Vm -1 is applied, what will be the speed of the particle that will pass through the selector? Given Data: Magnetic field , Electric Field To Determine: Velocity Calculations: 14.4 A coil of 0.1 m x 0.1 m and of 200 turns carrying a current of 1.0 mA is placed in a uniform magnetic field of 0.1 T. Calculate the maximum torque that acts on the coil. Given Data: Area of Coil Current , Number of Turns , Magnetic Field To Determine: Maximum Torque Calculations: 14.5 A power line 10.0 m high carries a current 200 A. Find the magnetic field of the wire at the ground. Given Data: Distance from Ground , Current To Determine: Magnetic Field at Ground Calculations: By Ampere’s Law: F.Sc. Physics, (2nd Year), Complete Physics Notes CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-2nd-year-completephysics.html 9|Page Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 14.6 You are asked to design a solenoid that will give a magnetic field of 0.10 T, yet the current must not exceed 10.0 A. Find the number of turns per unit length that the solenoid should have. Given Data: Magnetic Field , Current , To Determine: Number of Turns per unit length Calculations: For Solenoid 14.7 What current should pass through a solenoid that is 0.5 m long with 10000 turns of copper wire so that it will have a magnetic field of 0.4 T? Given Data: Length , Number of Turns , Magnetic Field To Determine: Current Calculations: For Solenoid 14.8 A galvanometer having an internal resistance Rg = 15.0 Ω gives full scale deflection with current lg = 20.0 mA. It is to be converted into an ammeter of range 10.0 A. Find the value of shunt resistance Rs. Given Data: Internal Resistance of Galvanometer , Current Range Current for Full Scale Deflection To Determine: Shunt Resistance Calculations: For Ammeter 14.9 The resistance of a galvanometer is 50.0 Ω and reads full scale deflection with a current of 2.0 mA. Show by a diagram how to convert this galvanometer into voltmeter reading 200 V full scale. Given Data: Internal Resistance of Galvanometer , Voltage Range Current for Full Scale Deflection To Determine: Series High Resistance Calculations: For voltmeter F.Sc. Physics, (2nd Year), Multiple Choice Questions (MCQs) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-2nd-year-multiplechoice.html 10 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 14.10 The resistance of a galvanometer coil is 10.0 Ω and reads full scale with a current of 1.0 mA. What should be the values of resistances R1, R2 and R3 to convert this galvanometer into a multi-range ammeter of 100, 10.0 and 1.0 A. Given Data: Internal Resistance of Galvanometer Current for Full Scale Deflection (b) Current Range , , (a) Current Range , , (c) Current Range To Determine: (a) Shunt Resistance for 100 A Current Range (b) Shunt Resistance for 10 A Current Range , (c) Shunt Resistance for 1A Current Range Calculations: (a) (b) (c) 11 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 15: ELECTROMAGNETIC INDUCTION 15.1 An emf of 0.45 V is induced between the ends of a metal bar moving through a magnetic field of 0.22 T. What field strength would be needed to produce an emf of 1.5 V between the ends of the bar, assuming that all other factors remain the same? Given Data: Case 1: Induced emf Case 2: Induced emf , Magnetic field strength , To Determine: Magnetic field strength Calculations: For case 1: , For case 2: Dividing (1) and (2): 15.2 The flux density B in a region between the pole faces of a horse-shoe magnet is 0.5 Wbm-2 directed vertically downward. Find the emf induced in a straight wire 5.0 cm long, perpendicular to B when it is moved in a direction at an angle of 60° with the horizontal with a speed of 100 cms-1. Given Data: Flux Density Speed , Length , , Angle with Horizontal To Determine: Induced emf Calculations: Angle with B: By expression of Motional emf 15.3 A coil of wire has 10 loops. Each loop has an area of 1.5 x 10-3 m2. A magnetic field is perpendicular to the surface of each loop at all times. If the magnetic field is changed from 0.05T to 0.06 T in 0.1 s, find the average emf induced in the coil during this time. Given Data: Number of Loops Initial Magnetic Field , Area of Loop , Time , Final Magnetic Field , Angle with normal To Determine: Induced emf Calculations: Change in Magnetic Field By Faraday’s Law 15.4 A circular coil has 15 turns of radius 2 cm each. The plane of the coil lies at 40° to a uniform magnetic field of 0.2 T. If the field is increased by 0.5 T in 0.2 s, find the magnitude of the induced emf. Given Data: Number of Loops Initial Magnetic Field , Radius of Circular Loop , Final Magnetic Field , Time , Angle of plane with B: To Determine: Induced emf Calculations: Change in Magnetic Field Angle of normal to plane with B , , Area of Loop By Faraday’s Law 12 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 15.5 Two coils are placed side by side. An emf of 0.8 V is observed in one coil when the current is changing at the rate of 200 As-1 in the other coil. What is the mutual inductance of the coils? Given Data: Induced emf , Rate of Change of current To Determine: Mutual Inductance Calculations: From definition of Mutual Inductance ( ) 15.6 A pair of adjacent coils has a mutual inductance of 0.75 H. If the current in the primary changes from 0 to 10 A in 0.025 s, what is the average induced emf in the secondary? What is the change in flux in it if the secondary has 500 turns? Given Data: Mutual Inductance Time , Change of current in Primary Coil , Number of Turns of Secondary Coil To Determine: (a) Average Induced emf , (b) Change in Flux in Secondary Coil Calculations:(a) From definition of Mutual Inductance ( ( ) ) (b) By Faraday’s Law: 15.7 A solenoid has 250 turns and its self inductance is 2.4 mH. What is the flux through each turn when the current is 2 A? What is the induced emf when the current changes at 20 As-1? Given Data: Number of Turns , Self Inductance , Current , Rate of Chang of current To Determine: (a) Flux (b) Induced emf Calculations: (a) For the case of a coil: (b) As Self Inductance ( ) ( ) 15.8 A solenoid of length 8.0 cm and cross sectional area 0.5 cm2 has 520 turns. Find the self-inductance of the solenoid when the core is air. If the current in the solenoid increases through1.5A in 0.2 s, find the magnitude of induced emf in it. (µo= 4π x 10-7 WbA-1m-1) Given Data: Length of Solenoid , Number of Turns Cross-Sectional Area , Change in Current To Determine: (a) Self Inductance , Time , (b) Induced emf ( Calculations: (a) For the case of a coil: (b) As Self Inductance ( ) ( ) ) ( ) 15.9 When current through a coil changes from 100 mA to 200 mA in 0.005 s, an induced emf of 40 mV is produced in the coil. (a) What is the self-inductance of the coil? (b) Find the increase in the energy stored in the coil. Given Data: Initial Current Time , Final Current , Induced emf , , To Determine: (a) Self Inductance , (b) Increase in Energy Stored Calculations: Change in Current (a) As Self Inductance ( ) ( ) ( (b) 13 | P a g e ) [ ] Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 15.10 Like any field, the earth's magnetic field stores energy. Find the magnetic energy stored in a space where strength of earth's field is 7 x 10-5 T, if the space occupies an area of 10x108 m2 and has a height of 750 m. Given Data: Magnetic Field Strength , Area , Height To Determine: Magnetic Energy Calculations: ( ) 15.11 A square coil of side 16 cm has 200 tums and rotates in a uniform magnetic field of magnitude 0.05 T. If the peak emf is 12 V, what is the angular velocity of the coil? Given Data: Length of side of square loop Magnetic field strength , Number of turns , , Peak emf To Determine: Angular Velocity Calculations: For square As 15.12 A generator has a rectangular coil consisting of 360 turns. The coil rotates at 420 rev per min in 0.14 T magnetic field. The peak value of emf produced by the generator is 50 V. If the coil is 5.0 cm wide, find the length of the side of the coil. Given Data: Number of turns Magnetic field strength , Angular Velocity , Peak emf , , Breadth of Coil To Determine: Length of Coil Calculations: As 15.13 It is desired to make an a.c. generator that can produce an emf of maximum value 5 kV with 50 Hz frequency. A coil of area 1 m2 having 200 turns is used as armature. What should be the magnitude of the magnetic field in which the coil rotates? Given Data: Peak emf , Frequency , Area , Turn To Determine: Magnetic Field Strength Calculations: As 15.14 The back emf in a motor is 120 V when the motor is turning at 1680 rev per min. What is the back emf when the motor turns 3360 rev per min? Given Data: Case 1: Back emf , Angular Velocity Case 2: Angular Velocity To Determine: Back emf for Case-2: Calculations: For Case-1: , For Case-2: Dividing eq (1) and (2): 15.15 A D.C motor operates at 240 V and has a resistance of 0.5 Ω. When the motor is running at normal speed, the armature current is 15 A. Find the back emf in the armature. Given Data: Operating Voltage , Resistance , Current To Determine: Back emf Calculations: As 14 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 15.16 A copper ring has a radius of 4.0 cm and resistance of 1.0 mΩ. A magnetic field is applied over the ring, perpendicular to its plane. If the magnetic field increases from 0.2 T to 0.4 T in a time interval of 5 x 10-3 s, what is the current in the ring during this interval? Given Data: Radius of Ring Initial Magnetic Field , Resistance , Final Magnetic Field , Loops , Time To Determine: Current in the Loop Calculations: Change in Magnetic Field , Area of Loop By Faraday’s Law, Induced emf Induced Current 15.17 A coil of 10 turns and 35 cm2 area is in a perpendicular magnetic field of 0.5 T. The coil is pulled out of the field in 1.0 s. Find the induced emf in the coil as it is pulled out of the field. Given Data: Number of Turns Initial Magnetic Field , Area of Coil , Final Magnetic Field , Time To Determine: Induced emf Calculations: Change in Magnetic Field By Faraday’s Law, 15.18 An ideal step down transformer is connected to main supply of 240 V. It is desired to operate a 12 V, 30 W lamp. Find the current in the primary and the transformation ratio? Given Data: Primary Voltage , Secondary Voltage To Determine: (a) Current in Primary Coil , Output Power , (b) Transformation Ratio Calculations: (a) As for ideal transformer, (b) As Transformation Ratio F.Sc. Physics, (1st Year), Complete Physics Notes CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-complete-physicsnotes.html F.Sc. Physics, (2nd Year), Complete Physics Notes CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-2nd-year-completephysics.html 15 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 16: ALTERNATING CURRENT Q # 1. An alternating current is represented by the equation maximum and the rms value of current. . Compute its frequency and the Given Data: Equation of current To Determine: Frequency , Maximum Current , RMS Current Calculations: General Equation of A.C. Comparing eq (1) and (2), we have: i. ii. iii. √ √ Q # 2. A solenoidal A.C. has a maximum value of 15 A. What is its rms values? If the time is recorded from the instant the current is zero and is becoming positive, what is the instantaneous value of current after 1/300 s, given the frequency is 50 Hz. Given Data: Maximum Current , Time To Determine: RMS Current , Frequency , Instantaneous Alternating Current Calculations: i. √ ii. √ ( Equation of Instantaneous Alternating Current ) Q # 3. Find the values of the current and inductive reactance when A.C. voltage of 220 V at 50 Hz is passed through an inductor of 10 H. Given Data: Voltage , Frequency To Determine: Inductive Reactance , Inductance , Current Calculations: i. ii. Q # 4. An inductor has an inductance of H and resistance of . A 50 Hz A.C. is supplied to it. Calculate the reactance and impedance offered by the circuit. Given Data: Inductance , Resistance To Determine: Inductive Reactance , Frequency , Impedance Calculations: i. ii. √ 16 | P a g e √ Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems Q # 5. An inductor of pure inductance H is connected in series with a resistance of . Find (i) the peak value of current (ii) the rms value, and (iii) the phase difference between the current and the applied voltage . Given Data: Inductance , Resistance , Equation of Instantaneous Voltage To Determine: Peak Value of Current , RMS Current , Phase Difference Calculations: General Equation of Instantaneous Voltage Comparing equations (1) and (2), we have: , Inductive Reactance √ Impedance √ i. ii. √ √ ( ) iii. Q # 6. A 10 mH, ( ) coil is connected across 240 V and Given Data: Inductance Hz source. How much power does it dissipate? , Resistance , Peak Value of Voltage , Frequency To Determine: Power Dissipation Calculations: Inductive Reactance √ Impedance √ Peak Value of Current ( ) Phase Difference ( ) Power Dissipation Q # 7. Find the value of the current flowing through a capacitance when connected to a source of 150 V at 50 Hz. Given Data: Capacitance , Peak Value of Voltage , Frequency To Determine: Current Calculations: Capacitive Reactance Current Q # 8. An alternating source of emf 12 V and frequency 50 Hz is applied to a capacitor of capacitance series with a resistor of resistance of Given Data: in . Calculate the phase angle. , Frequency , Capacitance , Resistance To Determine: Phase Angle Calculations: Capacitive Reactance ( ) 17 | P a g e ( ) Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems Q # 9. What is the resonance frequency of a circuit which include a coil of inductance 2.5 H and a capacitance ? Given Data: Inductance , Capacitance To Determine: Resonant Frequency Calculations: √ √ Q # 10. An inductor of inductance be changed from to is connected in parallel with a variable capacitor whose capacitance can . Calculate the maximum frequency and minimum frequency for which the circuit can be tuned. Given Data: Inductance , Initial Capacitance , Final Capacitance To Determine: Minimum Frequency , Maximum Frequency , Calculations: 18 | P a g e √ √ √ √ Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 17: PHYSICS OF SOLIDS 17.1 A 1.25 cm diameter cylinder is subjected to a load of 2500 kg. Calculate the stress on the bar in mega pascals. Given Data: Diameter of Cylinder , Load To Determine: Stress Calculations: As ( ) 17.2 A 1.0 m long copper wire is subjected to stretching force and its length increases by 20 cm. Calculate the tensile strain and the percent elongation which the wire undergoes. Given Data: Length , Elongation To Determine: (a) , , (b) Calculations: (a) (b) 17.3 A wire 2.5 m long and cross-section area is stretched 1.5 mm by a force of 100 N in the elastic region. Calculate (i) the strain (ii) Young's modulus (iii) the energy stored in the wire. Given Data: Length , Cross-Section Area , Force Elongation To Determine: (i) (ii) (iii) Calculations: (i) ( ) (ii) ( ) ( (iii) ) 17.4 What stress would cause a wire to increase in length by 0.01% if the Young's modulus of the wire is 12 x 10 10 Pa. What force would produce this stress if the diameter of the wire is 0.56 mm? Given Data: , Young Modulus , Diameter To Determine: Force Calculations: ( ) ( ) [ ( )] ( ) ( )[ 19 | P a g e ( )] [ ][ ] Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 17.5 The length of a steel wire is 1.0 m and its cross-sectional area is . Calculate the work done in stretching the wire when a force of 100 N is applied within the elastic region. Young's modulus of steel is . Given Data: Length of wire , Cross-Sectional Area , Force To Determine: , Here ( ) Calculations: ( ) Now 17.6 A cylindrical copper wire and a cylindrical steel wire each of length 1.5 m and diameter 2.0 mm are joined at one end to form a composite wire 3.0 m long. The wire is loaded until its length becomes 3.003 m. Calculate the strain in copper and steel wires and the force applied to the wire. (Young's modulus of copper is and for steel is ). Given Data: Case 1 (Copper wire): Length Case 2 (Steel wire): Length , Diameter , Diameter Length of Composite Wire , Final Length Young Modulus for Copper , Young Modulus for Steel To Determine: (a) Strain in Copper Wire Calculations: As Elongation , (b) Strain in Steel Wire , (c) Force , For Copper wire , For Steel wire ( As both wire experience equal stress: Let ) ( ) , then Equation (3) Becomes: . Therefore, by equation (4) and (5): & (a) Strain in Copper Wire & (b) Strain in Steel Wire (c) As ( ) F.Sc. Physics, (1st Year), Multiple Choice Questions (MCQs) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-1st-year-multiplechoice.html F.Sc. Physics, (2nd Year), Multiple Choice Questions (MCQs) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-2nd-year-multiplechoice.html 20 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEMS F.Sc. Physics, Chapter # 18: ELECTRONICS 18.1 The current flowing into the base of a transistor is 100 µA. Find its collector current , its emitter current and the ratio , if the value of current gain β is 100. Given Data: Base Current , Current Gain To Determine: (a) Collector Current , (b) Emitter Current , (c) Calculations: (a) Collector Current (b) Emitter Current (c) 18.2 Fig. shows a transistor which operates a relay as the switch S is closed. The relay is energized by a current of 10 mA. Calculate the value which will just make the relay operate. The current gain β of the transistor is 200. When the transistor conducts, its can be assumed to be 0.6 V. Given Data: Collector Current , Current Gain , , To Determine: Base Resistance Calculations: As Applying KVR on input circuit: 18.3 In circuit (Fig.), there is negligible potential drop between B and E, if β is 100. Calculate i. ii. iii. iv. base current collector current potential drop across Given Data: , , To Determine: (a) base current (c) potential drop across , , (b) collector current , , , (d) Calculations: (a) Applying KVR on Input Circuit: (b) Collector Current (c) Potential Drop Across (d) Applying KVR on Output Circuit: 21 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 18.4 Calculate the output of the op-amp circuit shown in Fig. Given Data: Let , , To Determine: Output Voltage Calculations: Let , , By Kirchhoff’s Current Rule: 18.5 Calculate the gain of non-inverting amplifier shown in Fig. Given Data: Let , To Determine: Gain Calculations: For Non-Inverting Op-Amp: F.Sc. Physics, (1st Year), Complete Physics Notes CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-complete-physicsnotes.html F.Sc. Physics, (1st Year), Multiple Choice Questions (MCQs) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-1st-year-multiplechoice.html F.Sc. Physics, (1st Year), Exercise Short Questions CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/exercise-short-questions-fscphysics.html 22 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEM F.Sc. Physics, Chapter # 19: DAWN OF MODERN PHYSICS 19.1 A particle called the pion lives on the average only about when at rest in the laboratory. It then changes to another form. How long would such a particle live when shooting through the space at 0.95 c? Given Data: Proper Time , Relative Speed To Determine: Relativistic Time Calculations: √ √ √ √ 19.2 What is the mass of a 70 kg man in a space rocket traveling at 0.8 c from us as measured from Earth? Given Data: Proper Mass , Relative Speed To Determine: Relativistic Time Calculations: √ √ √ √ 19.3 Find the energy of photon in a) Radiowave of wavelength 100 m b) Green light of wavelength 550 nm c) X-ray with wavelength 0.2 nm Given Data: (a) Wavelength of Radiowave , (b) Wavelength of Green Light To Determine: (a) Energy of Radiowave , (c) Wavelength of X-ray , (b) Energy of Green Light , (c) Energy of X-ray Calculations: (a) Energy of Radiowave (b) Energy of Green Light (c) Energy of X-ray 19.4 Yellow light of 577 nm wavelength is incident on a cesium surface. The stopping voltage is found to be 0.25 V. Find a) the Maximum K. E. of the photoelectrons b) the work function of cesium Given Data: Wavelength of Yellow Light , Stopping Potential To Determine: (a) Maximum K. E. , (b) Work Function Calculations: (a) Maximum K. E. (b) By Quantum Theory of Photoelectric Effect 19.5 X-rays of wavelength 22 pm are scattered from a carbon target. The scattered radiation being viewed at 85° to the incident beam. What is Compton shift? Given Data: Wavelength , Scattering Angle To Determine: Compton Shift Calculations: 23 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 19.6 A 90 keV X-ray photon is fired at a carbon target and Compton scattering occurs. Find the wavelength of the incident photon and the wavelength of the scattered photon for scattering angle of (a) 30° (b) 60° Given Data: Energy of Photon To Determine: (a) Wavelength of Incident Photon (b) Wavelength of Scattered Photon at : , , (c) Wavelength of Scattered Photon at : Calculations: (a) As (b) (c) 19.7 What is the maximum wavelength of the two photons produced when a positron annihilates an electron? The rest mass energy of each is 0.51 MeV. Given Data: Energy To Determine: Wavelength Calculations: As 19.8 Calculate the wavelength of a) a 140 g ball moving at b) a proton moving at the same speed c) an electron moving at the same speed Given Data: Speed (a) Mass of Ball (b) Mass of Proton , (c) Mass of Electron To Determine: (a) Wavelength associated with Ball (b) Wavelength associated with Proton , , , (c) Wavelength associated with Electron Calculations: (a) (b) (c) 19.9 What is the de Broglie wavelength of an electron whose kinetic energy is 120 eV? Given Data: , Mass To Determine: De Broglie Wavelength Calculations: As De Broglie Wavelength √ As √ Putting values in (1): 19.10 An electron is placed in a box about the size of an atom that is about the electron? Given Data: Size of Box . What is the velocity of , Mass To Determine: Velocity Calculations: By Uncertainty Principle: 24 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEM F.Sc. Physics, Chapter # 20: ATOMIC SPECTRA 20.1 A hydrogen atoms is in its ground state (n = 1). Using Bohr's theory, calculate (a) the radius of the orbit (b) the linear momentum of the electron (c) the angular momentum of the electron (d) the kinetic energy (e) the potential energy and (f) the total energy. Given Data: , Mass of electron To Determine: (a) Radius (d) Kinetic Energy , (b) Linear Momentum (e) Potential Energy (f) Total Energy . For 1st orbit, Calculations: (a) As Radius of 1st orbit: ( (b) Linear Momentum ( ( Linear Momentum (c) Angular Momentum . Therefore, ) ). For 1st orbit, ) . Therefore, ( ( ) ) (c) Angular Momentum ( (d) Kinetic Energy ( ) ) . For 1st Orbit, ( ( ( (e) Potential Energy . Therefore, ) ) ) (f) Total Energy 20.2 What are the energies in eV of quanta of wavelength? λ = 400, 500 and 700 nm. Given Data: Wavelengths of Quanta: (a) (b) (c) To Determine: Energies of Quanta: (a) (b) (c) Calculations: (a) (b) (c) 20.3 An electron jumps from a level to . What is the wavelength of the emitted light? Given Data: Energy in ground state ,Energy in Excited State To Determine: Wavelength Calculations: 25 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 20.4 Find the wavelength of the spectral line corresponding to the transition in hydrogen from n = 6 state to n = 3 state? Given Data: To Determine: Wavelength Calculations: ( ) ( ( ) ) ( ( ) ) 20.5 Compute the shortest wavelength radiation in the Balmer series? What value of n must be used? Given Data: For Balmer series , For Shortest Wavelength To Determine: Shortest Wavelength Calculations: ( ) ( ) ( ) ( ) ( ) 20.6 Calculate the longest wavelength of radiation for the Paschen series. Given Data: For Paschen Series , For Shortest Wavelength To Determine: Longest Wavelength Calculations: ( ( ) ( ) ( ) ) 20.7 Electrons in an X-ray tube are accelerated through a potential difference of 3000 V. If these electrons were slowed down in a target, what will be the minimum wavelength of X—rays produced? Given Data: Potential Difference To Determine: Minimum Wavelength Calculations: 20.8 The wavelength of K X-ray from copper is . What is the energy difference between the two levels from which this transition results? Given Data: Wavelength To Determine: Energy Difference Calculations: 20.9 A tungsten target is struck by electrons that have been accelerated from rest through 40 kV potential difference. Find the shortest wavelength of the bremsstrahlung radiation emitted. Given Data: Potential Difference To Determine: Minimum Wavelength Calculations: 26 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems 20.10 The orbital electron of a hydrogen atom moves with a speed of (a) Find the value of the quantum number n associated with this electron. (b) Calculate the radius of this orbit. (c) Find the energy of the electron in this orbit. Given Data: Speed of Electron To Determine: (a) Quantum Number , (b) Orbital Radii , (c) Energy of Electron ( Calculations: (a) As ( (b) As Orbital Radii (c) Energy of Electron ( ) ( , ) ) ( ) ( ( ) ) ) F.Sc. Physics, (2nd Year), Complete Physics Notes CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-2nd-year-completephysics.html F.Sc. Physics, (2nd Year), Multiple Choice Questions (MCQs) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/fsc-physics-2nd-year-multiplechoice.html F.Sc. Physics, (2nd Year), Exercise Short Questions CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/exercise-short-questions-fscphysics_10.html 27 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems NUMERICAL PROBLEM F.Sc. Physics, Chapter # 21: NUCLEAR PHYSICS 21 .1 Find the mass defect and the binding energy for tritium, if the atomic mass of tritium is- u. Given Data: Mass of Tritium , Mass of Proton Mass of Neutron , , For Tritium To Determine: (a) Mass Defect , (b) Binding Energy [ Calculations: (a) ] [ ] (b) 21.2 The half-life of is 9.70 hours. Find its decay constant. Given Data: Half Life To Determine: Decay Constant Calculations: As 21.3 The element the daughter nuclei. is unstable and decays by β-emission with a half-life 6.66 s. State the nuclear reaction and Given Data: Parent Nucleus: , Half Life To Determine: Nuclear Reaction, Daughter Nucleus for Calculations: As for : For Present Case: : . , where 21 .4 Find the energy associated with the following reaction: (Mass of ) What does negative sign indicate? Given Data: Mass of , Mass of , Mass of , Mass of To Determine: Associated Energy Calculations: Mass Defect Now Associated Energy The negative sign indicate that energy is needed to start nuclear reaction. 21 .5 Determine the energy associated with the following reaction: Given Data: Mass of , Mass of , Mass of To Determine: Associated Energy Calculations: Mass Defect Now Associated Energy 28 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems decays twice by α-emission, what is the resulting isotope? 21 .6 lf Given Data: Parent Nucli: : To Determine: As for : Calculations: 1st Decay: , Here 2nd Decay: , Here So resulting isotope is radium 21 .7 Calculate the energy (in MeV) released in the following fusion reaction; Given Data: Mass of , Mass of , Mass of , Mass of To Determine: Associated Energy Calculations: Mass Defect Now Associated Energy 21 .8 A sheet of lead 5.0 mm thick reduces the intensity of a beam of γ-rays by a factor 0.4. Find half value thickness of lead sheet which will reduce the intensity to half of its initial value. Given Data: Case 1 Thickness , Intensity Case 2 Intensity To Determine: Thickness of Lead Sheet for case 2: Calculations: As For Case 1: For Case 2: Dividing (1) and (2): 21 .9 Radiation from a point source obeys the inverse square law. If the count rate at a distance of 1.0 m from Geiger counter is 360 counts per minute, what will be its count rate at 3.0 m from the source? Given Data: Case 1 Count Rate , Distance Case 1, Distance To Determine: Count Rate for case 2: Calculations: Given For Case 1: Dividing (1) and (2): , For Case 2: ( ) ( ) ( ) ( ) 21.10 A 75 kg person receives a whole body radiation dose of 24 m-rad, delivered by α-particles for which RBE factor is 12. Calculate (a) the absorbed energy in joules, and (b) the equivalent dose in rem. Given Data: Mass of Person , RBE factor Radiation Dose To Determine: (a) Absorbed Energy in joules , (b) Equivalent Dose in rem Calculations: (a) As (b) 29 | P a g e Publisher: www.HouseOfPhy.Blogspot.com F.Sc. Physics (Part-II) Solved Numerical Problems B.Sc. Mechanics (Physics) (In accordance with syllabus of UNIVERSITY OF THE PUNJAB AND UNIVERSITY OF SARGODHA) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/bsc-physics-mechanics-complete-book.html B.Sc. Waves and Oscillations (In accordance with syllabus of UNIVERSITY OF THE PUNJAB AND UNIVERSITY OF SARGODHA) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/bsc-physics-waves-and-oscillations.html B.Sc. Thermodynamics (In accordance with syllabus of UNIVERSITY OF THE PUNJAB AND UNIVERSITY OF SARGODHA) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/bsc-physics-thermodynamicscomplete.html B.Sc. Electricity and Magnetism (In accordance with syllabus of UNIVERSITY OF THE PUNJAB AND UNIVERSITY OF SARGODHA) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/bsc-physics-electricity-and-magnetism.html B.Sc. Electronics (In accordance with syllabus of UNIVERSITY OF THE PUNJAB AND UNIVERSITY OF SARGODHA) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/bsc-physics-electronics-completenotes.html B.Sc. Modern Physics (In accordance with syllabus of UNIVERSITY OF THE PUNJAB AND UNIVERSITY OF SARGODHA) CLICK THE LINK TO DOWNLOAD https://houseofphy.blogspot.com/2017/12/bsc-physics-modern-physics-complete.html 30 | P a g e Publisher: www.HouseOfPhy.Blogspot.com