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Practice Questions for I Year/I Part Engineering Physics Submission date:2073/07/22 1. An electron with kinetic energy 1.2 keV circles in a plane perpendicular to a uniform magnetic field . The radius of the orbit is 25 cm . Calculate i) The speed of the electron (ii) flux density of the magnetic field (iii) number of revolutions per second (iv) period of motion . Here, Kinetic energy(Ek) =1.2 keV =1.2 × 103 × 1.6 × 10−19 =1.2 × 1.6 × 10−16 =1.92 × 10−16 J Radius of orbit (r) = 25cm =0.25m Speed of electron (v) =? Flux density of magnetic field (B)=? Number of revolutions per sec (f)=? Period of motion(T)=? We have , 1 Ek = mv 2 2 1 = 1.92 × 10−16 = × 9.1 × 10−31 × v 2 2 = v = 2.05 × 107 ms−1 Centripetal force = Lorentz force mv 2 = = BeV r mv =B= re 9.1 × 10−31 × 2.05 × 107 B= 0.25 × 1.6 × 10−19 = 4.66 × 10−4 T Also, Be Frequency(f)= 2πm 4.66 × 10−4 × 1.6 × 10−19 = 2 × 3.14 × 9.1 × 10−31 = 13.05 × 106 rev/sec 1 Time period (T)= f 1 = 13.05 × 106 = 76.58 × 10−9 sec 2. A 10 eV electron is circulating in a plane at right angle to a uniform field of magnetic induction of 1х10-4 T . (a) What is its orbit radius ? (b) What is cyclotron frequency? (c) What is the period of revolution ? (a) A flat silver strip of width 1.5 cm and thickness 1.5 mm carries a current of 150A. A magnetic field of 2T is applied perpendicular to the flat face of the strip . The emf. developed across the width of the strip is measured to be 17.9V . Estimate the number density of free electrons in the metal. Here, Thickness of strip(t)=1.5mm=1.5× 10=3 m Current(I)=150A Magnetic flux density (B)=2T Hall emf(VH)= 17.9μV =17.9× 10−6 V Number density of free electrons (n)=? We have, BI Hall emf((VH ) = ten BI n= VH te 2 × 150 = −6 17.9 × 10 × 1.5 × 10−3 × 1.6 × 10−19 = 69.8 × 1027 /m3 3. A strip of copper 150 mm thick is placed in a magnetic field 0.65 T perpendicular to the plane of the strip and current of 23A is set up in the strip . What Hall P.d. would appear across the width of the strip if the number of electron per cm3 is 8.4х 1022 ? (b) A solenoid 1.3m long 2.6cm in diameter carries a current of 18 A. The magnetic field inside the solenoid is 23mT. find the length of the wire forming the solenoid. Here, Length of solenoid (l)=1.3m Diameter of cross section(d)=2.6cm Radius of cross section(r)=1.3 cm =0.013m Current through solenoid (I)= 18 A Magnetic field inside solenoid (B)= 23mT = 0.023T Length of wire forming solenoid (L)=? We have, N B = μ0 I l Bl N= μ0 I 0.023 × 1.3 ≅ 1322 4π × 10−7 × 18 Now, L= No. of turns × circumference = N × 2πr = 1322 × 2 × 3.14 × 0.013 = 107.9 = 108m 4. A solenoid is designed to produce a magnetic field of 0.14 T at its centre. The radius is 3 cm and the length 50 cm, carries a current of 10 A. (a) what is the minimum number of turns per unit length of the solenoid? What total length of wire is required? (a) In the Bohr model of H- atom, an electron circulates around the nucleus in a path of radius 5.1 × 10−11 m at a frequency of 6.8 × 1015 rev/sec, what is magnetic flux density at the centre of the orbit? Here, Radius of path(r) = 5.1 × 10−11 m Frequency of revolution (f)= 6.8 × 1015 reV/sec Magnetic flux density(B)=? We have, μ0 I B= 2r μ0 fe = 2r 4π × 10−7 × 6.8 × 1015 1.6 × 10−19 = 2 × 5.1 × 10−11 = 13.39 T 5. In a hydrogen atom of radius 5.3 × 10−11 m, an electron revolves round the nucleus with a speed of 2.2 × 106 m/ s.calculate the magnitude of magnetic field at the centre of the atom. 6. A closely wound circular coil with radius 2.4cm has 800 turns. a. What must be the current in the coil if the magnetic field at the centre of the coil is 0.0580 T? b. At what distance x from the centre of the coil, along the axis, is the magnetic field half of its value at the centre? Mechanics 1. A body of mass 0.2 kg is executing SHM with an amplitude of 10 cm and time period 1 sec. Find (i) maximum acceleration and velocity at a displacement of 5 cm. (0.628m/sec, 3.94m/sec2). Hints, Mass(m)=0.2kg Amplitude(A)=10cm=0.1m Time period(T)=1 sec We have, 2π Maximum velocity Vmax = A. ω = A. t 2π = 0.1 × 1 = 0.62m/s maximum acceleration amax = Aω2 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 2π 2 = 0.1 × ( ) T = 3.94m/s2 A mass of 0.1 kg vibrates with an amplitude of 0.2 m with a period of 0.75 sec. Calculate the maximum k.E(0.14J). A spring is stretched by 8 cm by a force of 10N. Find the force constant. What will be the period of vibration of a 4 kg mass suspended by it ? (125 N/m; 1.12 sec) A spring of force constant 1000 N/m is mounted horizontally on a horizontal table and object of mass 0.25 kg is attached to the free end of the spring. It is then pulled side ways to a distance of 1.5 cm and released. Calculate its frequency ,maximum acceleration and maximum speed.(3.15 Hz, 6 m/sec2 , 0.3 m/sec) A small body of 0.12 kg is undergoing SHM of amplitude 8.5 cm and period of 0.2 sec. What is the maximum value of force acting on it? If the oscillations are produced by a spring, what is the spring constant. ( 10.06 N, 118.35 N/m) The equation of transverse wave travelling in a rope is given by y = 10 sinπ (0.01x-2.00t) where x and y are expressed in cm and t in sec. (i) Find the amplitude frequency, velocity and wavelength of wave. (ii) Find the maximum transverse speed of particle in rope. (10 cm, 200 cm, 1 Hz 2m/sec, 0.628m/sec) A wave has the equation y = 0.02 sin(30t − 4x), where x is in m and t in second. Find its frequency, speed and wavelength. (4077Hz 7.5 m/sec, 1.571 m) With what tension must a rope with length 2.50 m and mass 0.120 kg be stretched for transverse wave of frequency 40.0 Hz to have a wave length of 0.750 m? (43.2N) The intensity level from a loud speaker is 100dB at a distance of 10 m. What is the intensity level at a distance of 200 m ? (74dB) Optics Two slits are spaced 0.3 mm apart and are placed 50 cm from a screen. What is the distance between the second and third dark lines of interference pattern when the slits are illuminated with light of 600nm wavelength ? (1mm) Here, Slit separation(d)=0.3mm=0.03cm Separation between slit and screen D=50cm Fringe width(β)=? Wavelength of light (λ)=600nm=600× 10−7cm We have, λD β= d 600 × 10−7 × 50 = 0.03 = 0.1cm = 1mm The arrangement given in Question (10) is immersed in water. Find the distance between the second and third dark fringes (𝜇 = 1.33). (0.750mm) A parallel beam of monochromatic light falls on a single slit 1 mm wide. When the diffraction pattern is observed on a screen 2 m away the central band is found to have a width of 2.50 mm. Find the wavelength of light used. (625mm) Plane waves of light are incident normally on a narrow slit 0.356 mm wide. A lens with a focal length of 150 cm located directly behind the slit forms a diffraction pattern in the focal plane if the wavelength of light used is 656nm, Find the width of central maxima. (5.25mm) Red light of particular wavelength falls normally on a plane diffraction grating having 400 lines/ cm. If the second order spectrum makes an angle 360. Determine the wavelength of light used (734.7 nm) Solution, Here, 1 (a + b) = cm 400 angle of diffraction (θ) = 360 order of diffraction(n) = 2 wavelength of light(λ) =? we have, (a + b)sinθ = nλ sin36 λ= cm 2 × 400 λ = 7.3473 × 10−4cm A plane transmission grating has 15000 lines/ inch. Find the angle of separation of the 5048 A0 and 5016 A0 lines of helium in the second order spectrum. The polarizing angle for glass is 57.50 . What is the refractive index. Also find the angle of refraction. (1.569,32.50) The critical angle of water is 480. What is the polarizing angle.(53.350). Electrostatics 18. Two equal charges repel each other by a force of 1 N when situated 1 m apart in vacuum. Calculate the value of charge. If the space between them is filled with an insulating medium whose relative permittivity is 10, Calculate the new force between them. (1.05×10-5c , 0.1 N) Here, Force(f)=1N Distance of separation (d)=1m Value of charge(q)=? 1 qq We have , force F= 2 4∈0 π d 1 q2 1= × 4π × 8.85 × 10−12 12 q = √4π × 8.85 × 10−12 = 1.05 × 10−5 coulomb q1 q2 New force of repulsion F’= 4π∈d 2 q2 = 4π ∈r ∈0 d2 𝐹 𝐹′ = ∈𝑟 1 = 10 = 0.1N 19. A point charge of +3×10-6 c is 10 cm distant from a second point charge of -1.5 × 10-6 c. Calculate the magnitude of force on each charge. (1.05 N) 20. Two capacitors of capacitance 4 μF and 12μ F respectively are connected in series and the combination is connected momentarily across a 200V battery. The charged capacitors are now isolated and connected in parallel, similar charge plates being connected, together, Calculate common potential. (75 v) 21. Three capacitors have capacitances 0.5μF, 0.3μF and 0.2μF What is the maximum and minimum value of capacitances that can be obtained by using these three (1μF, 0.097 μF ) 22. Two point charges of magnitude +2×10-7c and 8.5 ×10-8 c are 12 cm apart what electric field does each produce at the site of other. What force acts on each. ( 1.5×105 N/c, 5.3×104 N/c, 1.06×10-2N) 23. What is the magnitude and direction of an electric field that will balance the weight of (a) an electron (b) proton. (5.6×10-11 N/c, 2.05×10-7 N/c). 24. Calculate the drift velocity of electron for the copper wire if the diameter of copper wire is 16 cm carrying a current of 10 A. (3.7×10-8m/ sec) 25. A pd of 1V is applied to a 30.48 m length of copper wire of diameter 0.04 inch. Calculate (a) current (b) current density (c) Electric field strength and (d) rate of heating. ( 1.6 A, 1.96×106A/m2 , 3.3×10-2 v/m, 1.6 watt) 26. A wire 2 inch long carries a current of 5A and is placed at angle 300 to the magnetic field of 0.50T. What force will act on wire? 27. What is the flux density at the centre of circular coil of radius 10 cm and current is 10 A? 28. A solenoid is 1 m long and 3 cm in mean diameter. It has 5 layers of windings of 850 turns each and carries a current of 5A. What is B at the centre of the solenoid. Also Calculate magnetic flux for the cross section of solenoid at its centre. 29. A source of sound has a frequency of 256 Hz and amplitude of 0.50 cm. calculate the energy flow across a square cm per sec. the velocity of sound in air is 330 m/s and density of air is1.29kg/m3. 30. Two small positively charged spheres have a combined charge of 5.0×10-5 C. if each sphere is repelled from the other by an electrostatic force of 40. N when the spheres are 2.0 m apart. What is the charge on the sphere with the smaller charge? 31. Two fixed charges 1.07 𝜇C and -3.28𝜇C are 61.8 cm apart. Where may a third charge be located so that no net force acts on it?