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1 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 1 Q1. A standing wave having three nodes is set up in a string fixed at both ends. If the frequency of the wave is doubled, how many antinodes will there be? A) 4 B) 3 C) 2 D) 5 E) Q2. A stationary motion detector sends sound waves of frequency MHz towards a truck approaching (the detector) at a speed of 50.0 m/s. What is the frequency of the waves reflected back to the detector? [Speed of sound = 343 m/s] A) 0.11 MHz B) MHz C) MHz D) MHz E) 0.18 MHz Q3. A box with a total surface area of 1.20 m 2 and a wall thickness of 4.00 cm is made of an insulating material. A 10.0 W electric heater inside the box maintains the inside temperature at 15.0 o C above the outside temperature. Find the thermal conductivity of the insulating material. A) W/m.K B) 2.20 W/m.K C) W/m.K D) 0.01 W/m.K E) 1.23 W/m.K Q4. An ideal gas initially at 330 K is compressed at a constant pressure of 25.0 N/m 2 from a volume of 3.0 m 3 to a volume of 1.00 m 3. In the process, 75.0 J is lost by the gas as heat. What is the change in internal energy of the gas? A) 25.0 J B) 125 J C) J D) +5.0 J E) 75.0 J Q5. A Carnot engine has an efficiency of ε when operating between TH = 400 o C and TL = 200 o C. What will be the efficiency of the same Carnot engine when operating between TH = 800 o C and TL = 400 o C. A) 1.25ε B) 2.0ε C) 0.50ε D) 1.5ε E) 0.77ε

2 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 2 Q. Two identical 0.20 kg masses are placed 1.0 m apart (center to center) on a frictionless surface. Each has +10 µc of charge. What is the initial acceleration of one of the masses if it is released from rest and allowed to move? A) 4.5 m/s 2 B) 2.3 m/s 2 C).3 m/s 2 D) 1.4 m/s 2 E) 5.2 m/s 2 Q7. Two point charges q1= +15 µc and q2 = 10 µc are placed in xy plane. If q1 is placed at (20 cm, 0) and q2 is placed at (0, 10 cm), find the resultant electric field at the origin. A) i ˆ ( ˆ) j N / C B) i ˆ ( ˆ) j N / C C) i ˆ ( ˆ) j N / C D) i ˆ ( ˆ) j N / C E) i ˆ ( ˆ) j N / C Q8. FIGURE 1 shows portions of a large non-conducting sheet placed in parallel with long line of charge having a uniform charge per unit length. The surface charge density of the 2 non-conducting sheet is 4.0 C / m. If the electric field intensity at point P, 2.0 cm on right of the line charge, is zero, find the linear charge density. A) 0.25 µc/m B) µc/m C) µc/m D) 0.38 µc/m E) 0.3 µc/m

3 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 3 Q9. A thick spherical conducting shell of outer radius 5.0 cm has a net charge Q = +10 µc. A point charge of 3.0 µc is placed at its center. Find the surface charge density on the outer surface of the shell. A) 223 µc/m 2 B) 414 µc/m 2 C) 318 µc/m 2 D) 203 µc/m 2 E) 19 µc/m 2 Q10. Two conducting spherical shells of same outer radius r = 5.0 cm are placed at center to center distance of 20 cm. The charge of +10 µc and 20 µc is uniformly distributed over the outer surface of sphere 1 and 2, respectively, find the total potential at the center of sphere 1. (Assume potential is zero at infinity) A) +900 kv B) +270 kv C) 900 kv D) +450 kv E) +00 kv Q11. In FIGURE 2 C1 = 2.0 µf, C2 = 4.0 µf, and C3 =.0 µf. Find the equivalent capacitance between points a and b. A) 8.7 µf B) 18 µf C) 9.8 µf D) 12 µf E) 2.0 µf Q12. A current of 3.20 A exist in a copper wire whose diameter is 4.00 mm. The number of charge carrier per unit volume is m 3. Assuming the current density is uniform, calculate the electron drift speed. A) m/s B) m/s C) m/s D) m/s E) m/s

4 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 4 Q13. Two real batteries with some internal resistances are shown in FIGURE 3. Find the potential difference between points A and B (VA VB). A) 13.0 V B) 23.5 V C) 11.8 V D) 24.5 V E) 18.0 V Q14. In a circuit shown in FIGURE 4 if the potential of point A is zero find the potential of point B. A) 2.0 V B) +2.0 V C) +.0 V D).0 V E) 4.0 V

5 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 5 Q15. For the circuit given in FIGURE 5, if the current through one of the.00 Ω is A find the current through the 4.00 Ω resistor. A) 2.25 A B) 0.33 A C) 3.50 A D) 1.55 A E) 0.50 A Q1. If the current through the 150 Ω resistor is 1.00 A as shown in FIGURE, find the current through the 51.0 Ω resistor. A) 8.47 A B) 3.00 A C) 5.42 A D) 11.4 A E).45 A

6 Coordinator: Saleem Rao Monday, January 01, 2018 Page: Q17. Switch S in FIGURE 7 is closed at time t = 0, to begin charging an initially uncharged capacitor C = 15.0 µf through a resistor R = 20.0 Ω. At what time is the potential difference across the capacitor double to that across the resistor? A) s B) s C) s D) s E) s Q18. A proton enters with the same speed in four regions of uniform magnetic fields of same magnitudes but in different directions, as shown in FIGURE 8. Rank regions according to magnitude of the force on the protons, GREATEST FIRST. A) a and b tie, d, c B) b and c tie, a, d C) b and c tie, d, a D) a, then b and c tie, d E) a, d, b, c

7 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 7 Q19. In FIGURE 9 a charged particle electron or proton (you must decide which) moves in uniform magnetic field B (out of the page), goes through half circle, and then exits that region. The charged particle spends 240 ns in the region, find the magnitude of magnetic field. A) T B) T C) T D) T E) T Q20. An 80.0 cm long wire, laying along the positive x axis (with one end at the origin), carries a current of 0.80 A in the negative x direction and placed in a magnetic field. B 4.0iˆ 12 ˆj, where x in meters and B in mt. Find, in unit vector notation, the magnetic force on the wire? 3 A) ( k) ˆ N 3 B) ( kn ˆ) 3 C) ( k) ˆ N 3 D) ( ˆj ) N 3 E) ( i) ˆ N Q21. A rectangular loop with height h =.50 cm and width w = 5.40 cm is in a uniform magnetic field of magnitude B = T, which points in negative y direction as shown in FIGURE 10. The loop makes an angle of θ = 30 o with the y axis and carries a current of 9.00 A in the direction indicated. What is the magnitude of the torque on the loop?

8 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 8 A) N.m B) N.m C) N.m D) N.m E) N.m Q22. Two concentric circular loops of radii r1 = 20.0 cm and r2 = 30.0 cm are located in xy plane; each carries current of same magnitude i = 7.00 A but in opposite direction as shown in FIGURE 11. Find the net magnetic dipole moment of the loops. A) 1.10 A.m 2 into the page B) 2.8 A.m 2 into the page C) 1.10 A.m 2 out of the page D) 2.8 A.m 2 out of the page E) 1.98 A.m 2 into the page Q23. Wire 1 and wire 2 placed parallel to y axis at x = 0 and x = 10 cm, respectively, and carries currents i A and i 8. 0A 2 in opposite directions as shown in FIGURE 12. A third wire carries current in positive y direction is to be placed parallel to wire 1 and wire 2 such that net force per unit length on wire 3 due to wire 1 and wire 2 is zero. Find the position x of wire 3.

9 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 9 A) 10 cm B) +20 cm C) +15 cm D) 5.0 cm E) 15 cm Q24. In FIGURE 13 wire 1 consist of a circular arc of radius R with central angle of θ = 120 o and two radial lengths and carries current i A in the direction indicated. Wire 2 is long and straight and it carries a current i 2 and placed at a distance of R/2 from the center of circular arc. If the net magnetic field at the center of the arc O is zero find the current i 2. A) 1.05 A B) 2.75 A C) 0.84 A D) 1.34 A E) 2.05 A Q25. FIGURE 14 shows a cross section across the diameter of two long cylindrical conducting wires 1 and 2 of same radius R carrying same uniform current but in opposite directions. Four square paths (of side length R) of same dimensions are indicated for the line integral B ds.. Rank the paths according to the magnitude of B ds. taken in the directions shown, GREATESR FIRST.

10 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 10 A) 4, then 1 and 3 tie, 2 B) 1 and 3 tie, 2, 4 C) 4, then 1, 2, and 3 tie D) 4, 3, 2,1 E) 3, 4,1, 2 Q2. A circular wire loop has radius of 0.12 m and carries current i 0. 10A placed in the xy plane in a uniform magnetic field B 1.5kˆ T, as shown in FIGURE 15. Find the potential energy of the loop in the position shown. A) J B) J C) J D) 0 E) J Q27. A solenoid has a length L = 1.55 m and an inner diameter d = 4.15 cm, and carries a current i = 4.80 A. The solenoid consists of six close-packed layers, each with 750 turns along length L. What is the magnitude of magnetic field at its center? A) 17.5 mt B) 23.8 mt C) 5.5 mt D) 13.5 mt E) 19.8 mt Q28. IGURE 1 shows three situations in which a wire loop lies partially in a uniform magnetic field. The magnetic field is either increasing or decreasing, as indicated. In each situation, a battery is part of the loop. In which situation(s) is/are the induced emf and the battery emf in the same direction along the loop.

11 Coordinator: Saleem Rao Monday, January 01, 2018 Page: 11 A) b only B) b and c C) a, b, and c D) c only E) a and c Q29. The magnetic flux through a loop increases according to the relation B.0t t, where ΦB is in mt.m 2 and t is in seconds. What is the magnitude of the emf induced in the loop when t = 2.0 s? A) 31 mv B) 38 mv C) 24 mv D) 17 mv E) 40 mv Q30. A 0.0 cm copper wire is formed into a square loop and placed perpendicular to a uniform magnetic field that is increasing at the constant rate 12.0 mt/s. If the resistance of the loop is 20.0 Ω, at what rate is thermal energy generated in the loop? A) W B) W C) W D) W E) W

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