1. A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region x > b is
a) m charge q is placed at the origin. The change in the electrical potential energy of q, when it is displaced by a small distance x along the x-axis, the approximately proportional to
a) x b) x2 c) x3 d) 1/x
3. A long straight wire along the z-axis carries a current I in the negative z direction. The magnetic vector field BG conducting loops separated by some distance. When the switch S is closed, a clockwise current Ip flows in P (as seen by E) and an induced current IQ1 flows in Q. The switch remains closed for a long time. When S is opened, a current IQ2 flows in Q. Then the direction of IQ1 and IQ2 (as seen
6. A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current
induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be
9
a) halved b) the same c) doubled d) quadrupled
7. Two identical capacitors have the same capacitance C. One of them is charged to potential V1
and the other to V2. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is
2 2 2 1
2 2 1
2 2 2 1
2 2
1 C(V V)
4 ) 1 d )
V V ( 4C ) 1 c ) V V ( 4C ) 1 b ) V V ( 4C ) 1
a − + − + a
8. The magnetic field lines due to a bar
magnet are correctly shown in fig.3
9. An ideal gas is taken through the cycle A →B→C→A, as shown in the figure 4. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process C →A is
a) -5 J b) -10 J c) -15 J d) -20 J
10. Which of the following graphs correctly represents the variation of β = -(dV/dP)/V with P for an ideal gas at constant temperature
11. A Hydrogen atom and a Li++ ion are both in the second excited state. If lH and lLi are their respective electronic angular momenta, and EH and ELi their respective energies, then
a) lH > lLi and |EH| > |ELi| b) lH = lLi and |EH| < |ELi| c) lH = lLi and |EH| > |ELi| d) lH < lLi and |EH| < |ELi|
12. An ideal black-body at room temperature is thrown into a furnace. It is observed that a) initially it is the darkest body and at later times the brightest
b) it is the darkest body at all times c) it cannot be distinguished at all times
d) initially it is the darkest body and at later times it cannot be distinguished
13. The potential difference applied to an X-rays tube is 5 kV and the current through it is 3.2 mA. Then the number of electrons striking the target per second is
a) 2 x 1016 b) 5 x 1016
c) 1 x 1017 d) 4 x 1015
14. Which of the following processes represents a gamma-decay ? a) AXZ + γ→ AXZ-1 + a + b
b) AXZ + 1n0 → A-3XZ-2+c c) AXZ → AXZ + f d) A XZ + e-1 → AXZ-1 +g
15. The half-life of 215At is 100 µs. The time taken for the radioactivity of a sample of 215At to decay to 1/16th of its initial value is
a) 400 µs b) 6.3 µs c) 40 µs d) 300 µs 16. An observer can see through a pin-hole the top
end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is (fig.6 below)
a) 5/2 b) (5/2) c) 3/2
d) 3/2
17. Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams.(fig 6 next column)?
18. In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wave-length λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is
a) 2λ b) 2λ/3
c) λ/3 d) λ
19. Two plane mirrors A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of 300 at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
a) 28 b) 30 c) 32 d) 34
20. A wooden block, with a coin placed on its top, floats in water as shown in fig. The distance l and h are shown there. After some time the coin falls into the water (fig.8). Then
a) l decreases and h increases b) l increases and h decreases c) both l and h increase d) both l and h decrease
21. A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a is correctly shown in (fig.9)
22. A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are
a) up the incline while ascending and down the incline while descending b) up the incline while ascending as well as descending
c) down the incline while ascending and up the incline while descending d) down the incline while ascending as well as descending
23. A circular platform is free to rotate in a horizontal plane about a vertical axis passing through
its center. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ω0. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform ω(t) will vary with time t as (fig.10)
24. A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = -kx + ax3. Here k and a are positive constants. For x ≥ 0, the functional form of the potential energy U(x) of the particle is (fig.11)
25. Two blocks of masses 10 kg and 4 kg are
connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of the lighter block.
The velocity of the center of mass is
a) 30 m/s b) 20 m/s c) 10 m/s d) 5 m/s
26. A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. during his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is
a) 242/252 b) 2 c) 5/6 d) 11/6
27. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. when this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is
a) 25 kg b) 5 kg c) 12.5 kg d) 1/25 kg
28. An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. the mass is released with the spring initially unstretched. Then the maximum extension in the spring is
a) 4 Mg/k b) 2 Mg/k c) Mg/k d) Mg/2k
29. A geo-stationary satellite orbits around the earch in a circular orbit of radius 36000 km. Then, the time period of a spy satellite orbiting a few hundred kilometers above the earth’s surface (REarth = 6400 km) will approximately be
a) 1/2 h b) 1 h c) 2 h d) 4 h
30. The effective resistance between points P and Q of the electrical circuit shown in the figure is a) R r
Rr 2
+ b)
r R 3
) r R ( R 8
+ + )
c) 2r+ 4 R d)
1. The radius of a charged particle in a uniform magnetic field is r = mv/qB. If the particle is not to enter the region x > b, the radius should have only a maximum value b-a. So b-a = mv/qB ⇒ b = qB (b-a) /m. Ans.B
2. The potential energy between the two charges q,q and the charge Q at the origin is
1 when charge is displaced by a distance x. Before displacement the
potential energy is
difference between the two terms. This will be 3
0
3. The radius vector joining the conductor to the point is r = ix+jy. The magnitude of the field will be
µ . (1) The direction of the field will be unit vector perpendicular
to the radius vector r. This will be
4. In a parallel connection power is same. So power across B3 is the same as power across B1
and B2 together. So W3 is maximum. In a series connection power is directly proportional to resistance. 60 W lamp has greater resistance. So it has greater power. i.e. W2 > W1. Thus W1 < W2 < W3. Ans.D
5. When the current is increasing in P clockwise induced current in Q is anti-clockwise by Lenz’s law. When current is decreasing in P, the induced current in Q is clockwise. Ans.D 6. Induced emf e is proportional to number of turns N. Power is proportional to (emf)2. When
the number of turns is made for four times, power increases to 16 times. When radius of wire is halved, resistance increases to four times. Since length increases to four times, resistance increases to 4 x 4 = 16 times. Thus power e2/r remains constant. Ans.B
7. Use the short cut equation for loss of electrostatic energy 1 2 2
2
8. Magnetic lines of force start from north pole and end at south pole outside and continue from south pole to north pole inside the magnet. Ans.D
9. Work done along AB = 10 (2-1) = 10 J. Work done along BC = 0 (no change in volume).
Work done along AC be equal to W. Then 10 + 0 + W = 5, that is heat supplied. This gives W = -5J. Ans.A
10. Bulk modulus of an ideal gas = K = find β is inversely proportional to P. The graph between them will be a rectangular hyperbola. Ans.A
11. By Bohr’s postulate, the angular momentum in nth orbit = n(h/2π). So it is same for hydrogen and helium atom. The energy of hydrogen atom is -13.6/n2 eV for nth state and -13.6 Z2 / n2, for helium atom. So it is more for helium atom. Ans.B
12. A black body is a good emitter and a good absorber. When it is thrown into the furnace, it first becomes dark. Then it reemits all radiations. It becomes brightest. Ans.A
13. If n is the number of electrons striking the target, e its charge, current I = ne. n = I/e = 3.2 x 10-3/ 1.6 x 10-19 = 2 x 1016. Potential will not decide the number of electrons. It decides only the energy of electrons. Ans.A
14. Only in a γ decay there will be no change in mass number and atomic number. Ans.C 15. Use the short cut equation 0 2t/T
17. We use here Lens maker’s formula
18. If µ is the refractive index of glass, n is a number of fringes shifting, for central maximum to remain unchanged (µ-1)t = nλ ⇒ t = 2λ. Ans.A
19. During each reflection, there is a lateral displacement of x = d tan 300, where d is the distance between the glass plates. If n is the number of reflections, then n d tan 30 = length of the plate L. n x 0.2(1/ 3 ) = 2 3 ⇒ n=30. Total number = 30+initial+final = 32. Ans.C
20. By law of flotation, weight of floating body = weight of liquid displaced. When the coin is removed, the weight of body decreases. Hence it rises and ‘l’ decreases. When the coin falls into water, it displaces water equal to its volume. The volume of coin is numerically less than its mass. Hence water level falls ‘h’ decreases. Ans.D
21. A body in motion along a curve has two accelerations. They are tangential acceleration at
along the tangent and centripetal acceleration ar along the radius towards centre. Its vector sum aG=aGt+aGr. Ans.C
22. On an inclined plane the force of gravity is always downwards, even if the cylinder moves up or down. Hence frictional force is always upwards. Ans.B
23. The initial distance of the tortoise from centre of circle O is equal to radius of platform r. As it moves from A its distance from O decreases, reaches minimum at O, then increases. Its moment of inertia I = mr2 ecreases and then increases. As the platform is a closed system Iω
= Crms . So ω first increases and then decreases. Ans.B