This aptitude test is the ultimate challenge for a smart student. The questions push you to your limits, stretch your abilities, and of course, tease you.
This aptitude test is also scored, which means at the end we will tell you "how smart you are!" i.e. you are genius, expert, progressive expert, average or
1. A wooden block of mass 1 kg is attached to the hook of a spring balance. The spring balance is then raised with an acceleration of 9.8 m s~2. The apparent weight of the block is
(a) 1 kg wt (b) 2 kg wt (c) 3 kg w t (d) 4 kg wt
2. Two homogeneous spheres A and B of masses m and 2m having radii 2a and a respectively are placed in touch. The distance of centre of mass from first sphere is
(a) a (b) 2a (c) 3a (d) 4a
3. A flywheel rotates with a uniform angular acceleration. Its angular velocity increases from 20n rad s"1 to 4071 rad s"1 in 10 s. H o w many rotations did it make in this period?
(a) 80 (b) 100 (c) 120 (d) 150
4. The bob of a simple p e n d u l u m is of mass 10 g.
It is suspended with a thread of 1 m. If we hold the bob so as to stretch the string horizontally and release it, what will be the tension at the lowest position? (Take g = 10 m s~2)
(a) zero (b) 0.1 N (c) 0.3 N (d) 1.0 N
5. A current of 7 A flows through the circuit as shown in the figure. The potential difference across point B and C is
4 £2 B
—WWW^
7 A
A
2Q -A/WW
10 Q
•NMh- 5Q
-VWVW 7 A
(a) (c)
16 V 10 V
(b) 8 V (d) 5 V
6. The torque required to hold a small circular coil of 10 turns, 2 x 10"4 m2 area and carrying 0.5 A current in the middle of a long solenoid of 103
turns per m carrying 3 A current, with its axis perpendicular to the axis of the solenoid, is (a) 12ti x 10~7 N m (b) 6 7 t x l 0 "7N m (c) 4ti x 10"7 N m (d) 2 7 i x l 0 -7N m 7. A dynamo dissipates 20 W, when it supplies a
current of 4 A through it. If the terminal potential difference is 220 V, the emf produced is
(a) 220 V (b) 225 V (c) 215 V (d) 300 V
8. 200 V ac source is fed to series ICR circuit having XL = 50 £2, Xc = 50 Q and R = 25 Q. Potential d r o p across the inductor is
(a) 100 V (b) 200 V (c) 400 V (d) 10 V
9. The variation of velocity of a particle moving along a straight line is shown in figure. The distance transvered by the particle in 4 second is
(a) 60 m (c) 55 m
(b) 25 m (d) 30 m
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10. A rubber rope of length 8 m is hung from the ceiling of a room. What is the increase in length of the rope due to its own weight? (Given Young's modulus of elasticity of rubber = 5 * 106 N m~2
and density of rubber = 1,5 » 103 kg m~3 and g = 10 m s"2)
(a) 1.5 mm (b) 6 mm (c) 24 mm (d) 96 m m
11. A car sounding its horn at 480 Hz moves towards a high wall at a speed of 20 m s"1. If the speed of sound is 340 m s-1, the frequency of the reflected sound heard by the man sitting in the car will be nearest to
(a) 480 Hz (b) 510 Hz (c) 540 Hz (d) 570 Hz
12. An a-particle of mass 6.4 x 10~27 kg and charge 3.2 x 10~19 C is situated in a uniform electric field of 1.6 x 105 V m_1. The velocity of the particle at the end of 2 x 10~2 m path when it starts from rest is
(a) 2 V 3 x l 05 m s"1 (b) 8 x 105 m s"1
(c) 16 x 105 m (d) 4 \ / 2 x l 05 m s 13. The natural boron of atomic weight 10.81 is found
to have two isotopes B10 and B11. The ratio of abundance of isotopes in natural boron should be
(a) 11 : 10 (b) 81 : 19 (c) 1 0 : 1 1 (d) 1 9 : 8 1
14. The dimensions of Planck's constant and angular momentum are respectively
(a) [ML2T-1] and [MLT"1] (b) [ML2T_1] and [ML2T_1] (c) [MLT"1] and [ML2!"1] (d) [MLT"1] and [ML2T~2]
15. A body dropped from the top of a tower covers a distance 7h in the last second of its journey where h is the distance covered in the first second. How much time does it take to reach the ground?
(a) 3 s (b) 4 s (c) 5 s (d) 6 s
16. A body of mass M kg is on the top point of a smooth hemisphere of radius 5 m. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity 5 m s_1. At this
instant the angle made by the radius vector of the body with the vertical is
(Take g = 10 m s~2)
(a) 30° (b) 45°
(c) 60° (d) 90°
17. A toy gun uses a spring of force constant k. When charged before being triggered in the upward direction, the spring is compressed by a distance x. If the mass of shot is m, on being triggered it will go u p to a height of
kr2 r2
(a) (b) J L _
mg kmg (c) - ^ L (d)
2 mg mg
18. The escape velocity from the earth is 11.2 km s_1. The escape velocity from a planet having twice the radius and the same mean density as the earth is
(a) 22.4 km s-1 (b) 11.2 km s"1
(c) 5.6 km s"1 (d) 15.8 km s"1
19. A steel ring of radius r and cross-sectional area A is fitted onto a wooden disc of radius R(R > r).
If Young's modulus be Y, then the force with the steel ring is expanded is
(a) AY-R (b) AY R-r
(c) Y (R-r)
(d) "777 AR Xl
20. A rod 70 cm long is clamped from middle. The velocity of sound in the material of the rod is 3500 m s_1. The frequency of fundamental note produced by it is
(a) 700 Hz (b) 1250 Hz (c) 2500 Hz (d) 3500 Hz
21. A source of sound emits a sound of frequency 600 Hz and is rotating in a circle of radius 4 m at a linear speed of 40 m s_1. What is the lowest and highest frequency heard by an observer at long distance away at rest with respect to the centre of circle?
(a) 545 Hz and 687 Hz (b) 683 Hz and 535 Hz (c) 535 Hz and 683 Hz (d) 687 Hz and 545 Hz 22. 200 cc of a gas is compressed to 100 cc at the
atmospheric pressure 106 dyne cm-2. If the change is
74 PHYSICS FOR YOU | MAY '13 ;
sudden, what is the final pressure? (Given y = 1.4) (a) 1.6 x 106 dyne cnr2 (b) 2.0 * 106 dyne cnr2
(c) 2.6 x 106 dyne cnr2 (d) 3.0 * 106 dyne cnr2
23. Starting with the same initial conditions, an ideal gas expands from volume Vj to V2 in three different ways. The work done by the gas is W( if the process is purely isothermal, W2 if the process is purely isobaric, and W3 if the process is purely adiabatic, then
(a) Wr> W2> W3 (b) W2> W3> W , (c) W3> W2> W i (d) W2> W , > W3
24. The specific heat of water in cal g"1 is s = 0.5f2, where t is the temperature on the Celsius scale. If the temperature of 10 g of water is raised through 10°C, what is the amount of heat required?
(a) 60 cal (b) 200 cal (c) 0.6 kcal (d) 2kcal
25. A transistor connected at common-emitter mode contains load resistance of 5 k£2 and an input resistance of 1 k£L If the input peak voltage is 5 mV and the current gain is 50, find the voltage gain.
(a) 250 (b) 500 (c) 125 (d) 50
26. The surface of the metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of metal is
(a) 1.42 eV (b) 1.51 eV (c) 1.68 eV (d) 3.0 eV
27. A parallel beam of light of wavelength 3141.59 A is incident on a small aperture. After passing through the aperture, the beam is no longer parallel but diverges at 1° to the incident direction. What is the diameter of the aperture?
(a) 180 nm (b) 18 |um (c) 1.8 m (d) 0.18 m
28. An object is placed 30 cm to the left of a diverging lens whose focal length is of magnitude 20 cm.
Which one of the following correctly states the nature and position of the virtual image formed?
Nature of image Distance from lens (a) inverted, enlarge 60 cm to the right (b) erect, diminished 12 cm to the left
(c) inverted, enlarged (d) erect, diminished
60 cm to the left 12 cm to the right 29. In an ac generator, a coil with N turns, all of the
same area A and total resistance R, rotates with frequency oo in a magnetic field B. The maximum value of emf generated in the coil is
(a) NAB (b) NABR (c) NAB(o (d) NABRu)
30. The magnetic flux linked with the coil varies with time as <)> = 312 + 4f + 9. The magnitude of the induced emf at 2 s is
(a) 9 V (b) 16 V (c) 3 V (d) 4 V
31. The total current supplied to the circuit by the battery as shown figure is
(a) 1 A (c) 4 A
(b) 6 A (d) 2 A
32. If two electric bulbs, each designed to operate with a power of 500 W in 220 V line, are put in series in a 110 V line, what will be the power generated by each bulb?
(a) 31.25 W (b) 21.25 W (c) 11.25 W (d) 41.25 W
33. A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m s_1 to 20 m s_1 while passing through a distance 135 m in t second. The value of f is
(a) 12 (b) 9 (c) 10 (d) 1.8
34. A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass — is fixed to the block, which is pulled in the horizontal direction by applying a force F at the other end. The tension in the middle of the rope is
(a) (b) - F
7
74 PHYSICS FOR YOU | MAY '13 ;
(C) (d) 7-F
35. A particle is acted upon by a force F which varies with position x as shown in figure. If the particle at x = 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x = 16 m is
14 16 x ( m ) - +
(a) 45 J (c) 70 J
(b) 30 J (d) 20 J
36. A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system doubled. The kinetic energy of the system now is
(a) 2K (b) | (c) | (d) 4K
37. Two solid spherical planets of equal radii R having masses 4M and 9M have their centres separated by a distance 6R. A projectile of mass m is sent from the planet of mass 4M towards the heavier planet. What is the distance r of the point from the lighter planet, where the gravitational force on the projectile is zero?
(a) 1.4R (b) 1.8R (c) 1.5R (d) 2.4R
38. The terminal speed of a sphere of gold (density = 19.5 kg m~3) is 0.2 m s_1 in a viscous liquid (density = 1.5 kg nr3). Then the terminal speed of a sphere of silver (density 10.5 kg m-3) of the same size in the same liquid is
(a) 0.1 ms"1 (b) 0.4 ms"1
(c) 0.2 ms"1 (d) 0.3 ms"1
39. Two capacitors A and B are connected in series with a battery as shown in figure. When the switch S is closed and the two capacitors get charged fully, then
2 (iF 3fiF
(a) the potential difference across the plates of A is 4 V and across the plates of B is 6 V.
(b) the potential difference across the plates of A is 6 V and across the plates of B is 4 V.
(c) the ratio of electrical energies stored in A and B is 2 : 3.
(d) the ratio of charges on A and B is 3 : 2.
40. A copper wire of length 1 m and radius 1 mm is joined in series with an iron wire of length 2 m and radius 3 m m and a current is passed through the wires. The ratio of current density in the copper and iron wires is
(a) 2 : 3 (b) 6 :1 (c) 9 : 1 (d) 1 8 : 1
41. A horizontal long straight wire placed east-west carries a current 3.6 A. What is the distance of neutral point from the wire if the horizontal component of the earth's magnetic field from south to north is BH = 3.6 * 10~5 T.
(a) 1 x 10~2 m (b) 2 * 10"2 m (c) 1.5 x 10"2 m (d) 3 x 10-2 m
42. The mutual inductance of an induction coil is 5 H. In the primary coil, the current reduces from 5 A to zero in 10"2 s. What is the induced emf in the secondary coil?
(a) 2500 V (b) 25000 V (c) 2510 V (d) zero
43. A coil of resistance 200 £2 and self inductance 1.0 H has been connected to an ac source of frequency —— Hz. The phase difference between 200 voltage and current is
(a) 30° (b) 63°
(c) 45° (d) 75°
44. If an electron in n = 3 orbit of hydrogen atom jumps down to n = 2 orbit, the amount of energy released and the wavelength of radiation emitted
74 PHYSICS FOR YOU | MAY '13 ;
(a) 0.85 6V, 6566 A (b) 1.89 eV, 1240 A (c) 1.89 eV, 6566 A (d) 1.5 eV, 6566 A 45. A photon of energy 4 eV is incident of a metal
surface whose work function is 2 eV. The m i n i m u m reverse potential to be applied for stopping the emission of electrons is
(a) 2 V (b) 4 V (c) 6 V (d) 8 V
46. In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.12 x 10"10 m. The distance of the centre of mass from the carbon atom is
(a) 0.48 x 10"10 m (b) 0.51 x 10"10 m (c) 0.56 x 10"10 m (d) 0.64 x 10~10 m 47. A block of mass M is pulled u p by a uniform
string of mass-M tied to it, by applying a force F at the other free end of the string. The tension at the midpoint of the string is
(a) F (b) 0.5F (c) 0.75F (d) IF
48. The work done in increasing the size of a rectangular soap film with dimensions 8 c m x 3.75 cm to 10 cm x 6 cm is 2 x 10"4 J. The surface tension of the film in N n r1 is
(a) 1.65 xlO"2 (b) 3 . 3 x l 0 -2
(c) 6 . 6 x l 0 -2 (d) 8 . 2 5 x l 0 -2
49. Two capillaries of length L and 2L and of radii R and 2R are connected in series. The net rate of
flow of fluid through them will be (Given rate of the flow through single capillary X = nPR4/8r\L)
(a) | X (b)
f x
(c) ^ X (d) ^ X
7 5 50. A 2 kg copper block is heated to 500°C and then
it is placed on a large block of ice at 0°C. If the specific heat capacity of copper is 400 J kg- 1 °C_1
and latent heat of fusion of water is 3.5 x 10s J kg-1, the amount of ice that can melt is
(a) | k g (b) | k g (c) | k g (d) | k g
V Check Your Score! If your score is J •
> 90% you are a Genius 9 0 - 8 1 you are an Expert
8 0 - 7 1 you are a Progressive Expert 7 0 - 6 1 you are Average
< 6 0 you Need to work hard!
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74 PHYSICS FOR YOU | MAY '13 ;