paperb
TRANSCRIPT
FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 16, Ph: 46106000, 26569493, Fax: 26513942.
FACULTY RECRUITMENT TEST
(CAT-A)
ADVANCE PLACEMENT & SAT-II
PHYSICS
PAPER B
Time: 1 Hour Maximum Marks: 40
Name:.................................................................................
Subject:…………………………...........................................
Marks:
Instructions
* Attempt all questions.
* Paper 2 has Two Parts I and II. Each question of Part I carries 2 marks and each question of part II caries 5 marks.
* Calculators and log tables are not permitted.
PART – I
1. A particle parallel to x-axis as shown in the figure such that at
all instant the y axis component of its position vector is constant and is equal to ‘b’. The angular velocity of the particle about the origin is
x O
y
v
2. A motor boat is to reach at a point 30 upstream on other side of a river flowing with velocity 5 m/s.
Velocity of motor boat with respect to water is 5 3 m/sec. Calculate the angle with the flow of river at
which the driver should steer the boat.
3. Two blocks of mass 3 kg and 6 kg respectively are placed on a smooth horizontal surface. They are connected by a light spring of force constant k = 200 N/m. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.
3 kg 6 kg
2.0 m/s 1.0 m/s
j
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4. Two blocks of masses 0.2 kg and 0.5 kg, which are placed 22 m
apart on a rough horizontal surface ( = 0.5), are acted upon by two forces of magnitude 3 N each as shown in figure at time t = 0. Then, find the time t at which they collide each other.
3 N
0.5 kg
0.2 kg
3 N
=0.5
22m
5. A particle of mass m is released from height ‘h’ on smooth quarter circular fixed wedge. The horizontal surface AB following the circular
path at bottom of wedge is rough with coefficient of friction between surface and m. Find the distance from bottom of wedge where the mass will stop.
h
A B
m
6. A light cylindrical vessel is kept on a horizontal surface. Its base area is A. A hole of cross sectional
area a is made just at its bottom side. Find the minimum coefficient of friction necessary for sliding of the vessel due to the impact force of the emerging liquid. (a<< A)
7. Eight identical droplets each falling under gravity in the earth’s atmosphere with terminal velocity v
combine together to form a single drop. Find the terminal velocity of the resulting drop. 8. An air bubble of radius r in water is at a depth h below the water surface at same instant. If P is the
atmospheric pressure and d, T are density and surface tension of water, respectively, then find the pressure inside the bubble.
9. A solid sphere of mass m is placed on a rough incline plane as shown
in figure. The coefficient of friction () is insufficient to start pure rolling.
The sphere slides length on incline from rest and its kinetic energy becomes k. Find work done by friction.
10. When entire Young's double slit apparatus is immersed in a liquid the fringe width decreases by 20%.
Find the refractive index of the liquid.
PART – II
11. A satellite of mass 2 103 kg has to be shifted from an orbit of radius 2R to another orbit of radius 3R,
where R is the radius of earth. Calculate the minimum energy required.
[R = 6400 km and g = 10 m/s2.]
12. A cylinder of radius r = 0.1 m and mass M = 2 kg is placed such that it is in
contact with a vertical wall and a horizontal surface as shown in the figure. The
coefficient of static friction is (1/3) for both the surfaces. Find the distance d
from the centre of the cylinder at which a force F = 40 N should be applied so
that the cylinder just starts rotating in the anticlockwise direction. Take g = 10
m/s2
F
r
A
B
13. Two gases of different densities but same atomicity are mixed in proportions V1 and V2 by volume. If
v1 and v2 be the velocity of sound in them, respectively, find the velocity of sound in the mixture.
(Assume that after mixing gases there is no change in pressure)
14. In an ore containing uranium, the ratio of U238
to Pb206
nuclei is 3. Calculate the age of the ore
assuming that all the lead present in the ore is the final stable product of U238
. Take the half life of
U238
to be 4.5 109 years.
j
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FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 16, Ph: 46106000, 26569493, Fax: 26513942.
FACULTY RECRUITMENT TEST
(CAT-A)
IIT – JEE
PHYSICS
PAPER B
Time: 1 Hour Maximum Marks: 40
Name:.................................................................................
Subject:…………………………...........................................
Marks:
Instructions
* Attempt all questions.
* Paper 2 has Two Parts I and II. Each question of Part I carries 2 marks and each question of part II caries 5 marks.
* Calculators and log tables are not permitted.
PART – I
1. A battery of emf E is connected in series with three resistances R, 2R and 3R. The voltage across 2R
is measured with a voltmeter, whose resistance is 20 R. Find the percentage error (approximately).
2. Figure shows a plank with a block placed on it. There
exists friction between plank and block but horizontal
surface on which plank moves is smooth. A variable
force which grows with time is applied on plank as
shown It was observed that at time t = t0 relative
m
F = kt 2m
s =
k 2
= 0
slipping between block and plank starts and at t = 2t0, block separates from plank. Find the speed of
block at this instant as observed from frame of plank.
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3. A small block B is supported by a platform connected at A to rod OA. Point A describes a circle in a vertical plane at a constant speed vA, The
coefficient of friction between the block and the platform are s = 1 3 and
k = 1 5 . Find the maximum speed vA, for the block not to slide on the
platform.
A
vA B
O 400 mm
4. The diagram shows three infinitely long uniform line charges 2, 3
and placed on the X, Y and Z axis respectively. Calculate the work done in moving a unit positive charge from (1, 1, 1) to (0, 1,1).
Y
X
Z
(0, 0, 0)
3
5. The resistivity of a certain metal is , using a wire drawing machine, a wire of uniform cross-section is made out of a volume V of the metal. The wire is shaped in a square loop, which is placed in a uniform magnetic field B whose direction is parallel to the loop axis. Find the charge flown through any cross-section of the wire, when the magnetic field is switched off.
6. One end of an uniform rod of length 1 m is placed in boiling water while its other end is placed in
melting ice. A point P on the rod is maintained at a constant temperature of 800C. The mass of steam produced per second is equal to the mass of ice melted per second. If latent heat of steam is 7 times the latent heat of ice. Calculate the distance of P from the steam chamber.
7. The diagram shows a meter bridge with the wire AB, having
uniform resistance per unit length. When the switch S is open, AJ is the balance length and when the switch is closed, AJ' is the balance length. If AB = L and AJ = L/2 then what is the value of AJ' in metre?
[Take L = 4 metre]
A
r/2
G
B
r
J
S r
8. Calculate the amount of energy evolved when eight droplets of mercury (surface tension 0.55 N/m) of
radius 1 mm each combine into one.
9. A light ray incident along vector ˆ ˆ ˆ2i 4j 5k strikes on the x-z plane from medium I of refractive
index 3 and enters into medium II of refractive index 2. Find the value of 2 for which the value of
angle of refraction becomes 90. 10. Consider a hypothetical atom having atomic number z = 2. It has two electrons each having mass m.
Assume that both electrons always lie diametrically opposite and nucleus of atom contains two proton. Assume Bohr model is applicable. Find the radius of first orbit of this atom (upto one decimal
place in pm). 2 0
0
2
hgiven 1.65 A
me
PART – II
11. An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of
heat involved in these steps are Q1 = 5960 J; Q2 = 5585 J; Q3 = 2980 J; and Q4 = 3645 J. The
corresponding works involved are W1 = 2200 J; W2 = 825 J; W3 = 1100 J and W4, respectively.
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(a) Find the value of W4.
(b) What is the efficiency of the cycle? 12. There a cylindrical tank of cross sectional area A resting on a horizontal surface. There is a small
orifice of cross sectional area ‘a’ (a << A) at the bottom lateral surface of it. Initially the tank was filled
with a liquid of density up to a height of H. Find (a) the speed of the liquid flowing out when the height of the liquid in the tank becomes H/2. (b) the horizontal force required to kept it at rest initially.
13. A uniform straight rod of mass M and length L slips in
vertical plane with one end on horizontal plane and the
other end on an inclined plane inclined at an angle 600
from horizontal. Both planes are smooth. When rod makes
an isosceles triangle with inclined planes, lower end has
speed v as shown.
V
O
60
Calculate (a) Angular velocity of rod,,(b) Kinetic energy of rod, (c) Angular momentum of rod about O
14. A thin non conducting horizontal disc of mass m having total charge q
distributed uniformly over its surface, can rotate freely about its own axis. Initially
when the disc is stationary a magnetic field B directed perpendicular to the
plane is switched on at t = 0. Find the angular velocity acquired by disc as a
function of time, if B = kt, where t is time.
R
B=kt
FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi - 16, Ph: 46106000, 26569493, Fax: 26513942.
FACULTY RECRUITMENT TEST
(CAT-A)
International Olympiads (Senior)
(PHYSICS)
(PAPER B)
Time: 1 Hour Maximum Marks: 40
Name:.................................................................................
Subject:…………………………...........................................
Marks:
Instructions
* Attempt all questions.
* Paper 2 has Two Parts I and II. Each question of Part I carries 2 marks and each question of part II caries 5 marks.
* Calculators and log tables are not permitted.
PART – I
1. The electric field in a region is given by 3 ˆE A x i . What is the potential at any point in the region?
2. A radioactive sample has decay constant . The rate of production of nuclei in the given sample as 2
09 N
N
, where N0 is the number of radioactive nuclei in the sample at t = 0 and N is the number of
radioactive nuclei in the sample at time t = t sec. Find the number of nuclei present in the radioactive
sample at t . (Given N0 = 106 nuclei)
3. Four waves of the equation given by
y1 = 5A sin (wt – Kx + /2)
y2 = 2A sin (wt – Kx + 3/2)
y3 = 6A sin (wt – Kx)
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and y4 = 2A sin (wt – Kx + )
Calculate the amplitude of resultant wave.
4. Three equal masses are held up with three identical ideal
strings and these strings are connected with one another at point O. Whole assembly is placed on smooth horizontal
surface and rotating about O with constant angular speed such that each string is taut and equally inclined with one another. String OA is burnt. Find angular speed of string BOC when it again becomes taut.
x
y
O
A
C
B
5. A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis, the liquid rises at its
sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 revolutions per second, find
the difference in the heights of the liquid at the centre and at the sides of the vessel. (take g = 10 ms2
and 2 = 10)
6. The figure shows two rods A & B each of length . A is attached to B through a smooth pin and B in turn can rotate as well as
slide about the hinge O. If the angular velocity of the rod A is , then find the velocity of point P at the instant shown.
/2
O
B
P
A 30
O
7. A particle is moving in a circle of radius R with a speed v and
mirror of length 2R is rotating with an angular velocity in the same plane with axis of rotation passes through O and perpendicular to the plane of figure. Same centre of rotation as shown in figure. Find the speed of image.
v
O
8. Two point masses of 0.2 Kg and 0.5 kg are fixed at the ends of a light rod of length 1.4m. Find the
minimum moment of inertia of the rod about an axis perpendicular to the rod. 9. A horizontal telephone cord is 4 m long and has a mass of 0.2 kg. A transverse wave pulse is
produced by plucking one end of the taut cord. The pulse makes four trips back and forth along the cord in 0.8 sec. Find the tension in the cord.
10. A capacitor of capacitance C is charged to a potential difference
of 0/2 and after that it is connected to a circuit with the polarity shown in the figure. At t = 0, switch S is closed. Find heat energy generated through the resistance after a long time.
0 R
C
S
- +
PART – II
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11. Centre of uniform disk of mass M and radius R is connected to block of same mass M through spring of spring constant K. Initially system is held at rest and spring is in natural length position. Friction between disk and ground is sufficient to prevent slipping. Now system is released from rest position. Calculate
(a) The maximum deformation in spring is
K
M
M
R
(b) The minimum coefficient of friction between disc and ground required to prevent slipping of disc. 12. Two identical buggies move one after the other due to inertia (without friction) with the same velocity
0v . A man of mass m rides the rear buggy. At a certain moment, the man jumps into the front buggy
with a velocity u relative to his buggy. Knowing that the mass of each buggy is equal to m. Find the
velocity with which the buggies will move after that. 13. In the circuit shown in figure. Capacitor A has
capacitance C1 = 2F when filled with dielectric slab with dielectric constant K = 2. Capacitor B and C are
air capacitors and have capacitances C2 = 3F and
C3 = 6F, respectively. A is charged by closing switch S1 alone. Calculate
180 V
S1
A
+
S2
B
C
(a) Energy supplied by battery during process of charging is (when only switch S1 is closed) (b) Now switch S1 is now opened and S2 is closed. Then, calculate the charge on B when electrical
equilibrium is attained. 14. Two monochromatic coherent sources of wavelength 5000 Å
are placed along the line normal to the screen as shown in the figure.
(a) Determine the condition for maxima at the point P. (b) Find the order of the central bright fringe if d = 0.5 mm, D = 1 m.
S2 S1
O
P
d D
TOPIC OUTLINE Note: Although fewer topics are covered in Physics C than in Physics B, they are covered in greater
depth and with greater analytical and mathematical sophistication, including calculus applications.
Subtopics that are covered in Physics C, but not Physics B.
Content Area Physics B Physics C
I. Newtonian Mechanics
A. Kinematics (including vectors, vector algebra, components of vectors,
coordinate systems, displacement, velocity, and acceleration)
1. Motion in one dimension
2. Motion in two dimensions including projectile motion
B. Newton's laws of motion
1. Static equilibrium (first law)
2. Dynamics of a single particle (second law)
3. Systems of two or more bodies (third law)
C. Work, energy, power
1. Work and work-energy theorem
2. Forces and potential energy
3. Conservation of energy
4. Power
D. Systems of particles, linear momentum
1. Center of mass
2. Impulse and momentum
3. Conservation of linear momentum, collisions
E. Circular motion and rotation
1. Uniform circular motion
2. Torque and rotational statics
3. Rotational kinematics and dynamics
4. Angular momentum and its conservation
F. Oscillations and gravitation
1. Simple harmonic motion (dynamics and energy relationships)
2. Mass on a spring
3. Pendulum and other oscillations
4. Newton's law of gravity
5. Orbits of planets and satellites
A. Circular
B. General
3-CAT A Adavance Placement Test Physics B & C-2
Content Area Physics B Physics C
II. Fluid Mechanics and Thermal Physics
A. Fluid Mechanics
1. Hydrostatic pressure
2. Buoyancy
3. Fluid flow continuity
4. Bernoulli's equation
B. Temperature and heat
1. Mechanical equivalent of heat
2. Heat transfer and thermal expansion
C. Kinetic theory and thermodynamics
1. Ideal gases
A. Kinetic model
B. Ideal gas law
2. Laws of thermodynamics
A. First law (including processes on pV diagrams)
B. Second law (including heat engines)
III. Electricity and Magnetism
A. Electrostatics
1. Charge and Coulomb's law
2. Electric field and electric potential (including point charges)
3. Gauss's law
4. Fields and potentials of other charge distributions
B. Conductors, capacitors, dielectrics
1. Electrostatics with conductors
2. Capacitors
A. Capacitance
B. Parallel plate
C. Spherical and cylindrical
3. Dielectrics
C. Electric circuits
1. Current, resistance, power
2. Steady-state direct current circuits with batteries and resistors only
3. Capacitors in circuits
A. Steady state
B. Transients in RC circuits
D. Magnetic Fields
1. Forces on moving charges in magnetic fields
2. Forces on current-carrying wires in magnetic fields
3. Fields of long current-carrying wires
4. Biot-Savart's law and Ampere's law
E. Electromagnetism
1. Electromagnetic induction (including Faraday's law and Lenz's law)
2. Inductance (including LR and LC circuits)
3. Maxwell's equations
3-CAT A Adavance Placement Test Physics B & C-3
Content Area Physics B Physics C
IV. Waves and Optics
A. Wave motion (including sound) 1. Traveling waves 2. Wave propagation 3. Standing waves 4. Superposition
B. Physical optics 1. Interference and diffraction 2. Dispersion of light and the electromagnetic spectrum
C. Geometric optics 1. Reflection and refraction 2. Mirrors 3. Lenses
V. Atomic and Nuclear Physics
A. Atomic physics and quantum effects 1. Photons, the photoelectric effect, Compton scattering, x-rays 2. Atomic energy levels 3. Wave-particle duality
B. Nuclear physics 1. Nuclear reactions (including conservation of mass number and
charge) 2. Mass-energy equivalence