Bansal Classes Download JEE Problems for Physics in Eleventh Standard : Great for AIEEE
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Transcript of Bansal Classes Download JEE Problems for Physics in Eleventh Standard : Great for AIEEE
CONTENTS: -
1. Practice Tests for Chemistry [All levels, not just JEE!]
2. Copying content off .djvu files
3. Asking questions online
4. Benefits of asking questions online!
5. But how do I copy the questions to ask them online?
6. How do I store images online if I want to ask questions on any site/forum?
7. Why should I ask my doubts online?
8. I am not studying for the JEE! These files are of no use for me!
9. To hell with engineering! I am preparing for medical entrance exams!
10. Please get the original printed study material!
11. What next?
COPYING CONTENT OFF .DJVU FILES
Once you have the .djvu files with you, you have the content. If you want to use the assignments in your daily
work and don’t want to stick around your computer while doing all that, just print them out. *Printing all the
assignments might seem clumsy to you – and expensive. Why not buy the books themselves, then? But
different situations, different demands. You can consider getting a refilled cartridge and use the printer on fast
draft (low DPI/low quality). You’d be able to print around 250 pages with one refill.]
The .djvu files facilitate printing. For example, the original scan and the encoded .djvu files are given above.
Compare their clarity. The original file has the text on the other side showing up as well. The .djvu files just
clear them up, apart from doing a lot of other technical things!
ASKING QUESTIONS ONLINE.
You should consider asking your doubts online. Here are three sites to get you started: -
Answers is an online service by yahoo which asks other users to answer the questions other users set up
online, ranging from Physics/Chemistry/Bio to Jeans/Hollywood/Mascarah/Relationships/Law/Cooking etc.
etc. etc.
Targetiit.com is a site by an IIT-KGP alumni to help others preparing for JEE. Its specialized for JEE, check it out
once! The site recently produced an AIR-45 in IIT-JEE!
The last four are specialized help sites, and I seriously recommend them to you if you want to learn from the
hands of perfectionists. If you want to see an example of how the international sites can help you, scroll
further down!
1. www.answers.yahoo.com
2. www.targetiit.com and www.goiit.com
3. www.physicsforums.com PHYSICS HELP
4. www.mathhelpforum.com MATHEMATICS HELP
5. www.chemicalforums.com/ CHEMISTRY HELP
6. http://www.biology-online.org/biology-forum/ BIOLOGY
HELP
Benefits of asking Questions Online!
BUT HOW DO I COPY THE QUESTIONS TO PASTE THEM ONLINE?
It’s simple. Let’s see three ways you can do this. Suppose you want to copy a block of text, open up the .djvu
file in DJVU viewer – (google up DJVU Viewer Download. You will get a live direct link to djvu viewer! Well, just
in case you find learning new procedures/things like this kind of tedious, how are you gonna prepare for the
JEE in the first place? Screw JEE, if you can’t even be comfortable with googling up software why are you
studying in Science stream at all? I’m just assuming you downloaded this file yourself.)
(A) COPYING A BLOCK OF TEXT
Check the image above. I have opened up a page of S L Loney above. Note the fifth icon to the right of
Lizardtech logo in the bottommost toolbar, it’s the text selection tool. (The T surrounded by dotted lines.).
Click on it.
Now select the region you want to copy text from like you would do normally in a word/acrobat/notepad
window. Copy (Ctrl + C) and paste wherever you want.
Please note that if whatever text you are copying involves a lot of mathematical formulae, then it’s a good idea
to format the text before posting it online.
(B) COPYING A DIAGRAM/IMAGE FROM .DJVU F ILES.
On the menu bar, you will see a “Selection” menu item. Click on it and in the drop down menu, select the
“Select Region” option.
Now, select any region of the .djvu file that you want to use as a diagram. Look at the two examples below: -
The blacked out zone is the selected region that I want to use. After copying it, I can paste it anywhere, like I
did here...
Just in case your question has a lot of formulae/signs/symbols and it would be complicated for you to type the
question yourself, just copy the whole question as a region instead of text and paste it as you would paste a
diagram/image! This is particularly useful for questions of integration and so on...
Just be careful that if you are going to use these images online on one of those sites and pose them as
questions, not many people would be attracted to your question. There’s a simple reason, there are hundreds
of questions posted everywhere, if your question has no text – it won’t show up in searches/related questions
etc. etc. etc. and hence minimum visibility to people who know the answer.
HOW DO I STORE IMAGES ONLINE IF I WANT T O ASK QUESTIONS ON ANY
SITE/FORUM?
First off, make the image file yourself on your computer using DJVU viewer and paint. Store the files in GIF
format and NOT BMP format. [If you have no clue what they do, just remember that GIF format is low on
filesize and hence will save you a lot of time/data usage on your internet connection]
Once you have the image ready with yourself, just post online on any photosharing website that gives you a
direct link to images. Figure this yourself. Google “Image sharing for forums” or “Imageshack” or
“Photobucket” or whatever. Imageshack/PhotoBucket are meant for this. Try them out.
WHY SHOULD I ASK MY DOUBTS ONLINE?
Have you ever complained about your teachers/low competition/stress/environment? All of us have at some
point of time or the other, so don’t pretend you didn’t. But if there’s one percent of truth in the claim that you
didn’t complain about them to give an excuse for your own failure or to look smart in how well you can analyze
things – then God has listened to your complaints. Go out there and make the best use of the opportunities
given by your internet connection and those sites. It’s because those sites exist that we scanned 7000 pages of
text to help get you started with your preparations and reduce some stress off you.
But in case even this time you come up with an excuse about how asking doubts on those sites is not
productive, hats off to you. Somebody else is obviously going to reap the benefits of our labour work of over a
month of our summer vacations and spend their high school life without useless stress, simply because they
outsourced the job of clearing up their mental bottlenecks to the hundreds of online professors/students who
want to help you! In any case, if you don’t see these files as an opportunity, chances are that you haven’t
started studying as yet (explaining why you haven’t felt any stress as yet)! I just hope it’s not February with
your Chemistry fully remaining before your board exams.
I AM NOT STUDYING FOR THE JEE! THESE FILES ARE OF NO USE FOR ME!
Fine. Don’t use them. But we haven’t scanned material useful only for JEE either. We don’t care what an
exclusive bunch of students who can take care of themselves is doing.
A lot of the material we have scanned has many many generic questions, straight questions, common sense
based puzzles, actual test papers from previous years. Even Bansal Classes’ material has a lot of simple
examples that will help you with your basics (simple = common sense based. You might find them difficult, but
it’s not a big deal if you find even the simplest of questions difficult. After all, common senses are not so
common). Just avoid the Exercise II problems and the lengthier subjective problems that were asked in JEE.
The first half of exercise I would be fine.
And any/all of AIEEE material is essentially your board syllabus. Keep one thing in mind, contrary to what your
coaching classes might tell you, preparing for the AIEEE alongside reading NCERT text keeps you in touch with
everything. Do the AIEEE questions and you’re done with understanding your NCERT text.
Once you understand your text, its easier to rot/memorize/answer descriptive problems. I am assuming that
all of us have felt a little responsible at times and started reading NCERT texts and then, drifted off into other
thoughts while your eyes blankly scanned the sentences without you grasping their meaning. If you have that
experience, then definitely try AIEEE questions, purposefully generate doubts and then ask them online. If you
see no difference, double your doubts. Give it 15-20 days and then see the difference. What will matter here is
whether you want to change the situation that you do not get the meaning of texts. Emphasis on HOW MUCH
you want to change the situation. It all comes down to you.
TO HELL WITH ENGINEERING! I AM PREPARING FOR MEDICAL ENTRANCE EXAMS!
My dear boy, even medical entrance examinations have Physics and Chemistry! Just don’t use the JEE/AIEEE
specific questions, but you should have an idea of what difficulty level is usually maintained. Search for it, we
have a set of mock test papers, which are mock tests of JEE/AIEEE/Physics for PMT/Chemistry MCQs in medical
exams, so you’ll find plenty of resources online! We also have a chhota sa nanha sa munna sa set of Biology
mock tests of all difficulty levels.
Grab them and start solving. If you stumble, ask doubts. Simple. Will you succeed or will you not will just
depend on your attitude/determination/ambition. People have a tendency to use these words randomly as if
they are spraying salt and pepper over some dish. Grab a dictionary and check their literal meanings. After
that, ask yourself where you stand.
PLEASE GET THE ORIGINAL PRINTED STUDY MA TERIAL!
You should remember that we are not affiliated with Arihant Prakashan/Bansal
Classes/Fiitjee/Yahoo.com/Target IIT/HighschoolHelpForum in any ways. If you have these files and like the
content that’s inside them, just go out there and buy the original printed documents. After all, it’s someone’s
hard work!
WHAT NEXT?
Use google alerts for yourself! Alerts.google.com – set up alerts for IIT-JEE/IIT Study Material/AIEEE/AIEEE
Study Material/CBSE and all other tags you can think of. Basically, all that will keep you updated on whatever
stuff that is available online to help you study.
A SAMPLE LIST OF QUESTIONS THAT CAN
BE FOUND IN THE DJVU FILE A butterfly is flying with velocity 10 i +
12 } mls and wind is blowing along x
axis
with velocity u. Ifbutterfly starts
motion from A and after some time
reaches
point B, find the value of u.
�y
kx
Find the change in velocity of the tip of
the minute hand (radius = 10 cm) of a
c10ck in45 minutes.
�A, B & C are three objects each
moving with constant velocity. A's
speed is 10 mlsec in a direction PQ .
The velocity ofB relative to A is 6 mlsec
at an angle of, cos- I (15/24) to PQ .
The velocity orc relative
to B is 12 mlsec in a direction QP , then
find the magnitude of the velocity ofC.
Rain is falling vertically with a speed
of20 ms.] relative to air. A person is
running in the rain with a
velocity of 5 ms-] and a wind is also
blowing with a speed of 15 ms- 1 (both
towards east). Find the angle
with the vertical at which the person
should hold his umbrella so that he
may not get drenched.
�The velocity-time graph of the
particle moving along a straight line is
shown. The _
rate of acceleation d decelertio is
constant and it is equal to 5 ms- 2 . If
the . r
average velocIty dunng the motIOn IS
20 ms- 1 , then find the value oft.
o t 25 see
�The fig. shows the v-t graph of a
particle moving in straight line, Find
the time when particle returns
to the starting point. v
20
�10
�Q.7 A particle is projected in the X- Y
plane. 2 sec after projection the
velocity of the particle makes an
angle 45° with the X - axis. 4 sec after
projection, it moves horizontally. Find
the velocity of
projection (use g = 10 ms- 2 ).
�Q.8 A small ball rolls off the top
landing of a staircase. It strikes the
mid point of the first step and then
mid point of the second step. The
steps are smooth & identical in height
& width.Find the coefficient
of restitution between the ball & the
first step.
�Q.9 A stone is dropped from a height
h . Simultaneously another stone is
thrown up from the ground
with such a velocity that it can reach a
height of 4h. Find the time when two
stones cross each other, . I
,
�Q.10 A particle is projected upwards
with a velocity of 1 00 mlsec at an
angle of 60° with the vertical, Find the
time when the particle will move
perpendicular to its initial direction,
taking g = 10 mlsec 2 .
A large number of bullets are
fIred in all direction with the
same speed v. What is the
maximum area on
ground on which these bullets
can spread?
Q .13 A boat starts from rest
from one end of a bank of a
river of width d flowing with
velocity u. The boat is
steered with constant
acceleration a in a direction
perpendicular to the bank. If
point of start is origin,
direction of bank is x axis and
perpendicular to bank is y axis.
Find the equation of trajectory
of the boat.
Q .14 A ball is thrown
horizontally from a cliff such
that it strikes ground after 5
sec.
The line of sight from the point
of proj ection to the point
ofhirting makes an
angle on 7° with the
horizontal. What is the initial
velocity of projection.
�Q .15 A ball is proj ected on
smooth inclined plane in
direction perpendicular
to line of greatest slope with
velocity of8m1s. Find it's
speed after 1 sec.
�Q .16 A glass wind screen
whose inclination with the
vertical can be changed,
is mounted on a cart as shown
in fIgure. The cart moves
uniformly along
the horizontal path with a
speed of 6 mls. At what
maximum angle a to
the vertical can the wind
screen be placed so that the
rain drops falling
vertically downwards with
velocity 2 mis, do not enter
the cart?
�Q.17 A particle is projected
from point P with velocity 5.fi
mls perpendicular
to the surface of a hollow right
angle cone whose axis is
vertical. It collides
at Q normally. Find the time of
the flight of the particle.
�Q .18 Find range of projectile
on the inclined plane which is
proj ected perpendicular
to the incline plane with
velocity 20mls as shown in
fIgure.
�Q .19 AB and CD are two
smooth parallel walls. A child
rolls a ball along ground
from A towards point P fInd PD
so that ball reaches point B
after striking
the wall CD. Given coefficient
ofrestitutione = 0.5
�L 'k-
37°
, ,
�y
�x
�'Sr"
�C P4i-X D
J z ·
A __l.5m_B
�Q .20 Initial acceleration of a
particle moving in a straight
line is a o and initial velocity is
zero. The acceleration
reduces continuously to half in
every to seconds as a = . Find
the terminal velocity of the
particle.
2
to
Q.21 Find the acceleration of
movable pulley P and block B if
accelerationofblockA= 1 mls 2
A weightless inextensible rope
on a stationary wedge forming
angle a with the
horizontal. One end of the
rope is fixed to the wall at
point A. A small load is
attached to the rope at point
B. The wedge starts moving to
the right with a constant
acceleration. Determine the
acceleration a] of the load
when it is still on the wedge.
�Q.26 The horizontal range of
a projectiles is R and the
maximum height attained by it
is H. A strong wind
now begins to blow in the
direction of motion of the
projectile, giving it a constant
horizontal
acceleration = g/2. Under the
same conditions of proj ection,
find the horizontal range of
the proj ectile.
�Q.27 COllSiderthe
acceleration of a particle for a
given time 't' at 'a' mls 2
followed immediately by
retardation
at the same rate of , a' rn/s 2
for time 't/2', as one cycle. If
the particle started from rest,
find the distance
travelled by it after 'n' such
cycles in succession.
�Q .28 A particle is thrown
horizontally with relative
velocity 10 mls from an
inclined
plane, which is also moving
with acceleration 10 mls 2
vertically upward. Find
the time after which it lands
on the plane (g = 10 mls 2 )
Block A of mass m and block B
of mass 2m are placed on a
fixed triangular
wedge by means of a massless
inextensible string and a
fuctionless pulley as
shown in the figure. The
wedge is inclined at 45° to the
horizontal on both
sides. The eoetticient of
friction between block A and
the wedge is
2/3 and that between block B
and the wedge is 1/3. Ifthe
system of A and B
is released from rest, fmd (i)
the acceleration of A, (ii)
tension in the string, (iii)
the magnitude and the
direction of fuction acting on
A. [JEE 1997]
�Q.3
�A spring offorce constant k is
cut into two pieces such that
one piece such that one piece
is double
the length of the other. Then
the long piece will have a force
constant of
(A) (2/3) k (B) (3/2) k (C) 3k (D)
6k [JEE 1999]
�Q.4
�In the figure masses mp m 2
and Mare 20 kg,S kg and 50 kg
respectively. The co-efficient
of friction between M and
ground is
zero. The co-efficient of
friction between m] and M and
that between
m 2 and ground is 0.3. The
pulleys and the string are
massless. The
string is perfectly horizontal
between p] and m] and also
between P 2
and m 2 ' The string is
perfectly vertical between p]
and P 2.An external
horizontal force F is applied to
the mass M. Take g = 10 m/s 2
.
Draw a free-body diagram for
mass M, clearly showing all the
forces.
Let the magnitude of the force
of friction between m] and M
be f] and that between m 2
and ground
be f 2 . For a particular F it is
found that f] = 2 f 2 ; Find f]
and f 2 . Write down equations
of motion
of all the masses. Find F,
tension in the string and
accelerations of the masses.
[lEE 2000]
The pulleys and strings shown
in the figure are smooth and of
negligible mass. For the
system to remain in
equilibrium, the
angle 8 should be [JEE (Scr)
2001]
(A) 0° (B) 30°
(C) 45° (D) 60°
�(a)
(b)
�Q.5
�Q
�Q.6
�A string of negligible mass
going over a clamped pulley of
mass
m supports a block of mass M
as shown in the figure. The
foree on the pulley by the
clamp is given [JEE (Scr) 2001]
. (A) .fi Mg (B) .fi mg
(C) (M+m)2 +m 2 g (D)
(M+m)2 +M 2 g
�Q.7
�A block of mass .J3 kg is
placed on a rough horizontal
surface whose coefficient
of fuction is 1/2.J3 minimum
value of force F (shown in
figure) for which the
block starts to slide on the
surface. (g=l Omls 2 )
(A) 20 N (B) 20.J3 N
(C) 1O.J3 N (D) None of these
Two blocks A and B of equal
masses are released from an
inclined
plane of inclination 45° at t =
O. Both the blocks are initially
at rest. The
coefficient of kinetic fuction
between the block A and the
inclined plane
is 0.2 while it is 0.3 for block B.
Initially, the block A is .fi m
behind the
block B. When and where their
front faces will come in a line.
The bob of a simple pendulum
oflength I is released from-
point P. What
is the angle made by the net
acceleration of the bob with
the string at
point Q.
�Q.2 A ball of mass 1 kg is
released from position A inside
a wedge with a hemispherical
cut of radius 0.5 m as shown in
the figure. Find the foree
exerted by the vertical
wall OM on wedge, when the
ball is in position B. (neglect
fuction everywhere).
Take (g = 10 mls 2 )
�Q.3 A particle P is moving on
a circle under the action of
only one force acting
always towards fixed point a
on the circumference. Find
ratio of
d 2 8 & ( d8 ) 2
dt 2 dt
�Q
�N
�o
�p
�o
�Q.4 A particle is moving in x
direction, under the influence
offoree F = rr sin nx. Find the
work done by
another external agent in
slowly moving a particle from x
= 0 to x = 0.5 m.
Q.5 A particle moves in a circle
of radius R with a constant
speed v. Then, find the
magnitude of average
rrR
acceleration during a time
interval 2 v .
�Q.6 In the figure shown,
pulley and spring are ideal.
Find the potential energy
stored
in the spring (m i > ).
�Q.7 A spring of mass m is
pulled such that a given
instant"ve10city of both of its
end is v in the opposite
direction. Find the kinetic
energy ofthe spring, vv
�Q.8 A particle of mass 3 kg is
rotating in a circle of radius 1
m such that the angle rotated
by its radius is given
by 8 = 3 (t + sint). Find the net
foree acting on the particle
when t = rr/2.
�Q.9 For a particle rotating in a
vertieal circle 1th uniform
speed, the maximum and
minimum tension in the
string are in the ratio 5 : 3. If
the radius of vertical circle is
2m, then find the speed of
revolving body.
�Q.10 Two strings oflength I =
0.5 m each are connected to a
block of mass m = 2 kg at
one end and their ends are
attached to the point A and B
0.5 m apart on a vertical
T
pole which rotates with a
constant angular velocity 0)= 7
rad/sec. Find the ratio t
2
oftension in the upper string (T
1 ) and the lower string (T 2 ).
[Use g = 9.8 m/s2]
�B
0.5
m 0.5
0.5
A
�Q.11 A force F = -k(x i + y })
[where k is a positive constant]
acts on a particle moving in
the x-y plane.
Starting from origin,
thepartic1e is taken to (a, a)
and then to (a/.J2, 0). Find the
total work done by the
foree F on the particle.
�@Bansal Classes
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 x of the
particle from the origin as
F(x) = - kx + ax 2 . Here k and a
are positive constants. For x;:::
0, the functional form of the
potential
energy U (x) ofthe particle is
[lEE (Scr.)'2002]
U(X)j .
(A) x
�...--
�Q.12
�U(X)j U(X)j\ U(X)j /\
(B) x (C) x (D) ---r---r x
�Q.13 An ideal spring with
spring-constantkis hung from
the ceiling and a block of mass
M is attached to its
lower end. The mass is
released with the spring
initiallyunstretched. Then the
maximum extension in the
spring is [lEE (Scr.)'2002]
(A) 4 Mglk (B) 2 Mglk (C) Mg/k
(D) Mg/2k '
Q .14 A spherical ball of mass
m is kept at the highest point
in the spaee between two
fixed, concentrie
spheresAandB (see figure). The
smaller sphereAhas a radius R
and the space between the
two spheres has a width d. The
ball has a diameter very , .
slightly less than d. All surfaces
are frictionless. The ball is
given a gentle push 18
(towards the right in the
figure). The angle made by the
radius veetor of the ball with -
+ d +- R 0
the upward vertieal is denoted
by e (shown in the figure). [JEE
' 2002]
(a) Express the total normal
reaction foree exerted by the
spheres on the ball as a
funetion of angle 8.
(b) Let N A and N B denote the
magnitudes ofthe normal
reaction force on the ball
exerted by the spheres A
and B, respectively. Sketch the
variations ofN A and N B as
funetions of cos8 in the range
0 S 8 S 1t by
drawing t\"IO separate graphs
in your answer book, taking
cos8 on the horizontal axes.
Q.15 In a region of only
gravitational field of mass 'M'
a particle is shifted
from A to B via three different
paths in the figure. The work
done in B
different paths are WI' W 2 , W
3 respectively then [JEE
(Ser.)'2003]
(A) WI = W 2 = W 3 (B) W] = W
2 > W 3
(C) W] > W 2 > W 3 (D) W] < W
2 < W 3
Q .16 A particle of mass m,
moving in a eireular path of
radius R with a eonstant
speed v 2 is loeated at point
(2R, 0) at time t = 0 and a man
starts
moving with a veloeity v I
along the ,ve y-axis :ITom
origin at time t = O.
Calculate the linear
momentum of the particle
w.r.t. the man as a funetion
oftime. [lEE'2003]
�V2
�'...X
�A particle is plaeed at the
origin and a force F = kx is
acting on it (where k is a
positive constant). If
U(O)= 0, the graph ofU(x)
versus x will be (where U is the
potential energy funetion)
x u _ \(X)i )
0) ( I )X )x
�Q.17
�U(X)v _
(D) x
[JEE' 2004(Ser)]
�@Bansal Classes
A particle of mass m is
projeeted with a veloeity u at
an angle ofe with horizontal,
Find the intial angular
momentum ofthe particle
about the highest point of its
projeetory.
�Q:2 A hollow sphere is
released from the top of a
movable wedge as shown in
the
figure. There is no friction
between the wedge and the
ground. There is sufficient
frietion between sphere and
wedge to provide pure rolling
of sphere. Find the
velocity of centre of sphere
w.r.t. ground just before it
leaves the wedge
horizontally. (Assume masses
of the wedge and sphere are
equal & h» R the
radius of sphere) _\ \ - \" ,\ _\
,,' \ - ,,\ \,
�Q,3 A bit of mud stuck to a
bicycle's front wheel of radius
r detaehes and is flung
horizontally forward when
it is at the top ofthe wheel.
The bicycle is moving forward
at a speed v and it is rolling
without slipping.
Find the horizontal distance
travelled by the mud after
detac.hing from the wheel.
�Q,4 In the figure shown, the
ball of mass m (having velocity
v 0) hits the surrace of a
stationary square plate of
mass m and side L, with center
pivoted at C on a
smooth horizontal table .Due
to the collision, the ball stops.
Find the angular
veloeity of the plate after
collision.
�..,..,'...t Ll3
C
�Q,5 A wheel, of radius 1 m, is
rolling purely on a flat,
horizontal surfaee. It's centre
is moving with aeonstant
horizontal acceleration = 3 mis
2 , At a moment when the
centre ofthe wheel has a
veloeity 3 mis, then
find the aeeeleration of a point
113 m vertically above the
centre ofthe wheel,
",Q. l) A force of constant
magnitude F starts acting on a
uniform rod AB in gravity free
space at the end A of
the rod. The foree always
remains perpendicular to the
rod, even as it moves, The
mass ofthe rod is M
and its length L. Then, find the
value of the dot product F. a A
at any later time( where a A is
acceleration
of point A.)
�'Q.8
�A uniform horizontal rod
oflength I falls vertically from
height h on two identical
bloeks plaeed symmertrically
below the rod as shown in
figure, The coefficients of
restitution are e 1 and e 2 ,
Find the maximum height
through which the eentre of
mass of the rod will rise after
bouncing off the blocks.
�.C2.9
�A uniform rod oflength I is
given an impulse at right
angles to its length as shown.
Find the distanee of
instantaneous centre of
rotation fTom the eentre of
the rod,
A plank oflength 2L, leans
vertically against a wall, It
starts to slip
downward withoutfiiction.
Show that the top of the plank
loses contact
with the wall when it is at
tVv'O-thirds of its initial height
�"
8
I II I I
�(i)
(n)
(ill)
�A solid metallic cylinder of
mass ill = 1 kg and radius R =
20 em is free to roll /i
(without sli ding) over the
incJined surface of a wooden
wedge of mass M = 0.28 kg, I'V
I :
Surface of wedge is inclined at
37° with the horizontal and the
wedge lies on a 'yJ
smooth horizontal floor. When
the system is released rrom
rest, calculate I
acceleration of the wedge, / / /
,i / / I / / j / / I
angular acceleration of the
cylinder and
force of interaction between
cylinder and the wedge, (g =
10 ms- 2 )
�Q,27
�Q.28 A uniform slender bar
AB of mass m is suspended as
shown from a
small cart of the same mass m,
Neglecting the effect of
fiiction, determine
the acceleration of points A
and B immediately after a
horizontal force
P has been aDD lied at B.
< ,
�I
f W
Li illl i'-J i! - illll
, ')
! B oJ
�Q. 29 A solid spheric::d ball
which rests in equilibrium at
the interior bottom of a fixed
spherical globe is perrectly
rough, the ball is struck a
horizontal blow of such
magnitude that the initial
speed of its centre is v. Prove
that, if v lies between (l 0
dg/7j112 and (27 dg/7)1/2, the
ball will leave the globe, d
being the difference
between the radii of the ball
and globe
�Q,30 A240 nun radius
cylin.der of mass 8 kg rests on
a 3 kg carriage, The system is
at rest when a force P of
magnitude ION is applied as
shown for 1,2 s, Knowing that
the cylinder rolls without
sliding on the
carriage and neglecting the
mass ofthe wheels of the
carriage determine the
resulting velocity of (a)
the carriage, (b) the center of
the cylinder,
An aluminium container of
mass 100 gm contains 200 gm
of ice at - 20°C. Heat is added
to the
system at the rate of 100 calls.
Find the temperature of the
system after 4 minutes
(specific heat of
ice = 0.5 and L = 80 cal/gm,
specific heat of AI = 0.2
cal/gmJ°C)
Q.2 A V-tube filled with a
liquid of volumetric coefficient
of 1O- 5 jOC lies in a vertical
plane. The height of
liquid column in the left
vertical limb is 100 cm. The
liquid in the left vertical limb is
maintained at a
temperature = O°C while the
liquid in the fight limb is
maintained at a temperature =
100°C. Find the
difference in levels in the two
lin1bs.
�Q.3 A thin walled metal tank
of surface area 5m 2 is filled
with water tank and contains
an immersion
heater dissipating 1 kW. The
tank is covered with 4 cm thick
layer of insulation whose
thermal
conductivity is 0.2 W/m/K. The
outer faee ofthe insulation is
25°C. Find the temperature
ofthe
tank in the steady state
�Q.4 A glass flask contains
some mercury at room
temperature. It is found that at
different temperatures
the volume of air inside the
flask remains the same. If the
volume of mercury in the flask
is
300 cm 3 , then find volume of
the flask (given that coefficient
of volume expansion of
mercury and
coefficient of linear expansion
of glass are 1.8 x 10-4 eC)-]
and 9 x 10-6 (Oct 1
respectively)
�Q.5 A clock pendulum made
ofinvar has a period of 0.5 sec
at 20°C. If the clock is used in a
climate
where average temperature is
30°C, aporoximately. How
much fast or slow will the
clock run in
10 6 see ( a. =1 x 10- 6 /°C )
. mvar
�Q.6 A pan filled with hot food
cools from 50.1 °c to 49.9 °c in
5 sec. How long will it take to
cool
from 40.1 °c to 39.9°C if room
temperature is 30°C?
�Q.7 A composite rod made of
three rods of equal length and
cross-section as shown in the
fig. The
thermal conductivities ofthe
materials ofthe rods are K/2,
5K and K respectively. The end
A and
end B are at constant
temperatures. All heat
entering the face A goes out of
the end B there being
no loss of heat from the sides
of the bar. Find the effective
thermal conductivity of the bar
Toluene liquid of volume 300
cm 3 at O°C is contained in a
beaker an another quantity of
toluene of
volume 110 cm 3 at 100°C is in
another beaker. (The
combined volume is 410 cm 3
). Detemnne the
total volume of the mixture of
the toluene liquids when they
are mixed together. Given the
coefficient
of volume expansion 'Y =
O.OOllC and all forms of heat
losses can be ignored. Also
find the final
temperature of the mixture.
�Q.9 Ice at -20°C is filled upto
heighth = 10 cmina uniform
cylindrical vessel. Water at
temperature SOCis
filled in another identical
vessel upto the same height h=
10 cm. Now, water from
second vessel is
poured into first vessel and it
is found that level of upper
surface falls through
h = O. 5 em when thermal
equilibrium i reached.
Neglecting thermal capacity of
vessels, change
in density of water due to
change in temperature and
loss of heat due to radiation,
calculate initial
temperature S of water.
Given, Density of water, Pw =
1 gm cm- 3
Density of ice, Pj = 0,9 gm/em
3
Specific heat of water, Sw = 1
cal/gm °C
Specific heat of ice, Sj = 0.5
cal/gmOC
Specific latent heat of ice, L =
80cal/gm
Q. lOA composite body
consists of two rectangular
plates of the same dimensions
but different thermal
conductivities K A and . This
body is used to transfer heat
between two objects
maintained at
different temperatures. The
composite body can be placed
such that flow of heat takes
place either
parallrl to the interface or
perpendicular to it. Calculate
the effective thermal
conductivities KJJ and
K.l of the composite body for
the parallel and perpendicular
orientations. Which
orientation will
have morc;; thermal
conductivity?
�Q.ll Two identical thermally
insulated vessels, each
containing n mole of an ideal
monatomic gas, are
interconnected by a rod of
length I and cross-sectional
area A. Material of the rod has
thermal
conductivity K and its lateral
surface is thermally insulated.
If, at initial moment (t = 0),
temperature
of gas in two vessels is TI and T
2 « T j ), neglecting thermal
capacity of the rod, calculate
difference
between temperature of gas in
two vessels as a function
oftime.
�Q .12 A highly conducting
solid cylinder of radius a and
length I is surrounded by a co-
axial layer of a
material having thermal
conductivity K and negligible
heat capacity. Temperature of
surrounding
space (out side the layer) is To,
which is higher than
temperature of the cylinder. If
heat capacity
per unit volume of cylinder
material is s and outer radius
of the layer is b, calculate time
required
to increase temperature of the
cylinder from T] to T 2 .
Assume end faces to be
thermally insulated.
�Q.13 A vertical brick
duct(tube) is filled with cast
iron. The lower end of the duct
is maintained at a
temperature T 1 which is
greater than the melting point
T m of cast iron and the upper
end at a temperature
T 2 which is less than the
temperatLlfe of the melting
point of cast iron. It is given
that the conductivity of
liquid cast iron is equal to k
times the conductivity of solid
cast iron. Determine the
fraction of the duct
filled with molten metal.
In which of the following
phenomenon heat conveetion
does not take place
(A) land and sea breeze
(B) boiling of water
(C) heating of glass surface due
to fIlament of the bulb
(D) air around the furance
�[JEE' 2005 (Scr)]
�Q.26 2 litre water at 27°C is
heated by a 1 kW heater in an
open container. On an average
heat is lost to
surroundings at the rate 160
J/s. The time required for the
temperature to reach 77°C is
(A) 8 min 20 sec (B) 10 mill (C)
7 min (D) 14 min
[JEE' 2005 (Scr)]
�Q.27 A spherical body of area
A, and emissivity e = 0.6 is kept
inside a black body. What is
the rate at which
energy is radiated per second
at temperature T
(A) 0.6 cr AT4 (B) 0.4 cr A'f4 (C)
0.8 (j' AT4
�Q.28
�(D) 1.0crAT4
[JEE' 2005 (Ser)]
1 calorie is the heat required
to increased the temperature
of 1 gm of water by 1°C from
(A) 13.5°Cto
14.5°Cat76mmofHg (B)
14.5°Cto 15.5°Cat760mmofHg
(C) O°C to 1°C at 760 mm ofHg
(D) 3°C to 4°C to 760 mm ofHg
A spherical tank of 1.2 m
radius is half filled with oil of
relative density 0.8. If the tank
is given
a horizontal acceleration of 10
m/ 82. Calculate the
inclination of the oil surface to
horizontal and maximum
pressure on the tank.
A piston of mass M = 3 kg and
radius R = 4cm has a hole into
which a thin pipe
ofradiusr= lcmisinserted. The
piston can enter a cylinder
tightly and without ''':': "_'.::.'
-. - - -...
ftiction, and initially it is at the
bottom of the cylinder. 750gm
of water is now , .:' ;::.
. - -.. -..
poured into the pipe so that
the piston & pipe are lifted up
as shown. Find the : :=: :
height H of water in the
cylinder and height h of water
in the pipe. .-, :- ,-.:,
A rectangular vessel is filled
with water & oil in equal
proportion (by volume), the oil
being twice lighter
than water. Show that the
force on each wall of the
vessel will be reduced by one
fifth if the vessel is
filled only with oil. (take into
consideration the fact that the
oil is found at the top of the
vessel).
A solid ball of density half that
of water falls fteely under
gravity ftom a height of 19.6 m
and then enter
water. Upto what depth will
the ball go? How much time
will it take to come again to
the water
surface? Neglect air resistance
& velocity effects in water.
Place a glass beaker, partially
filled with water, in a sink. The
beaker has a mass 390 gm and
an interior
volume of 500cm 3 . You now
start to fill the sink with water
and you find, by experiment,
that if the
beaker is less than half full, it
will float; but ifit is more than
half full, it remains on the
bottom ofthe sink
as the water rises to its rim.
'What is the density of the
material of which the beaker is
made?
Two spherical balls A and B
made up of same material
having masses 2m and m are
released ftom rest.
Ball B lies at a distance h below
the water surface while A is at
a height of2h above water
surface in the
same vertical line, at the
instant they are released.
Obtain the position where
they collide.
lfthe bodies stick together due
to collision, to what maximum
height above water surface
does the
combined mass rise?
Specific gravity of the material
ofthe balls is 213. Neglect
viscosity and loss due to
splash.
Two very large open tanks A
and F both contain the san1e
liquid, A
horizontal pipe BCD, having a
constriction at C leads out of
the
bottom of tank A, and a
vertical pipe E opens into the
constriction at
C and dips into the liquid in
tank F. Assume streamline
How and no
viscosity, If the cross section at
C is one half that at D and if 0
is at
a distance 1.1 1 below the
level ofliquid inA, to what
height h 2 (in
terms of h 1 )wililiquid rise in
pipe E ?
For the system shown in the
figure, the cylinder on the left
at L has a
mass of 600kg and a cross
sectional area of800 cm 2 . The
piston on
the right, at S, has cross
sectional area 25cm 2 and
negligible weight.
If the apparatus is filled with
oil,(p = 0.75 gm/cm 3 ) Find
the forceF
required to hold the system in
equilibrium.
�EXERCISE # I
�:
A :
�600kg I
A nonviscous liquid of constant
density 1000 kg/m 3 flows in a
streamline motion
along a tube of variable cross
section. The tube is kept
inclined in the vertical plane
as shown in the figure, The
area of cross section ofthe
tube at two points P and Q
at heights of2 meters and 5
meters are respectively 4 x 10-
3m 2 and 8 x 10- 3 m 3 .
The velocity of the liquid at
pointP is 1 mls. Find the work
done per unit volume by
the pressure and the gravity
forces as the fluid flows from
point P to Q.
�[ JEE '97]
�u
p
Sm
m
�Q,7 Water from a tap
emerges vertically downwards
with an initial speed of 1,0 ms-
I . The cross-sectional
area ofthe tap is 10- 4 m 2 .
Assume that the pressure is
constant throughout the
stream of water, and that
the flow is steady. The cross-
sectional area of the stream
0.15 m below the tap is [ JEE
'98, 2 ]
(A) 5.0 x 10- 4 m 2 (B) 1.0 x 10.
5 m 2 (C) 5.0 x 10- 5 m 2 (D)
2.0 x 10- 5 m 2
�Q,8 A wooden stick oflengthl,
and radiusR and density p has
a small metal piece of mass m
(of negligible
volume) attached to its one
end, Find the minimum value
for the mass m (in terms of
given parameters)
that would make the stick float
vertically in equilibrium in a
liquid of density (j (>p), [ JEE
'99, 10]
�Q,9 A large open tank has
two holes in the wall. One is a
square hole of side L at a
depth y from the top and
the other is a circular hole of
radius R at a depth 4y from the
top. When the tank is
completely filled with
water, the quantities of water
flowing out per second ITom
both holes are the same, Then,
R is equal to:
�L
(A)
-..j2n
�(C) L
�L
(D) 2 n
�(B) 2nL
�Q, lOA hemispherical portion
of radius R is removed from
the bottom of a cylinder of
radius R. The volume of the
remaining cylinder is V and its
mass is M. It is suspended
by a string in a liquid of density
p where it stays vertical. The
upper surface of the
cylinder is at a depth h below
the liquid surface, The force on
the bottom of the
cylinder by the liquid is [JEE
2001 (S cr.)]
(A)Mg (B)Mg-vpg
(C) Mg + rr R 2 h p g (D) pg (V +
nR 2 h)
�Q.ll A wooden block, with a
coin placed on its top, floats in
water as shown in
figure. The distances I and h
are shown there, After some
time the coin falls
into the water. Then [JEE 2002
(Scr.)]
(A) I decreases and h inereases
(B) I increases and h decreases
(C) both I and h increase (D)
both I and h decrease
�[JEE 2000 (Ser,)]
�h
�Q. 12 A uniform solid eylinder
of density 0,8 gm! em' floats in
equilibrium in a combination
of
two non mixing liquids A and b
with its axis vertical. The
densities of the liquids A and B
are 0,7 gmicm 3 and 1.2 glcm 3
, respectively. The height
ofliquidAis h A = 1.2 cm. The
length of the part of the
cylinder immersed in liquid B is
= 0.8 cm.
(a) Find the toal force exerted
by liquid A on the cylinder.
(b) Find h, the length of the
part ofthe cylinder in air.
( e) The cylinder is depressed
in such a way that its top
surface is just below the upper
sulface of liquid A and
is then released. Find the
aceeleration of the cylinder
immediately after it is
released,