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,