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Practice questions

1. + Ni sino mme into es
Me gvendy Fa CA +15) +6) N. Wir ls
Some By force in moving the hay Cane
vt done he Fann

One

(100)
y nee Brie 02d acting on a une ac à
pement d= —4í + 2j ~38. tthe work done 06,
vei ale te will be ves
Fr os
o Or)
u face Fo RO + 3), wher is a postive constant
‘Ailes panicle moving inthe xy plane Stine et
rein. e particle is taken along the pontine see
be pnt a. 0) and then parallel othe Dane une
io a. The total work done by the forces Fon the

lease Par
@ 1803 es

1) 1903

[CBSE Patt 2003),

eis TEE 195
ei CF y
oar ie

3, À on places à Dock by 5 m on a rough surface
(ni?) by applying «force SON ang at 3 to he
ane he wor done by te applied force
tho} @) 1003
os oo

Là À block of mass 10 Ag i placed on a rough surface

| © felted plane of inclinan 37 wi hora Now
ec released. The work don by the gravitational
‘ee a ion fre when he ick mons rom Ao

AS

Pons due 10 a fore Pis JON. M
incemimcer then work done wi bo
Fra 2
ron (25)
|

ES
(2) -6003, 1603
(4) -6003,-1603

7. A block of mass m is pled along a horizontal surface
"o applying a force at an angle 9 withthe horizontal, The
fection coefficient between the lock andthe surface.
be block raves at a uniform velocity the work done

"y this applied force during a displacement of te block
site

mp con

Er

org

4 Amin ter ery fm a
hte oa a no
Sent stk doy hd
wi a

2 a A
D Tete ee
Scene
CEA CE

A A”
rer
Ira
ce een aa
ee ses

Moment TUE 20091
(6 ate Sue
Ge @ 2 Joue

1H. AE, Wy and 1 represent the work done in moving a

particle fom A o B along thee diferent paths 1. 2 and
Screspectively (a shown) inthe gravitational eld of a
‘Point mass m. Find the comet relation between Wy, 1.

nam, TER (Sereening)2003)

DS Wyo

DI wow
12. A force F acting on an object varies with distance x as
‘shown here. The fore sin newton and x in mtr. The
‘work done by the force in moving the obec from =010
[CBSE PMT 2005}

2. 320 Crepe
19. A block of mass mat resis acted y

ms tn eit yf
F we ae "ee
: = m 5
mt os wr
z =
(D 451 @ 1353 Sica e o
Bee! Bi eg he wey Br,
gen byte na ceo pare en.
ag Cie "net
Chin omen (a
er, 21. A panicle of mass 01 Kg is ab m m
varies with distance as shown inthe m oc
un" Journey rom rest atx = 0, it veloc Hing
3 root
Sis ry

A postion dependent force F= 7-24 + 3 newton acta
02 al body of mate 2g and dl in

sox 3m Te van je (CBSE I neue CRE

on fe

os Ss Dim Wim

18. A fre ae om a 308 pile in such a way at de 3p, A Bock of mass 2 à resting ona
net EEE ct
SP +0 here

one
iw ae ie eee of 1 an a

30" @ ase
«sass 0) 430m Sr CES
CES ) 330 md 23. Two blocks A and 8 have masses mand 4,
16, The displacement x ofa panicle of mas kg moving in Each one is acted upon by a force Finer
‘ne dimension, under the action of a force related ne

the a
same kinetic cry in ime on
{he timer by th equation = 4x-+3 where xis in maes

inal nin seconds. The work done by lose tr 02 CE
seconds joe 5
wo @3m os Or
6m om aan
1 RD a re ni ie Ales op ony Econ
‘locity varying withthe distance traveled according to Orme cl ery of pare mr
De ea vals ar ais a constant Twat 2 ES ior
TUG de y ae forces ring placement E, a
Be 0 25. The kinetic energy acquired by a Body ol ms a
nad ma delia cram distance stating fem ae
oF “7 ‘constant force is
a es (0 ice proportional tm
3 e (9 directly proportional to Vm
Y es) RUA long te ax an oe acingen @Dimeselypepontonato Jr
woran by F=Fosin es, N, where avis a constant The (9 independent of m
‘on done by te fee rome On oes ca 25. the fre ating on a body is invest por
o oo 8 is speed the kinetic energy othe bly
CRE. {constant
RE {2 dicey proportional to ime
ey R €) inver proportional tine

Dur (9 dircety proportiona square of ine

3. er a body rectly proportion
ee ci on be ay”
repro Vi
y proportion to i
D Pr oh pend a
o
vo, o
PO cres in à sen ne with renden

po placement It vs ine

Pare Ziegen
fay ae 7
of 0 lon, x

0 eof ie following i not conservative fore?
wi asa ree

:
PE na q
RE D et onc do
Beer ee eee

ae nie
comet co Me
at co Me

uo ental clinical vessels ld be bases at he
Tre sel cach contains a liquid o denso. The et
old on veses y and hat inthe erh, The
Nbr tases is The work done By te gran in
Sn ne levels when the vessel ae interconnected

of] ©
mf] co [22]

is reiche by 2 m. tores 1003 of

When a sein
M ii fuer setched by Dem, he stored ner
SE creas y

(ior @) 2003

EN Go 4003

Te pole! energy of à rin spring when setched
Ence 55 10 Joe, The amount of work
“nis spring to sr e

injec) hat mst be done on
‘Gough an alien disance » willbe
fer 202)

uso a»

Bio CET

So cat sping of natural length aná force constant
Shed By

2 reiche ey length 1 fuer,
A The work done in second etching 5

ES

».

eh ory nd Pee 224

one bua nr

ter à Lp

To spin X and Yk, = 2, ae etched by opina

Te eng
Sins

a
ow we

A ring of force constant 800 Nim has a extension of 5

‘Gin The work done send rom 3 cm Sms
aie 20031

oies wu
oa Os

A spring 40 mm tong i srta bythe aplication of»
free ION force required vo set De sping ro
mm then he work Soe

‘mnie

yeas

a
‘To equal muses re anche 10 the rue ends of à

‘ig ping conan Te as a lle eat
‘nme ese e spring by ana = ove
DR The work done by the spring on cach mast

oh ole

ao
os

IA ie projected vericaly upwards rom the round
ASSEN am heit Whe sat big 38
‘Sci ots Kini and portal energies is

os rss

a3 Oat

(Reais projected vray upwards with certain inital
pos bal of he same mass projected at
re et th vera wits e ame nial Pee.
A highest pnts of tele Journey e ratio of tee
Dein en il Be

Orr Sr
Ea Kr]
[Reavy stone is thrown fom a
Pet sn a de q

ola

of ght with à
th mamans

‘peed
serial domar

KO ray pur

none

{A ed des not depend on he nt direcion
Ve ut given an nal velocity von smooth curved
Fee spec wea teaches © Bil be

4. ss.

a.

o.

7

wm Dn
(30% + 20m") None
A aphercal ball of mass 20 kg ls stationary atthe top of
Ai af neigh 100 m. I sides down a smooth surface 10
Abe ground the elimbs up another hl of height 30 m and
{nally sides down to a horizontal base at a height of 20m
Ave the ground. The velocity attained bythe balls
{AIEEE 2005: ATIMS 2007]

om 2) 10 S36 mvs
40m (4) 20m

A projectes fred from the top of an 80 m high li with

an nl speed of 30 m/s at an unknown angle The speed

‘when i hits the ground

Som 0) 100 ms

45 ms. om

Three different objects of masses m, m; and m, are

allowed to fall from res and fom he same point O along

tree different frictionless paths. The speeds of the three

Objects, on reaching the ground, will be in the ratio of
¡Armas 2002)

Mmmm

ana

“The figure shows a particle siding on afctonles tack,
Which terminates in a straight horizontal section. IF the
panicle srt sipping from the point A, how far away
from the track will the particle it the ground?

me @ 2m
din Din
A simple pend of enga 1 m has à bb of mass

1 i place though an angl o 60" om the
veria! and then elenco. The Kinetic every of bob
Shen pacs tough mean postion
W023 © 081 O 107 a
A mas of Ag moving with speed af 1 mon
Berzonal smooth re lie witha masses ping
toc constant = 50 Non Te main compet
the spring woul be
Gorm orm
Dia (05m
Abockofmssmisatacbedotwouastetched

nscthed pings

Spring comas each an shown, Th och df
towards ht though a its x and ie reach Set

50.

si

s

a ot e ck Pe on,

mn

m Pe
me a
x
Le CEE
ort 5

“The figure shows à smooth curved tack
ot horizontal par. A spring of
00 Nm is atached a one end os wg.
Kit the horizontal part. À 40 g ma ein
tata eight of mon the curved ace fees
Compresion of be spring willbe D

PaaS

tem @ 2em

@3em © 4m

One end ofa spring of natural length hand

is aed atthe ground and the oer ny

“mooth ring of mass m which is alloneg gs

Forizomalrod fixed ata height see pg Sn

the spring makes an angle of 37 with ne

the system I released from rest. The y

‘then the spring becomes vera, 4
F

are’
oF ote

a fe a [E
oz wt fE
intl i BA ina
ori mie he Sean
De a

5
“a

me me
Dee
oF am

5. wm
5

o

2 ring with ore casan ls id on tab
stata et hoe e heen
Avan er on pin otha he png
de ‘bya distance, Te nt wok done ihe

se CBS PT 0)
e

ir

mir DA TS

yet DE mine

lock of mass M is hanging over a smooth and li
4 Ao ag a Mo sing, he ober end of stig
ria try econ os Tc
mate
RL ange
one count me À
PTE ds ye eno he ck 20)
pee
PE to ty ri ll de
esi
se Asal Dock of ms mis etc gh nad
cn 6 ii nen dl
uno cy van ec e
ese te wet ce ins
Erie
dm Co mercado
Gmgvr sin? 9. (4) mgvr sin 20°
5 D fm Lg a on pert wi lay
cad coms ot sero
PE 1 m How ouch emg a an
‘fection (g = 10 mvs")
a o @ 101
p Abaya mat m ppd tom gh race de
round with a speed of 1.2 tH . The work done by air
Les
Came 02
Glen 60m
1 ta is down verily oar wih pe 1 m
se pean wh gcd mh The
See De iman e tr

the ball wi
(dtm @ sim
O61m @ Tim

speed of 150 mi, strikes a

+ A tll, moving with a s
rh he plan, peed

wooden plank. After passing

CPR

becomes 128 m/s. Anoter hl of he same mass and
peed of 90 ms. a seed

ETA
(0 Toms

som
(0, À bal dropped from a height of 2m rebounds 10 eis
SES m afer biting the ground. Then the percentage of

wos CE
so @ 100

61, bullet moving wit speedo 10 m/s can just pente
feo plans of qual thickness. Then the number of sh
Planks penetrated bythe same bullet when the speed of

Pallet double
0 CD
as (o 10 ve

62. A cris moving ona sah rod with speed vo
‘oscen or ction between te tyes aná tb road is
th distance traveled by the car before it comes Fest

a “
a

os CE

A 24

ay E

o ©

Zur
163. body of mas 05 kg ls taken up an inclined plane of

Ian 10 ı and high $ m and then allowed to slide
‘don 10 the botom again. The coefficient of fection
‘between the body and the panei 0.1. The work done by
the fictional force over he round ips

ms sá

est CE

64. A block of mass 1 kg is placed atthe pont À of a rough
‘tack shown nthe figure. 1 slighly pued towards right
It gps atthe pont of de tack. The work done by the

Final ore on the lock during its transit from A 0 Bis.

z a
f cen
ms Fer
2 oa

65. Acar weighing 100k moi a sped of 4h
when the mote sop fit Jul able rs
cron whic as o ate De
Frit cael te work done aan ton negate
te wok one byte ton)

195003 128003
(625000) {8 500003

6. À Bock of mass 10D gs moved witha peed of ms at
ieh pi ina ed ier tte of as 10cm
leptin vel pao. The croesecton ofthe tube
Sith hat the lok Jas tint The Week makes serra
‘elon iid the tue nd nal sop at te ln

6. a4

o

a.

n.

».

C2
point. The work done bythe tbe on he block during te
Process wil be

tn aos

ras (4) 2083

‘A bck weighing 10 kg travels down a
tack AB Joined lo a ough te
figure). The rough surface has a friction coefficient of
020 withthe tock the Block stats tipping on the
track fom a point 1 m above the horizontal surface

{ar will move on the rough surface?

Y

1 a
3m atm
sm @ om

“The curved portions are smooth and horizontal surface
ough. The block i release from P. At what distance

from A iwi sop?
par
t
> 4
— —
1m @ 2m
sm «4m

A 2Ag block slides on horizontal floor with a speed of
‘Tin. I strikes an uncompressed spring and compresses
del the block is motionless. The kinetic fiction force
is 15 N and spring constants 10,000 N/m. The spring

compresses by
(ssem @25em
nom (0) 85 em

A panicle moves with a velocity 6

the influence of a constant force À = 20 +18) SEN

‘The instantaneous power applied to the parce is
[CBSE PM 2000]

DEA @ 451

an € 105%

AA
Pi AA
PI ee

Sit, EA
‘eye th tr
Seance tt oe
efficiency as 50%, will be im
st nit eget
some a ge tn
PESETAS:
E

2”

1%.

n.

78

so.

a

pump is2W. Ig = 10m

rowers i,

ae n io o hgh or
E 2) 10000 Om
io (or.

ae ey
yo en
Cy in tp

ala)

wy
tal 5) © Es)

ae of ms M ating or re
con. speed acquired in tine rng
Sneed eck CBSE Pr ak
'"

ver D LM
ote o

ue @ LME
oe @ LM

A bly ial et, undergoes oe
Ace with constant acceleration. The posses
ins papa un
oe
me
ar ol mas 1250 Kg moving u
dales 30 KW while rive foe du y met
FEN wae nas cen pet

o baw?

Da
Lan!
CL

H a

oun Lave

A car of mass m i ven ith acceleration «aps

Stat level road against constant exer ake

fore À When the velo of the car Venen

hich the engine ofthe cars doing work wie

wav 2 mv

DRrmoY (mae

‘Wat fling fom a SO m high fal st be ate

ene cri energy FAX 10 of wate aoe

{nd half e gravitational potential cnn tene

ino lie energy. bow many 100 W lang aes?

ws (2) 100

@ ns Go 150

An unmly demonstrator its stone of mas mig

{he ground and vows i this opponent A Ed

‘ojecton the stones at height A meer above be =

And has sped of y mi, what horsepower os =
1m Pr

aim
das CET

LES 14
we HUE
AREA paa

7

7. mass at an angle of
Pete on en
a pal force ut ks the ground y
et

DELL
T

© mas m gen à vi
cc on à ro
An es a ton cefcen je The wre
ey ton moe
Pr ñ

@ Sma

ee
oe 4 2umgu
(268 sk A oa sol nna
NEST he hoon Te bc one win
cio of 1.0m the power ered bythe
eet tne 4 safer he oon ar wl

on Da
En aw
Neos problem. Wha the average power

a ton iit ws
ne en

Be en in

inc by an engine delivering constant power P. The

A anaes oe

off wt
Fi a EL
off wf

+. A body is moved along a stright line by a machine
“averia constant power. The distance moved By the
Body i ine is proportional o.

am a
oe we
The potential energy of a particle in a force feld is
var
=A. where À and B are positive constants adr
aon es

iste distance of partit from the entr of el. For
Be sable equilibra he distance of particle is
[CBSE PMT (Pre) 2012)

Wk are end Power 325

«ana
Da
The poten

owe
oa

Ti penal cfr te ae e ie

int dtm nl ee

ACA pi
o tem ond a com mare

the distance bet
nce Between the atoms. If the disociaion ene
‘ofthe molecules sD = [Ute =) =

».

man Dis

TAIERE 2010)
oe oe
oF ef ot w

bad NC]
Dental endgy oa 1 panicle fee o move along
the canis is given by

me (#3),

‘The total mechanical energy of the parce is 2 J. Then

the maximum sped in mi) is TAIEEE 2006)
of @ Wi
a Ea

91. A panico is placed atthe origin and a force F = x is
‘cing on (here ki poste constant). I U) = 0,
the graph of Ut) versus wil be (where U isthe potential
‘energy funcion) II IEE (Sereening) 2008),

Go om o w

© us ww
92. The force acting on a body moving along the «ans varies

‘vith the position ofthe particle as shown in the Bre

“The body isin stable equilibrium at
De x=
baths andas (O Neither; nor

ANSWERS KEY
1m E 0 a SO BETO
RE ta sem AO eer we em]
O al Aa sa A wu 0
O ET EA O sat mat ECON EAT A
uo feas tao je «oleo ECG 50.0
RAR RG HO so EI D so
or ta a et sa ICAO RENE
soles CO ON ON EX EN EL mn
Eee OS BE CHEND CT ta) EXC EX
na

8. 216 Oper
SOLUTIONS
Te Fein O= me
Name-Fsin 0

joo
eri

fener} ohh
den jeans
Fetal sj430N
we Páncreas io?
War,y= 15x10. 1503
re

um

20
un We Ped
eer
un awe har

kod + 2) x Cd + di)
a traite
wer acoso

» mu
rer
pr

ork done byte ple Frei
«2005377 (8)= (50%) 6)=2001

66

Work done by gravitational force is

Img sin 0d = 10x 10 «sn 37° I
Work done by fiction is
Sam = umg cos Od

02% 10x 10% 608 37° x 10,

601

6003

4
=-20xixıo

10

Since ihe block is moving

Jonna tg = Fin 9
iva uniform
St
eos D mime = Fin 0 ö
wor pino

Eo

Work done bythe applied force is

ume cos Od
Fon Od= gs pino

ri

mu

Work done by the cord is

Med
ran 2

an DEE o
es

Displacement of blocks in the 4% second

1 1
= Fear p= ica 27m

Work done by the gravity in the dih second is

G8 ~2g)x7=705

11.2) Work done by a conservative force i independent
followed by par
12.2) The area of force-displacement graph gives wie

We3x34$xax30135)

9. ngs

we.

ere
f

Vin traen DO 2404 6-2)

= 10+ 00+ 90-1753

2

un mracfe-mane

mer)
A =38-25 18
sass)

ee

so
Kur
=

10m dm

aa
2332448 om

mi

1,20
x3 as =
2

mois «22% 16-5283

sm iman bond

contes

Since the velocity is constat.
Weak=0

sali

no
Former)
sede ad

Wank Ketel

1 cad = 09= 4 ma?
= Ima oe 5 mad

a ee and Pet

10) we Jr der fr merde

Feo o yon 2ay (<0 04

= Bacs Blt 280? o]

METAS

wa eL
atar
weak

proa k= EL

EUR

Amor 12m
We are of Foe graph

1 a+ Imx10=803

see

wenn

ont mon 017
ater som

220) ARR Ke 10-0107
Aka We Frees 0

10 10x 2x 608 0-9 cos D à
0-0

pay Parties e
a Prat yd

10. Der

wear

bel,
wear

zu Kommen
een
Kuna

0 Fx

Since the volume remains same.
Aly +Ahy=Ah + ah = he aah

(PAM gh + (DAN; dehy
2

pag
2

soX.

x2

Wer == Uy) = Us
= PEEL ag +22]

Morel (is
“a2 (i isOK.
280) ane

Ar À constant

ar

: 20
¡PA

11. gts

ue)
tag =10
ai”
patatas
ers mear
PET
gay tan pat Et pr
vaut
arme
= er are
pode bike
sm my

Mi ets
Lua paa
?
Ansmann)

mi) An 10 Nm

no ave bit

ot de by ine sh
D Ve me cy ars

ke me

ek tr dome 329

Uy” mate
(4) The speed with which the ball ses he ound I
Independent af ini recto,
42.0) By conser of mecanica energy (aking ground a
Rte ev)
Rs Dan Ka Un

i Mimi
Ed: HOME:
vn OG + ah

50 memes Im

“un om

PROS
L mo + mgt) Im? +0
GO +280)!

om
so
2 CR
i

tn each case, the pie energy mah is conve ito
Kine energy

12. son

mat) = Im? + meros)
3 7
D 2261-09 2 10

05-2 10
2200) su

so
ever eu,
Or malt —cos60)=K +0
48.0), ni
90)
42) Loss in potential energy = gain in energy of spring
da
= hee
me
2me

k
53.0) Loss in PE. = gain in the spring energy

13. gi
me
rer
Network done = 20 3
À M) (splcement) = 20
(F-Ms)(Gisplacement) = 20
so

Diplacement ofthe Block in timer

Work done by friction =
mg sa? Ove

de

sn

Ki9U=K,+ Us
1W; work done again fico

Lans +0 =0+ on +
= new,

Energy lon ue to fon = 20 3
sus

Wek nr a ewer 391

Ketek suysw,
Wa work done against ton

Sema = Lm? +04 1,
mas Lm? +04 0,

malt = Liha) ett ow,

We 028m
Work done by fiction W;

sn ES IRRE,
ine % 1

Upward meo: EMO? = mgh + Rh o

Downward motion: meh ce + Rh aw

From (and (i). we get
pa

1 ny
Smo? + Emo)

qn 002207 _ 168

sim

7

$90) mo? = bas? ena o
0 «oon w
(98-0297 en
ne

0 Urmel) Uemsls)

sua

a

14. 2 os
Lo + me 428 = W,
Lim? + mg 2
sw y 4
x sm 2 2
À weiss
| IA
a
s 9
men ha lomo
677 T
Jaume ® i nad
Wr done y ton I

0.1 x05 x 10c0s 30 x 10 —

Ki+0,=K,+ U,+W,
0+ mgh=0+0+ umpd

de

02

(68.1) As in the previous problem, the distance
on) block on the rough surface = 5 m LT

PR

The lock stops a
nes
90 mi
1 1 3
Fa = 10000) € + x
1625 x 10% + 154
SKI + 150-16=0

ASAS

3x10"

u
Em iiem

1
Im? mph + Wy

4} 1400057 = 14005 10% 10 +, BE OR in
102) P= B-¥ = (201 +15) sb ajo

We 500) E »
66) =120-60-15=45W
HE, B = MBh _ CUONIOALIO) _ 40000 w
J = =40kW
7244) Output power = 220010100 _ 2900 w
“ 3600
a Efficiency = Output power,

input power

15. 200
05° pat power
ON = AW
se en HG 10260
pu in
so
Pen
von
MA
u melon
sone
x= 20018
ayo water 1000 kn
sonne fear = iy =12
= 12% 1000 12001
ga nana oran es À

pensa ore

x v=0+aræ a À

vo

pen

Wh. Ene and Pore 333
BOL) Loss in PE, = mgh = LA x 10 x 10% 50

Energy ose ener power = SUD 1500

72080
Number of butbs = 12500 125
i
\
ele
mo pe 2
m
nw
oo von foe fm A 0
Peo
so =
La =,
roto ME y
‘ete tre ok os
oa ann
Du
Lat
=
i
so 3
aA
5
>, $
F-20003 =
AS
paros raza
a
65.0 Digi inn

Work done by the applied force Wis
PEN PTE

16. ER
Zur,
Er
En
ae Fur
atm
ñ ; manel,
face FE fra
po
m
Br >
wo u4-2
77 ou)
av.
Buoar- 4
a [2 UU vi x graph will be a parabola, open downward
84 Us sur 92.2) Atx> xy, Fis ave, ie. repulsive force
E x> Xq, F is —ve, ie. attractive force