Resonance Dpp n4c

,

pRAffiTtGffi pffiffiffitffif;ws TAffiGHT : n$Y-Jffiffi ffiffi$,m

nAurv

cffi

w#'g tt't6*onfi

oc€: wi

th llT-J E E

13to {5

DP,P

Class : Xll

ll,'p

t

Course Name : VIJETA

Batch : P

*g 3

DP Ns. 1 Jp r were h { 9.4.-Q$ :Q:91-o" 0 $*ES.$ sJ Tokl,Marks, : 42 lir.1qle .choice objective ('-1' negative marking) e.t to e.? {3 rnark* s rn in. ) 9unject_ive Ques_ti9ns {'-1' negative marking)-A.g to e.6 {4 nra rks 5 rn in. ) c_om:pr€hen,bioq'{'.1' n€gative ,frarking} e,r I; e.g tg rnarks 3 min.) -(no

Match the

Foilowing

negigtr*1"*"iringJ o.io Assertl.onandReafon'itao.nL'iiiivemar:king)Q.11

{.

A standing,wwe'peftern

J

2"

*T) 1t

*

kx

' (C)' Yr*'"^,cos,qot

i

fx *---al

a,sin

2n

(B) V, = a cos l

3'

,

rrnrJ

"$.i

(rrri

+ kx

1

n +-_ \ 3t 4x

\

3/

p;;itilnX .

area 2..4 cmz, at rhe surface of rhe (us6 n = 22J7,\

zp from the souice. Thewaves reach perpendicutarty I$Y*nqfffgl*lto]i1.an99 oeEctor. I he Ftatpower emitted by the source in ihe form of sortnd is * 2.2

A small cube of mass m slides down

3 ci,rc.utar path of radius R cut into

1oaw. r"rg* ;ocr

LJ ui"Ili"

of mass M. M rests on a table and both blocis *ove *'itnout friction." initially are at rest and m starts from tn" top or in; p;th.'Fi;;]ir" cube as it teaves the "-jr""t,,';oii;;

btock.

5.

i-P .,"

i ;*jf " -:i**_ i_

-

stowtyf tajr. l'l ,r J. figj. (a) Drayv tfre process on the T-V diagram. (b) Find tne maximum :lgyl ,"561-'"1 'lthe thegasduringtheprobess. "L;_ -- >s temperatureof ,ero. enclosed

in a cylinder under a piston is transferred quasistaticaly (i.e. ?991^"L!? tPmst?tg.AalprgssurelSatmandvolume4lit.tostateBls.Batmandvotumee.+ilt

.t_-,_s?_*v

.

6. .

A uniform square plate of mass m is ed as shown. lf the cable suddenly

assuprqlgcentreof massisonhorizontaliineingthroughAdeterminei

.(a) The angular acceleration of the (b) The acceteration of corner C.

(c)The reaction

comprchension:

io.

s]

a pulse of sourid that travets radiany outward frorn the |||fpfjffi:fy$-"l Tytq of.ffgq 1 = 't0{!, emitts [email protected]**n to,Lo.y_"lfl_T-Ylltit"rygpted by an_a'coustic cytinoiiiai olGcior ot surface

4.

9.

i,,^5 ,

3t}"}

9]

Fiquge gt*eft$q|$ryi,P$g$F unifor:rnly c-harged, thin rod of tength L and four rrom trne rod, with ;;!'f-V;, V., V;,ar.e their- respective potentials then

V;

8.

fA

)

)ormeO.

cos ir*t + kx

J

poihbA;,$1b"*ils'At{& $ffieoii'tand;

7.

rlrin.

s,

[s, [s,

b formed on a string. One of the wavile is qiven bv eouation vr = a oo$ tCIt * kx .+ nr'3)

({*}t

=i'

[s, s] , ["tr

I min.)

then the equationof the offirer wave such that at x = 0 a node is (A) y,

Max. T{n'le : 4S mlm.

breaks, - --":'

plate.

tlyy

sU

,,,n\.r,

'\g +*/ '\ ".V" /:1

atA.

A.light inextensible string connects a block of mass m and top of wedge of mass M. The-strihg is paralleito inclin:ed surrace anJille ir"ir"o surface makes an t'[', horizontat as shown. Alt s.urfaces are smooth. No* a constant llgF 9. yltn horizontal force of minimum. magnitude F is applied to wedge towards right such that the.norma,l reaction'on blocR'exerted by wboge just nelo*"s ,eio." .- - -- ' smaoih Jrirwl i horizontal uri4ui ridr su surrfa:ce r?ue ' Tfgphdgnitude of acceleratjgfr of wedge is ;ffig tan0 (c)g sino (D)g cbso lpfg corc The magnitude of tensionffitring is (A) mgFce (C) mg tane (D) mq cotg ld nrSj .d.."e . . ^ ". F

+ [ ;' f-"u{'J'lrir-'rt (D) Mg cosecg i' column:Igivesasituationinwhichtwodipolesof dipolemomentpiano n6plare ,,,_,,i t1l-* \ placed at origin. A circle of radius R with centre at origin is c]rawn as shown tn'frgure .,' * - ii---x Column II gives coordinates of certain positions on the circte Match tne staterients - 'r .7fT" in Column I with the statements in Column II. 'tlir

The-g{agni.tudeofnethorizgntal forceonwedqeis: Ie"rt; (B) (M + m)g secO ''M (M + mlg c1.rn QTMg cote

Ho.'

_

Column I

t;#1fl-xgT'tru r.

(A)

/ -..

iI Fl

The coordinate(s) of point on circle where potential is maximum

f*F' '1

L'\--

i',t\ .i" / I -"i ' I,t:

il I

,rilj,

i'li

,-\ ..:,..

i

:

i

i

Fgg.

$qlg.r"

#

'H

"The

ll-(i t u..J,l

( R "l5n) [-2,- , ) ( .6n R) (') [T'2)

(q)

ecorr1inateisi cf p*irit *n clr*le where

6rctential is zer* [q

The cnCIrdinate(m) nt point on cirele where

I

4p

1

{-nasniturde nf electric field intensity is

iL))

-The

4ne6 Rg

f.,6nRj (s)

c*ardlnate(s) cf point an clrcle where

magnitude of electric field intensity

fi*---'-

[-f'-

12p ir a* *p

4.

z) :

STATEMENT-{ : Two stones are projected with same initial speed u, onE frorn,top.ot {6Wer (of he{ght H} at an angle 0. with horizontal and other from bottom of a tower at an angle 0r with horizontal. lt rna
4d$

STATEMENT-2 : Two stones are projected with same speeds frorn ground. lf ang{es otgrojebtion with horhgntal for both arb different and complementary then the maximum helghts above groundbvetrficr both witt,teUifbrent. iNeglect air friction) ,{A) Statrement-1 is True, Statement-2 is True; Statement-2 is a correctexplanationrforStatement- 1 { B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation:for Statement-l (C)patement-1 is True, Statement-2 is False "1Df Statement-1 is False, Stratement-2 is True.

qt&F&j9 4"C5.D 6. q,s (B) (C) (D) p 1S" {A) r r #sgswqrg qf.gPf;fl-f ! 4.85. 6. A

Sgew.erp ,'rfi

-"t

!-q"

d

JYe

ry' E

4

ffi

Jr,.""

q^f

o

r.

qJ'"

A

& q#o

ffitrm

lc.{

AAE

{A} p,s

IT?R

.rg

f,"

vrrill

1*l

?-

i-*,1

tI

\4

(C)

d;tr

s.c

A

*$.

q,$ {Lt) r

, fi?,q

{h)

g"$ ei

10.

D

D

A

4.CS"A. V. (a) T*** = |(po /R)rffi lf " j (b) T*", =:F0 /epR.

"h. rJo

*n ADC (ii) ratin 2 : 3

tT]fi

gx R [fa

flcw

p,s

@r

;xt ffi

{ii

fltr &.f r

LJ

"R q 'tf

Nc nharse

4'fr n lr4

rn

,b

q

10" B

';

q/d

(*

11.

D

KffiS?" SY'!.LABU$ ffiffiWffiffiffiS Frmsm Kn

: 3z

rorat Marks

petre

DPP No.2

.::

n

SlllUl1 Fleat & Thermodynamics

Wf- -flq for week (04.05-09

{'-{'negative marking) e.1 to e.3 Multiple choice objective ('-1' negative marking) e.4 $ubjective Questions {'-1' negative marking) e.S to e.Z !-in.g!e choice Objective

Following

.

:

ll

.|.,t,t

to

"i:

'

:]

09,:Q5.r,,09t,

(3 merks 3 min;} (S marks 4 min.i

il marfs S'min.i'

(no negative marking) Q.8 (8 marks 8 min.i Asseltion and Reason (no negative marking) Q,9 (3 marks 3 min.| particles 1, ,' ! Two having positive charges +Q and +2Q are fixed at equal distance x from centre of an conducting sphere having zero net charge F' and radius r as shown. lnitially the switch S is open. After. the switch.S is closecJ, the net charge flowins CIut of $phere is Match-lhe

far \*id

t

tffi)

'\t\/ F.

'ry dC"

-;

fir

(D).ry

A uniforn r thin rod of ffiass m and length R is placed nCIrmally on surJace of €sr,th;:a$ ., ,, shown, "Fhf; fflass of earth is M anrJ its r-a,Cius is R. Then the magnitude of gr:avitatiOnal,,' i'rirc*: exertecl hy'earth un ttie nod is

-

+..

.,\'* -

,

ffitvtm

-ffi'1"' ", 1, 1,

?

&-t

ru"1.i l

-,".1

L-''',.1.'-"' $*..-'-'

/t'\\ IH.

GlVTrn I

\B'rl

4[Q"

ffi

,/crum -eR'-

e : 39 ,min. '.1 .r

c

5,

6 7

I

:+ir-' "

::

'':

t

s; ands4:at*sro-putetent sources of radiations separated by distance 1.0q 2q 1," where L is r,rudffu*:Si$*dSSirin pt"se byr/2.Aand'B arb t*o point, oi,ine rine;qining b,;;JSr;. the wave length of snorn in figure. The

('Y^\

ratioof ampl,itude,p atA and B of source s, and $, are in ratio 1:2.The ratio of intensity atAto that of ts i t& \ ln .

.

.

_.

,:.:,,...

.i,

: ':

*f{ f*Pf*

s.,

A

4--'__rJ

\

$,

,/

r

{B)

lase iflfuHberatr*fe and velume both aFe doubted. !€sg ifttemoerature anrJ volrlrne hn*h rro hehrort e doubled.

:

{l''''-' {:i,.e

A qarticle rnoves in x-y plane with constant acceleration a=6

axirnum

uo

(B)1/e 1re 'ffi^

(c)o (c) 0 (D) s {nr,l*ut ff,cgl$sisns,per unit time of molecules of a gas on the wall of a c0ntainer per m2 wili

ght H) at

l'-

I

(in m/:t) At time t = fi, the par"ti*t* is at

i*gi gginlnlvin$ grdinates,('0,'20 metre) and its initiat vetociiy is- il,= -12i"+-16j (in m/s) joshntof'tirne when"spegd particle of the is zero wIl be Llu #/'

for any

(A)

orieonhl

l sec

:

W.sec

@Caec

'd'&fl

The instant of time when the_particle crosses x-axis is {A) 3 sec Jpfr sec (Ci s sec of tirqp wtren,the particle crosses y-axis is I^t-:nstant

Jifferent.

sec

.

{n} 6 sec

(A)3sec ,' {D) 6 sec r vrrr'sr{rr uEr,rrv{ir{u(to}{vr iilltl [aul{.ls radys R dffldf*?:s M and i{ iies lles on on.aa nxed fixed fough 'Ly,lif.l* rough hori horizOntal suffaCe at time t = 0. lnitial angUlar ',fi'oriroorat 0igqim-aslitude and sense of rotatiori; vetocitv v^ of cenrre nr maee ic Yi9.9!-gt,",.:S ;;li#,ii;6'.ffii.,.',si []19il'ffi:f[,:ffi1::$:?,lillffi "no :

ent-1

.

ion in column-I with the results given ir: *olunrn-trI. f;1111#i:,11n",13?,SJn"":i"-#f :l,r;i::,':

GoHhnjr

ColummrHI

750

(") 4 t*l

(A)

(p)

tf

till the stops slipping.

It is givenrthat,vu = ZRaro (B)

(q)

rp)

-

velocity is nonzero and in cloctr<wise sefi$e

( -J*S,:tt) (1)

(r)

(D) (

39 min.

'

t ) [ptt

.l'

:

9.

that 2vo = __-tl..gLu_9n

STATE-MENT-I

:

Arter the disc stops srippins, the verocity of centre of disc is towards right

_ fr,_, It is grvtln,that vo = 2Raro Flt$o

After the disc stops slipping, the angulmr

$

It is given that 2uo = R*o

itl

The magnitude of angular speed keep$ frn ci**r*msinE

.' i'' i

:

(s)

Arter the disc stops stippins, the

kinetic energy of disc is less than rts initral value

Rrrio

Work done by force of kinetic friction acting on a body may be zero.

sref'dnrgrlr:'? : Alorce

+2Q

-

-).

aqts at a point on a body. tf velociv oJinJt point is atways zero or atways perpendicuiar is zero. r,lffitatement-1 is True, Statement-2 is True; Statement-2 is a correct e4planation for Statement_.1 @) statement-1 is True, is True; statement-2 ii Noi correct explanati.n for starement-.i -statement-2 (Q) 9Ftement-1 isTrue, Statement-2 is Fatse " \prStatement-1 is False, Statement-2 is True,

to.ry1qvan force, then work done by this force rn.any time

DPP Total.Merk6 : 45 S-in.gle.choice Objective ('-1'.negative marking)

- 15

A"Z

!o ('-1' negative marking)$.!e.B subj€ctive euesrions ('-1'negatiG marking) o.d 1o e.12 - Assertion and Reason (no negative martiiil O.rS Mu.ltiple choice objective

#2

;r;r;;;

{3 rnarks 3 min,}

.ii *"rlr* 4 min^) ii marxs 5 min.) 3 mifi.) ii ^".rr* i:nff ;ir*r; ;tr ;il

F+r a particie moving along x-axis, th'e acceleration a of the particle in of its x*coordinate x is given. by fr = -$x, where x is*in meters and a is in ml#.Take acceleration, velocity and displacement in positive xrriiection as positive. The iniiial velocity of particle at x = 0 is u = +6 m/s. The velocity of particle at.x= 2 (G) 72 O (B) 6n[ iA) + 5",,! possible he reaches the other end, he And when 10 second. of river in minimum time A swimmer crosses a starts swimming in a direction towards the point from where he initially started swimrning. Keeping the direction of his velocity relative to river current fixed, the swimmer crosses the river in 15 sec. The ratio of speed of swimmer with respect to water and the speed of river flow is (Assume constant speed of river & swimmer) -

-

m/s

2.

\ :1/? i\/ l\ iJ'vr,i"e dlit

#" 1#. ,:

N"\

, ,:'ril.-

v

""

'i.

{-} ''

";''-1"'"

-uq*"*',, ! itt i ""

A

(B) sl4 p

force

=

({

m/s

nr/s

-

(D) Js rz

'(.QJ'ztJs

lati + S]p.f acts on a particle due to which its position vector varies,as,5, = 1Zt2i'5j).rn'.whete t is

timeinseconds.Theworkdonebythisforcefromt=0tot=2sis:

J

{A) 23

(B) 32

J

(C)

zero

:,,

ry-* i

l,

:" Tot , S,in ,FifI Sui ', Asr i,

"

_,

.(D)cenrt be obtained

{.

i-iow long will it take sound waves to travel a distance / between points Ai&'B ,if th,e air temperature between them varie$ linearly from T. to T, ? (The velocity of sqund in air ati teffiperetfure T is,given by v = g.,/T, where u is a constant)

h.

'

L{:

/'\

,r ,i\ \ ____ t*.tt \''li*,*

ry itr

li

t

iB)

*/U [r'1, l'

d)

*r

2(

Jg

(c) a (frf+r'

2(,

(D)

Jrt

1

nr lreight reached by a rocket tiied with a speed equal to 50o/o of the escape (D) R/8 (c) R/3 (B) 16R1$ {l\} R/?

flt4axim

i*s" i t i

d'

u

.lt,)

2.

from e6rth's surface is

Two wires each of radius of cross section r but of different rnaterials are connectad.'t€dlilF!'end to end (i.e. in {fun#elections in the series). lf the densities of charge carriers in the two wires are in the ratio:1: 4, the tvro wires wilt be in the ratio: (D) 1 :,4 (c) 4' 1 2:''!

U3"

dtifr

iAil:?

{B} An infinitely long wire is kept along z-axis from.z =

f.p'

{"

10

f

N/c

S"

{.

N/c

1i .,ii

Acylinder rests in a ing carriage as shown. The sideAB of carriage makes an angle 3Q" with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration'a',. The magnitude of normal reactions exerted by sides AB and BC of carriage on,the everyvvhere. Then as themagnfrld€ No, and Nuo *vlinder No respectively. Neglect friction friition e\ren cylinder be Nou :k t4l uffie correct statement(d) : of acceleration 'a ' of the ca{tia$e is increased, pick (F) (l N* rernains Gonstant increases.. No* Nu. increases F)Nre *-@} "tgT N^u remains {A}

constant

tip"

A string is fixed at both ends. The tension in the string and density of the strirqg d-e aqqlrlately known but the length and the radiug of cross section of the string are known with sorne errcr- ffrn+iiwrum errors:made in the meqsurement of length and radius are 1oh and 0.59/o respectively thert whatfu thg'tnaximum possible i percentage error in the calculation of fundamental frequency of that

i

string,

10.

A man is Stahding on a cart of mass double the mass of the man. lnitially cart is atifeston thp

srnooth ground. Now man jumps with relative velocity'v' horizontally towards right With respect to cart. Find the work done by man during the process of jumpingr , , :': ,

!

'lt.

6. 7.

.

O

to t=

#

p,

canilse the for:rnula'of

instantaneous pCIwer lf you knowl Figure shows the variation of internal energy (U)with the pressure (P) of 2.0 molEge-$ in cyclic process abcda. The temperature of gas at q and d are 300'and'500 ,

K.

r

5:

The equation of atravelling wave in a uniform string of mass per unitlength'p lsgiVenthsy=Asin (cot'kx). Find the t*tal energy transferred through the origin in time lnterval from t =

'$ft"

3.

- o to z = * co, having unifOrm linear

nc/m. The electric field E at point (6 cm,8 cm, 10 cm) will be:' tdtzoo k) N/c {A) (160 i + 1201+ 200 k) (D) (120 i+ 160 j) NiC ic) (160 i+ t20 j)

charge density

q" '4I q"ll

', $U:b1

8.

CaIculatetheheatabsorbedbythegasduringtheprocess. STATEMENT-1 : A larEe block of mass M lies on a smooth horizontal,surfai€ g$d a 'small block of mass m is in with larger block as shown" NolV a,hoJ,iiffital force of magnitude F = 3t is applied on block towards right at t = 0, where t i*tinb in ' seconds. Then before the smali block reacheb the ho,rizonial surface, the.pa$.-nii[lde, I of acceleration of small block relative to larger. block increases with tjme. (All l9rfffi.es, o are

frictionless)

.

L

{0 f"f

f;/./

f f f'/

/.f

r f f I f ( r f { f f

smooth horizontal surface

STATEMENT-2 : ln the situation of statement-1, the magnitude of normal reaction'gxerted,:by larger block on sqraller block increases with time Hence nragnitude of acceleration of smallerbloek increqees with time. (e.I6iitement-1 is True, Statement-2 is TruJ; Statement-2 is a correctexRl$atlpn for'${atement-t . Siatemqnt-1 iS) Staterpeht-l is True, Statement-2 is True; Statement-2 is NOT a correct e*pldpatidiirf,b} : ' " '':\ (C) St#dment-1 is Trr:e, Statement-2 is False (t;")"Statefi1ent-1 is False, Staten-r.ent-2 is T'rue Pg" N0" # 4 :

1.r

{

f-,

8: ile,n. e,n":€#

DAILY FRACTICH

IFHI .Lrn

{t,'

, ilT,j ivg'. ff '''tive; .1,

I= 'z-2''

resonance with llT;JEE

I

PRffiffiIffiEKTS

: !$T-iHffi PS#-S

TARGHT

I

DPP No. 16

- eno rer rd, Irt lree nd, I

'ecti ,din )ction direc ofn sp€ spee{ eed o

f

to

Class : Xll

1B

Course Name : VI:JETA

DPP * t$i

Batch : F'

forvYeek

{1{-05-09 to i6-0S'091 ,'pP''?'Nb':l , : (':1' negatlve marking) e.1 to e.s (3 marks i min.) :ilS.l".9trot3.9 $Ule_ctina i4. llll,jn 11e-plan*sf-1ir:iQ$1tiiie,rpasllln1:g.5 '(4marks + *in.i srbJective Questlons ['-1'negative marking) e-.2 to e.1o marks s min.1,,

mer) me ]r) -

ro,tat Marksi:

vhere t is

.gs

Max" Time ; 4? n1in.

It 5, 15]

[4,4]

{t 6, 20}

Assertion and:'Redsor; (no nogaflve rnarking) e. i'l 1i marks 3 min.) 1. the_vglobitytime gr.aph of a particte moving atong a straight tine pick up the frorn ,ncor:rgcf staFrnent. -!{da6e, particlb crosses its n itia I pos iti on (B) therarceleratibn of the particle is constant (C)t!e:force on the particle is constant gffine sOeed'of flr e particle increa ses con ti nu ou sty.

perature griv€il'bf

13,3j i i 1,. i

..r

,./

1 i/

i

r'''

,'

i./ - *ff*-

-*-er

Y '

I

/,''t-\'t

Rtherrpcdyn-4,{n,nrocessof one mole idealrnonoatomic gas is shown in figure. Tfie effioienc;l,iif cyclic process ABCA wiil be

2.

sul'face is

i,

:

(A)25%

nd {i.e. in ),tls in the

A particle initially at rest starts moving from point A on the surface of a fixed smooth

3.

hefisj.ftrg

point B'. e is

fne partlite looses its *itn n"rnirpf.t"i" entre of the hemisphere. The equation relating ., and B is "i

of radius r as shown.

({l lsln o,= |

v

*f€ff,sin,$r=

---*X

,/laa (tr) ^^ %

(c) 50%

{,8) 12.5%

o.}

coe

2 cos

p cr

(B) 2 sin cr = 3 cos p iO1 Z sin p = 3 cos a

ln the givel frg,ur:e, lwo elastic rods A & B are rigidly ed to end s. A

smail uocK cn rnass I m' is moving with velocity v between the rods. All collisions are assumed to be elastic & the surface is given to be smooth. The tirne period of"oseillation of small mass 'm' will be:(n = area of cross section, Y = young's modulus, L = length of each rod)

+2nrl ffi'L *

trr.tzL (c)

{eV-

u

+Tr

ffrefunctioh

(A) 3

radiy!,fr with uniform charge q has p^oint charge electric:forces during shelt expansion from raoius h, to'R, rii.

6.

A spherical shell of

is

7.

the initial

lormula of

(b),Find:the initial

nt-

1

msnt-1

q.o

at its ceqtre. The work performed by the

{1"! .- .L

1

tirt:uttttttititi:"

, ': r i,,, A . .,i

rara+ir^^ ^r ^''rL - u -rt- :i accelerations of allthe balls if

thread.

.gq (

,.

-

we ci,t tt'e spring BC, which is

gI

,l,i.r*,u

ti

, "e,.q% t

ing r

' 'l'

J

:.

r-FC

10.

ln'

star system each star has the same mass as our sun and they revotve about thelr CM. The -?^._"1"i1p|n"ry distanqe between them is same as the distance between earth and the sun. wnttiiinliri-r*o'-t'r#irri";

11

$TATEMENT-1 : A block of mass m kg is kept on rough flxed l^inrizcilt;al $Lrrffiilr* r{$ shown. The coefficient of friction between bloe k ancj'hari;,anii;iii $urJifi,::* iIi ;:: f,-i "i li Then the magnitude of minimum horizontal forc* {"#qr-itf*d tr.:i i'Trr.;Uf,i 'i..i:ii,, i-;it.,ij|'., titi l:li

-i

h time,

g

1l ttg,l3t-"9 conducting sphere has a 10 cm radius. Two wires are connected to it, one caries a current of 1.CI00$02 A into it and the other:carries a curient of 1 .000000 Aoui of ii. H;* i"-g *"rrd it take for the s$herd to increaserits potential 'nv g00 Vlai. toltr iritij value ? (Ans in ms)

--1lrnl

,30Tfl*

"orp"rui

lfi fears,

.

block on

\t

L

i

rr

.

A billiard ball at rest is.struck horizontally one tentntf the diameter betow the top. tf p he ,nthe blow find ttre,,initial.kinetic energy of 169 gsl;, the mass ot ftre oatt is tVt.

I

ontal surface

?[

i:

8. 'rf'l?

t-

-

instant

ball 3, instead of cutting the

'P

\v/

Three identical balls I ,2,3 are suspended on springs one below *J Ln.,t*f* shown in the figure. oA is a weightless thread. The balls are-in equilibriurr !fl lrge thread is cut, the system starts falling. Find the acceieration of ail the balts at

kx) Find

og erc

1r-\\

r= $, siventha)X*O. Transversevelocityof aparticteatx= 2m andt=2 seconds is. m/s x- F{- s k (c) 8 mrs trl_ r r;-"--"

nown but ors made I possible

-

ffil* tqY

Att=0,atransversewavepulsetravellinginthe,positivexdirectionwithaspeedof2m/sinawireisoescribeclby

5.

;onstant.

+2n

.

Newton (Take b = 10

'

i ...-, i

n"r/s2)

im.#4 ll# .

ri';, iitr,"r, r1f 'll a' cLr'f rr ! .:;J " 'i

tr

",

''

,--

..

'i

rept,on fixed rough horizontal surface. The limiting value of triction force fr is where p = coefficient, of friction (between the block and the horizontal surface) and N is

sT $\fr"ffifrb4ffiNT',** : A biock is ,*

';iVefi *y F ,,,' FiN,

fr{irn-[qi reactron on block due to horizontal surfqce. tu" Statement-1 is True, Stater"nent-2 is True; Statement-2 is a correct explanation for:statement-1 ifi};stHtennent-1 is True, Statement-2 is True; Staterrrent-2 is NOT a correct explanation for Statement-1 'h{fl) Staten"lent-tr is True, Statement-2 is False {UlX Statement-X is False, Statement-2 is True.

tffif

Answers of DPP - 13

'1

ll, +'V/2

,s|d

$A

* fitr q.,r

tl

It

Zfi ; T *un i$ nt

{ s"

r]

td.

iAi q,t.,$ iffi) p,$ iC)

tr5"

i:\

rih

e],r,s {A \ \.. )

{h &,n

i'.,

ffi rf,#"

l-,FLr

$F"

Torar Marks

:

\"_r

p,E,f',$

"4 r t\t I . S."/o

&

.

l-nv

{ffi"

3s

A

b.

C

{n+3) $q:cf = ''---J 24 K

C

7.

D

13.

12. dQ. = 400 R/n2

D

ffipP * 47

nnarB{!nE}

:

fillax,,Time : 3S min.

Q.5

5, I 5l [4; 5l '' [9, 9l

(3 mar&s 3 rnin,J t4 mark$'5 min.) (3 ma'rks 3 min,) {4 rnqrks 4 rnin.} (3 rnarks 3 Hlin.)

8.10

Q"1'f,

['t

[4, 4]

[3, 3]

{D)15m:

block and horizontalsurface is p. The string connecting both the'blocks,ir"riti$lty has zero tqnsion. The minimum force to be applied on block A ts just rnove the:two block system horizontally (without the string getting slack) is : 2pmg

I'

\*"

lrr/'

Bncxn

,'7

t/M

vr

ffi

(D)

Two fixed points A and B are 20 metres apart. At time t = 0, the distance between a third point C and A is 20 metres and the disiance between C and B is 10 rnetres. The.component.p! gqloctlygpoint C along both CA and CB at any instant is sm/s. Then the distance between n and.C;at ihe iodtani all the tlrree

points are collinear will be (B) 10 in) s

m

m

(C) 1s

m

Tot

.(p)itrtendbf tngpp

$.ir

A gas undergoes an adiabatic process and an isothermal process. The tWo:i,1 : processes are plotted on a P-V diagram. The resulting curves intersect at a point:f l \"

M'u

'.

P.

TanBents are drawn to the two curves at P. These rnake angles of 135o & 121o'lp Tangents '

vil|,lda nacif irra \/-avic witb,thepositiveV-axis

rn 600 - Cle *hA aac ic lileolr, tn l.ra ' lftan59o=5/3,thdgasislikelytobe: lf

f

*{dmoncatonric ffiatornic

{D)amixtureofmonoat#iI[JiuiJmiognsds.,'i'ff

s,

1'1.

2pirng

(c)

r' rJ,'-

.6t{

.*E

c

Two blocks each of mass m are placed on a rough horizontal surface and Connected ny a massless inelastic string as shown. The coefficient of friction between.e{ch

,

d,i0.

7,

DPP'l)lo'2 for week (1'1-05'09 to 1S-05-091

FolNcwing {no nesatlve

\Pfi eF{ffig {

D

6.

Thenthe.heightofthetowe'}f:(g=10rn/s,)l (A)Srn (C)20m {FfzSm

'

{R'

.

10

A stone projected at angle '0' with horizontal from top of a tower and it falls on the ground dter three seconds. Two second after the projection the stone was in the horizontal plane ing througfr the point of projectbn.

2.

cLJ x

r,s

fT

0f DpF ' ts

tt.

Assentfrsrt ffi$ld ffi,easom (nCI nsgatlve rnarking)

'l.

p {B) r,s (C) p,g (D}

'11

I,

A

s.

2

,t J

3,Mg^ (cw) (b)tsJ(c)

BC5.B

$ingle choice Objective {'-1'negative marking) Q.1 to ,ffiubje*t$vs ffiuestions {'*'$ ' nesetive mftrking} 8.6 ffimmpnehensicr! {'*t' negative Rnarklng} Q.7 to Q.9 ffimtc$] tfne

2.Et

4.DS.

ffi

uJ*

(A)

3q

cf tlPp : t4

4.

&mgwers ,4t

(e)

A tlr

S,nsttr€rs

*tr"A

,#3 -8t

8.

4.

=3235K

ffi

ft

.

rnff

?

7"

ln the figure shown the initial velocity of boat (30 kg)+person (15 kg ) is 2

Find vetocity of'person w i.i. ooat sJ

(trleglectfriction) : (A) 3 m1s towards right (C) 4 mls tovrards right

t

"i

u"rotitv

oTtff ;itl'il i

m/s.

r"iJ i" .gh'E-

:

(B) 3 rnls towards le{t (D)4 rn/s.towar:ds left

{

I|I I

S-u1

\\--t\. "\:-

-'r>v

,, , *.,jffiiE'r.n ";eOrr{\*=j;ffi; Fg: No.,# 2

Gor

Asr 1.

f. t ' I

,.t.ii.. ;

feB:';p

.:l.l

6. '

'i8,

A clowd, organ p,ipe has leng th,{, ln the air it is

vibrating in 3'd overtone with nnexirnurn amplitude ,&,. : the arnp,titu;e ai,:d';isi;nce of t t7 fromclosgdendottnupipg ''r"I'Lv{rtrfr'r'Lt'ru* {? Find #" t Comprehension : Asolid&,con$'rctilrg block in'theshapeof a cuboid has a cross sectional area of zcml,a front-to-rear bngtr of 18 ctn, an'il a resi*hnce of gob o' rnsbi;k s m-ati-riar contains !l iblr*"onou"tion erectronsrm3. between its rionia;; ;;;' r";".1"' tL,o'o,masntude 200 V/m is 3,lriltgJfl3,triilEf1fl:rence "i""iH" 7. .A:..!nmg,curr:b:nt.density io Oguaiffo-rm, its magnitude is '(A) 100A/mz . ,{Wz6

hnd',.S"ib; r-1

tent-1

.

r'

N^' fdl aoo-'*, 8. The curreDt in the block is gllYA (B)2x1o4A (c)3x10{A 9. T,he dlffqOeed of the conduction etectrons is (B) S crn/s (C)7.5 cm/s ryFfrhts 10' ln :

(D) 400 A/mz

(D)4*1alzA

:

(D) 15 crn/s lies on m, block of mass m2 ,, lies over smo6th 'horizontal'surifacbi xh"iei" Tals ilm"ieinttriction a.nd m, to preventisripping "no between both the blocksi tlorje$i:ffitii ro'rces ormaoniiuoe r, anu ?et*r";;;, and m, respectiveiy as shown. March l;ii;;ilito the stateme.o with that in coiumn-ii " T; riiiriT".i t,:1,,"'*:_,i'".t" each situation:of column-I, a block.of

["Til1;

&rr

(A)

The frictio,nal,f,sr** on block of mass

q{

(r) is tolarcts

v'

The frictional for.ce on block of mass (D)

i

J

#fr"[* -fiij

The frictional,',forde on block o f rnass m,

ieconds. ojection.

r_

t,\r

rq) has rnasnitud-

\,

(c)

,+ ffin

m1

(B) : 36 min.

*t 5 L | r-il2 [ e-n1 mz /*F\

(p) has rnagnitude

l*fi

m1

{si !s rcwards riqht.

1e

The frictional force on block of mass ffi, 17"

blockA

STATEMENT-I:Ablockismovedonroughhorizontaiflxedsurfacearongacircularpath.Theworkdonebyforce horizonutsurfacl to. fi.'" ori"iio;ilt#;

of fribtion on g'iven rough

brock

compretes a circre is zer* STATEMENT-2 : For a moving body, if net displacement in a tinie iritervar is zero, ,n-,., ilr" iilnro c*n* ny a non zero constant force acting on this body is zero. (A) $isfement-1 is True, Staternlnt-2 is Tr:ue; gtatement_2 is a correct explanation for Statemenr_1

ff3gti#J,l;1.,'i,Tftl$5TfiXl#i'p:i3.;.*#"i;''i .(D) Statement-1 is Fatse; Si"i"*"rt+; iil

:CandA C along :he three L

Total fVlarks

: 31

o.3 il'J-nl:;iT:i"::r^:::I:l';.1,n$y,:r:tins)9i ehgice o,bjectilv€ eur'Grrv€ {';{' negatve rn"r1l "'!q'r'!',',e v,rvruE lt'uliipl.e r -1- n6gative marking) Q.3roto Q.4 ll!:Sy.

\

euestio_ns 1'-ri negatii" ,"rLi"gf Oll t"-O.i neg.ative ilarki;gf ,O,i io ?:g$ensio.frf,l. Assertion and Re,as.on {no, negitive marking) e.et e, 0

l2Ec .+r".t

.t-\

+

it1""u".o,,"uct expranation ror starement:-i

(3 marks 3 min.) {5 rnarks a min. j rn,,k. $E mim"} *i^ {4 ff}arks (3 snarks,3 nrin")

-. 'i

1.

lJ_".y"",:T,X.;::Jn{L:y:t?:**l?^r,flillg!.1:r"

{3 rnarks 3

nnnri"}

$Jlax" Tssm* :

[s,

(!) cqntinuously

rr

&

[$, $] r::}i 33

from the roof of a verticailyoperatins

rlltl

!i

decreasing at *." a \-'\.,r -w" rlf r/r constant rqf,rsr rL rcrtff (f IrL"riJL,;iri ili; rate thr*ur;ht r.il{:i jil[..{f'tr"1*ii, (D) continuously increasingat,constant rate thrnuilil(-ri.ii +r^;r, ii-i'r.irr;;,,

Nq"#2

il;;;

;,i{

s"r.r$ru.

trH '{j,, 43 [,s, ,!{ ,$ fiffi, 0] f,ffi,

i:HlH:13;$ff__:5fj'.'3.'nnj""::llxl,**d[{nli,$l;i;:_".;;:,,:1l8THllil'fi ?^rlrlce'showed 30 kg and 5o kg r€spoctivr L

3if

ffi]

lift ri

;mn{:i 1;*ir,\g

",i:3,",113

thr* ifi$ient clisnl * s"i illlfrfi#t r^lsrll l,s fil"

r

\ fi,

ffi

There exists a uniform electric field in.the space as shown. Four points A, H, C and D are marked which are equidistant from:the origin. lf V;, V* V. find '\,'D #r* their prrt*ntlal$ re$pffictively, then i ,*..) \ft :* \,/tt(-;" > " \iot,l 'f:: :" V '"''l "A.

ry

*-F'

ifi) 'tlr, ''* Vr, ,* Vc *

;ii;,

"ffi14oVn"VotV. (il; VntVctVntVn

\t,,

, , ., '. ' ,"

hir:nk cf mass ? kS is hansins #ver a $rn$CIth and light pulley thrnugh a light string The il'rhei '*nd of the string is puiled by a constant force F,= 40 N" At t = 0 the systern is at

$\

2

r*$t

ai$

slrcwri Then

iru

ihe tinre interval frorn t = 0 ,?

s.econds, pick up the

1";f;E6 {r%!" L*?o

r*1ilrref;'rstatenient (s) " tS = tr0 n:isl) itsion iri the strinff i$ 4S frU ) w*rk dorre by t$nsicn on block is 80 J

(ts) work done by gravity is

- 20 J

(D) None of these

4" '- [n Resonance tube experiment,

Total

Mult Subj eom Asst 1.

F=40N

if 400 {-lz tuning fork is used, the irst resonance -s,ccursrtfien tength of air column is 19 crn. lf the 4001'{2. tuning fork is replaced by 1600Hztuning forkthe#toge,tresonance, the water level in the tube should be further lowered by (take end Correction = 1 cm) (D) 20 cm {/\} s nm {B) 10 cnn {C} 15 cm

,Electric field in a region is given by E = -4x i + 6 y 3 . f nen find the charge enclosed irr the cube of side 1m oriented as shown in the diagram.

$"

Tlre arrangement shown in figure consists.of two identical unifopn solid cylindas, eaqh of mass m, on which two light threads are wound symmetrically. Find the iension

i,$,

of each thread,in the process of motion. The friction in the axle of the upper cylinder is assumed to be absent 5"

#*nmglrtrg'rmmsB*,n

Atank of basb area 4 m? is initially filled with water up to height 2m. An object of unifonlr cross-section 2m? and neighi 1 m is now suspended by wire into the tank, keeping distance between base of tank and that of objeot 1m.

7"

8.

d1)l

T-he rJervunwards

A1

(A) 2f;x'i [}.

-l-he

f

t x 1CI5 N

:

2,Jx105N

tension in the wire is

14,) fi.

#"

force exerted by the water on the top surface of the ohjeqt is (fi) (C) 2.2 x 105 N '' (D) 2.9 x fr05'N

05N

*,-ffiZx '1.il5N :

(C) 0.3 x 105 N

tD) 0.4 x

1,105 N, :

Tfim l:uuyant force on the ob.lqEbs 105 t/\i 0.1 H 105 N

:ffiTx

:

(D)04x1:05N {C) 0.1 x 105 N STATEMENT-1 : The force on a rigid spherical body in with anotheririgjg:body ib.always:directed ru

0. 'towardsthecentreoftherigidsphericalbody..:

Col

$TATEMENT:Z : Whenevel two smooth rigid bodies are in ancl press eaeh o$br, tirby.exert a:

forceoneachotherindirectionperpendicuiaitosurfaceof..:

(A) Statement-1 is True, Statement.2 is True; Statement-2 is a coiiect expiangJio, fo-i,,Stat6fiient-1 (B) Statement-1 is True, Statement-2 is True; Statdmentr2 is NOT d,correct explaiati$n f6rl.Sfutement.1 ': (C) Stateggnt-1 is l'rue, Statement-2 is

(Dfffi6ment-1 is False, Statement-2 ,.-'.--/

False isTrue

t

I W*L E-6lvw,.*4t3{d-'LA ti'l* s\ll f'11{- & S

: ,

Ie

I *W\"fi.; {.t

ftlu*

ft

e-d

"4nsi

,,,1

,,,'

.

t'l

Pg.Np. #4

1 tulrT

10.