DPP_01 to 04

PHYSICS TARGET TARGET : JEE (MAIN + ADVA ADVANCED)

DPP No. : 01 to 04 Syllabus : XI class Syllabus DPP Syllabus : Thermodynam Thermodynamics, ics, Circular Circular motion, motion, Sound a!e, Pro"ectile Pro"ectile motion, motion, S#$, Neton%s la

DPP No. : 01

&NS'() *(+ - DPP N. 01 1. .

(C) . (D ) (A), (B), (C), (D)

1.

One mole of an ideal gas at a tempeatue ! "   e#pands slo$ly a%%oding to t&e la$

p '

/. 2.

(A) (A)

'

(A ) (C)

. .

(A), (B), (C), (D) (D)

  %onstant Its final tempeatue is ! *  !&e $o+ done by t&e gas is :

,d eksy vkn'kZ xSl tks p

4. 3.



!"

rkieku ij gS /khjs&/khjs QSyrh gS rFkk fu;e

fu;rkad dk ikyu djrh gSA bldk vfUre rki

!*

gSA xSl kjk fd;k x;k

dk;Z gS & (A) (! *

− !" )

(B) * (! *

− !" )

(C-)

 *

 ( ! *

−  ! " )

(D)

*  ( ! * .

−  ! " )

Pa5e No 6 1

.

 A be ad of ma ss m i s at ta %& ed to on e en d of a s p in g of na tu a l le ng t &  an d sp i ng %onstant + 

( .

+ ")mg

   !&e ot&e end of t&e sping is fi#ed at point A on a smoot& , /eti%al ing of adius  as s&o$n in figue !&e nomal ea%tion at B 0ust afte it is eleased to mo/e is ,d m n!";eku dk eudk  #kd$frd y%kbZ dh f#ax ds ,d (js ftldk y fu;rkad + 

( .

+ ")mg ls tks)*k tkrk gSA f#ax f#ax dk n+ljk n+ljk (jk f-kk f-kku.l u.lkj kj fduh ,



f-k;k dh 0/1kZ/kj 1y; ds fUn.  A ij fFkj (fi#ed) (fi#ed) gSA bldks (eudk ) xfr ds fy, 2ks)*us ds r.jUr kn B ij vf3ky% #frf4;k y 5;k gksxkA

(A)

mg *

(B)

(C) . .mg

. mg

Sol.7D8 !&e e#tension is sping is #  * %os .12 3  

(

(D-)

)

. . mg *

. −" 

 Applying 4e$ton5s 4e$ton5s se%ond la$ to t&e bead bead nomal to %i%ula ing ing at point B 4  + ( . − "   %os .12 6 mg %os .12

(

.  + "  mg , . . mg 4  * 

/.

(

. − "   %os .12 6 mg %os .12

 A sounding sounding body emitting a fe7uen%y fe7uen%y of "81 H9 is dopped dopped fom a &eig&t Duing Duing its fall unde ga/ity it %osses a balloon mo/ing up$ads $it& a %onstant /elo%ity of *ms one se%ond afte it stated to fall !&e diffeen%e in t&e fe7uen%y obse/ed by t&e man in balloon 0ust befoe and 0ust afte %ossing t&e body $ill be: (gi/en t&at ;/elo%ity of sound  .11ms< g  "1ms *) ,d /1fu /1fu 67iUu 67iUu djus 1k 1kyh yh 1r. ftldh ftldh vk1$f vk1$f8k 8k "81 H9 gS9 6ls d.2 0:kbZ ls fxjk;k tkrk gS x.71h; kjs tks fu;r 1sx *ms ls 0ij dh vksj xfreku gS9 dks ikj djrk gSa9 rks x.>kjs esa fFkr ";f5r

ds kjk x.>kjs dks ikj djus ds ?hd igys rFkk ?hd kn esa vk3kklh vk1$f8k esa vUrj gksxk  (fn;k x;k gS fd /1fu dh xfr  .11ms< g  "1ms *@ (A-) "* f 

Sol.

(B) =

(C) >

(D) ?

 v  ± v 1     = f 1    ± v  v  s    

$&en appoa%&ing : $&en e%eding :

 .11 + *   .11 − "1   .11 − *  f     "81   .11 + "1  f a 

"81 

⇒

 "* f a 3 f   ≅ "*

Hen%e (A)

Pa5e No 6 

4.

 A pa t i%l e is p o0 e% ted at an gl e =1 @ $i t& sp ee d "1

. , fom t&e point 5  A 5 as s&o$n in t&e

fig At t&e same time t&e $edge is made to mo/e $it& speed "1 .   to$ads ig&t as s &o $n i n t & e f i g u e ! &e n t &e t i me a f te  $ &i % & p a  ti % le $ il l s t i + e $ i t & $ ed ge i s (g  "1 mse% * ) : f-k esa n'kkZ;s vu.lkj fUn. 5A5 ls ,d d=k dks =1@ ds dks=k ij "1 . dh ky ls i!
yk;k tkrk gSA r 1g le; Ckr djks ftlds i'krD d=k x.Bds ls Bdjkrk gS &

(A-) * se% ? (C) se% . Sol.

(B) *

. se %

(D) none of t&ese

Suppose pati%le sti+es $edge at &eig&t S afte time t S  "8t 3 distan%e ta/elled by pati%le in &oi9ontal die%tion  8 distan%e

S "8 t − 8 t * #   tan .1 ° ": . !otal distan%e ta/elled by $edge in time t  "1 t  * se% ⇒ <ernate Sol. (by elati/e otion) !

⇒

*u sin .1° g %os .1°

 

* × "1 . "1

×

" .

. t  8

"

buesa ls dksbZ ugh "1 t*  "8t 3 8 t* Duing t&is time

* . t Also $edge &as ta/elled ta/elled e#ta

.  t 6

.  ("8 3 8t *)

 * se%

"8

t  * se%

.12

1 .9

 A pati%le pefoming SH undegoes displa%ement of

Sol.

It ! be t&e time peiod < time to go fom O to  is

.

8

.

 A

 ($&ee A  amplitude of SH) in one * se%ond At t  1 t&e pati%le $as lo%ated at eit&e e#teme position o mean position !&e time peiod of  SH %an be : (%onside all possible %ases)  A ljy vk1rZ xfr dj jgk ,d d=k ,d lSd=) esa (tgk: A  ljy vk1rZ xfr dk vk;ke ) * f1Fkkr gksrk gSA le;  t  1 ij d=k ;k rks fdlh ,d je fFkfr ij Fkk ;k ek/; fFkfr ij FkkA ljy vk1rZ xfr dk vk1rZdky gks ldrk gS : (l3kh l%3kkf1r fFkfr;ksa dks ysaA) (A-) "*s (B-) *? (C-) =s (D-) "*s

! !  and fom  to P is   = "* Pa5e No 6 /

!&e displa%ement is

 A

 $&en pati%le goes fom O to , fom O to 4 to , * fom O to 4 to O to P, and so on ! ! ! ! ! E! + = 8! ∴ t  o t  o t + = ? = "* "* * "* "* Hen%e possible time peiod ! is "* × " "* × " !  "* s o !   *? s o !  s 8 E  A similaly displa%ement is  $&en pati%le goes fom  to P o  to 4 to P * Hen%e t&e possible time peiod ! is = ×" !  " F =  = s o !  s  "* s 8

&ns. !  "* s, =s, *?s, "*s #indi.

;fn ! vk1rZdky gS9 O ls  rd tkus esa yxk le;

t

O ls , O ls 4 ls , O ls 4 ls O ls P rd

∴

t

! !  o t  ? "*

+

! =

=

8! "*

;k

blh i!dkj t d=k

!

;k

t

"* × "   *? s 8

! *

+

;k

 ls P ;k  ls 4 ls P rd = ×" 8

! "*

!

=

 A *

! =

gSA

gSA

E! "*

"* × " s E

tkrk gS rks f1Fkkiu

blfy;s la3k1 vk1rZdky ! gS & !  " F =  = s o ! 

gS rFkk  ls P rd le;

tkrk gS rks d=k dk f1Fkkiu

blfy;s la3k1 vk1rZdky ! gS & !  "* s

! "*

 A *

gSA

s  "* s

&ns. !  "* s, =s, *?s, "*s .9

In t&e figue s&o$n all t&e sufa%e ae smoot& All t&e blo%+s A, B and C ae mo/able, #;a#is is &oi9ontal and y;a#is /eti%al as s&o$n Gust afte t&e system is eleased fom t&e position as s&o$n n'kkZ;sa f-k esa l3kh lrg fduh gSA l3kh =)  A, B rFkk C xfr dj ldrs gSA #; v
fFkfr ls e.5r djrs gS rks blds r.jUr kn & y

A B

θ

# C

θ

H o  i9 o n t a l S u  f a % e

Pa5e No 6 4

Sol.

(A-) A%%eleation of 5A5 elati/e to gound is in negati/e y;die%tion (B-) A%%eleation of 5A5 elati/e to B is in positi/e #;die%tion (C-) !&e &oi9ontal a%%eleation of 5B5 elati/e to gound is in negati/e #;die%tion (D-) !&e a%%eleation of 5B5 elati/e to gound along t&e in%lined sufa%e of 5C5 is geate t&an g sin θ (A-) tehu ds lkis
esa nsrk gSA =) B uhs ds lkFk&lkFk =kk7ed #;fn'kk esa xfreku gksrk gSA  A rFkk B dk uhs dh vksj 71j=k Hrk ls jkj gksrk gS9 vrG B ds lkis
B

4 o  m a l e a % tio n d u e to C

C

 kj k v f3ky %& i !fr f4 ; k

Due to t&e %omponent of nomal e#teted by C on B, it mo/es in negati/e #;die%tion C ij B kjk vf3ky% ds IkBd ds dkj=k ;g =kk7ed, #;fn'kk esa xfreku

2 ?

gSA

A

2

>

) g !&e fo%e a%ting /eti%ally do$n$ad on blo%+ B ae mg and 4 A(nomal ea%tion due to blo%+ A) Hen%e t&e %omponent of net fo%e on blo%+ B along t&e in%lined sufa%e of B is geate t&an mg sin θ !&eefoe t&e a%%eleation of 5B5 elati/e to gound die%ted along t&e in%lined sufa%e of 5C5 is geate t&an g sin θ. >ykJd B ij 0/1kZ/kj uhs dh vksj y mg 6 4 A (>ykJd  A ds dkj=k vf3ky%

i!frf4;k ) gSA blfy;s >ykJd B ij dk;Zjr usB y dk IkBd mg sinθ ls vf/kd gSA blfy;s 3k+fe ds lkis
B dh B dk

ur lrg ds vu.fn'k 71j=k9 ftldh fn'kk

C$P)(#(NSIN  A *+g blo%+ &angs $it&out /ibating at t&e bottom end of a sping $it& a fo%e %onstant of ?11 4m !&e top end of t&e sping is atta%&ed to t&e %eiling of an ele/ato %a !&e %a is ising $it& an up$ad a%%eleation of 8 ms * $&en t&e a%%eleation suddenly %eases at time t  1 and t&e %a mo/es up$ad $it& %onstant speed (g  "1 ms *) y fu;rkad ?11 4m dh fi!ax ds fuys (js ls * fdx!kK dk =) fuk d%iUu ds yBdk gSA fi!ax dk 'khLkZ ( jk fyMB dh 2r ls t.)*k gSA fyMB 8 ehKNlsK * ds 0ijh 71j=k ls 6? jgh gSA t t  1 ij 71j=k vkud Ek7e gksrk gS9 fyMB ,d leku ky ls 0ij dh vksj xfreku gSA  (g  "1 ehKNlsK *) 2.

&at is t&e angula fe7uen%y of os%illation of t&e blo%+ afte t&e a%%eleation %eases

71j=k lekOr gksus ds i'krD  =) dh dks=kh; vk1$f8k 5;k gS & (A-) "1

Sol.

ω 

J m

*  ads



(B) *1

*  ads

(C) *1 ads

(D) .* ads

*11 ads Pa5e No 6 

Pa5e No 6 

3.

!&e amplitude of t&e os%illations is

d%iUu dk vk;ke gS & (A) E8 %m

.

(B) 8 %m

(C-) *8 %m

(D) " %m

!&e initial p&ase angle obse/ed by a ide in t&e ele/ato, ta+ing up$ad die%tion to be positi/e and positi/e e#teme position to &a/e π* p&ase %onstant, is e7ual to

fyMB esa l1kj ";fP kjk i!sf
⇒ # 

*("1 + 8)m ?11

 E8 %m

K#tension of t&e sping $&en it is stet%&ed to e7uilibium line is #5 mg +#5 * × "1 ⇒ #5    8 %m ?11 !&eefoe amplitude A  # 3#5  *8 %m If up$ad die%tion is ta+en as positi/e at t  1, #  3 A Msing #  A sin ( + t 6 f )  3 A  A sin f  .π f   * gy%  3,  fi!ax dh i!kd$frd fFkfr ls eg7re fEkak1 # gS A rks  mg 6 ma  +#

⇒ # 

(D-) .π* ad

K 7  li n e ΣL  1 '1

*("1 + 8)m  E8 %m ?11

lk%;1Fkk ls fi!ax fEkaus ij blesa fEkak1  #5 gS A ⇒

mg +#5 * × "1 #5   8 %m ?11

vrG vk;ke  A  # 3#5  *8 %m ;fn 0ij dh fn'kk dks /kuk7ed ysa9 rks #  A sin ( + t 6 f ) dk i!;ksx djus ij  3 A  A sin f  .π f   *

K 7  li n e ΣL  1 t  1 ij  #  3 A

'1

Pa5e No 6 2

PHYSICS TARGET : JEE (MAIN + ADVANCED)

DPP No. : 01 to 04

Syllabus : XI class Syllabus

DPP Syllabus : Thermodynamics, Circular motion, Sound a!e, Pro"ectile motion, S#$, Neton%s la, -riction, Strin5 a!e.

DPP No. : 02

&NS'() *(+ - DPP N. 0  1.

(B)

.

(C)

/.

(C )

3.

(C )

.

(A )

10.

(A) p,7 (B) 7, (C) 7, (D) s

1.

4.

(C)

.

(C )

.

(D )

2.

(B )

!&e /alue of γ   CpC/ fo a gaseous mi#tue %onsisting of *1 moles of o#ygen and .1 moles of &elium !&e gases ae assumed to be ideal *1 eksy vkJ5lhtu ,1a .1 eksy ghfy;e ds fe=k ds fy, γ   CpC/ dk eku gksxkA

xSlks dks vkn'kZ eku fy;k tk;sA (A) .

E 8

(B-)

*N "N

(C)

*. "N

(D)

*8 "N

Ligue s&o$s t&e +ineti% enegy J of a simple pendulum /esus its angle θ   fom t&e /eti%al !&e pendulum bob &as mass 1* +g !&e lengt& of t&e pendulum is e7ual to (g  "1 ms * ) f-k esa ljy yksyd dh xfrt 0tkZ J rFkk 6/1kZ/kj ls dks=k θ ds h x!kQ n'kkZ;k x;k gSA yksyd dk n!";eku 1  * fdx!kK gSA ljy yksyd dh y%kbZ jkj gS &  (g  "1 ehKNlsK * )

J (m G ) "8 "1 8 ;" 1 1 (A) *1 m

1

"11 (B) "> m

θ(m a d ) (C-) "8 m

(D) "* m

Pa5e No 6 3

Sol.

" *

*   "8 F "1 3. m'm

 A ω  gO

/.

' m  

1"81  ms



1"81 "11 × "1 −.



⇒

1"81

.m

 

g  O

m s 1"81  m s

1 "81   "8 m 1 "

 A pa t i% le is e /o l/ in g in a %i %l e in %e asi ng its spe ed un if om ly &i %& of t&e fol lo $i ng is %onstant

,d d=k dh ky dks ,d leku nj ls R*krs g., ,d 1$8kh; iFk ij Ik.ek;k tkrk gSA rks fu%u esa ls dkSulh jkf'k fu;r gksxh (A) %entipetal a%%eleation ( vf3kdsUn!h; 71j=k ) (B) tangential a%%eleation ( i'kZjsEkh; 71j=k) (C-) angula a%%eleation ( dks=kh; 71j=k ) (D) none of t&ese ( buesa ls dksb Z ugha )

Sol.

 An gu la  a% %e le a tio n ( α ) 

at  



Sin%e, a t =

d/ dt

  %onstant

∴

magnitude of α  is %onstant  Als o its di e %t ion is al $a ys %on sta nt (p ep en di %ul a to t& e pla ne of %i %u la  mo tio n)  $&eeas, die%tion of a t  %&anges %ontinuously a t  is not %onstant 4.

 A bead of mass m is lo%ated on a paaboli% $ie $it& its a#is /eti%al and /ete# at t&e oigin as s&o$n in figue and $&ose e7uation is # *  ?ay !&e $ie fame is fi#ed in /eti%al plane and t&e bead %an slide on it $it&out fi%tion !&e bead is eleased fom t&e point y  ?a on t&e $ie fame fom est !&e tangential a%%eleation of t&e bead $&en it ea%&es t&e position gi/en by y  a is :

f-kku.lkj ij1y; dh lehdj=k #*   ?ay gSA bldh 0/1kZ/kj v
(A) Sol.

g *

(B)

.g *

(C-)

g *

(D)

g 8

#   ?ay Diffeentiating $t y, $e get y ds lkis
∴

 At (*a, a),

dy   " d#

&en%e vrG θ  ?82 t&e %omponent of $eig&t along tangential die%tion is mg sin θ 3kkj dk i'kZ jsEkh; fn'kk esa IkBd mg sin θ g &en%e tangential a%%eleation is g sin θ  * g vrG i'kZ jsEkh; 71j=k g sin θ  *

⇒ 

Pa5e No 6 

.

In t&e s&o$n aangement if f " , f *   and ! be t&e fi%tional fo%es on * +g blo%+, .+g blo%+ and tension in t&e sting espe%t i/ely, t&en t&ei /alues ae: f-kku.lkj ;fn f " , f * 4e'kG  * + g rFkk  .+g ds >ykJd ij IkLkZ=k y gks rFkk jlh

esa ruk1 ! gks rks buds eku 4e'kG gkasxs

(A) * 4, = 4, .* 4 (C-) " 4, = 4, * 4 Sol.

7C8 L BD "4

*+g

(B) * 4, = 4, 1 4 (D) data insuffi%ient to %al%ulate t&e e7uied /alues (D) eku Ckr djus ds fy, vk:d)*s vi;kZOr gSA

!

!

.+g

>

fma#  * fma#  = 4et fo%e $it&out fi%tion on system is E4 in ig&t side so fist ma#imum fi%tion $ill %ome on . +g blo%+ IkLkZ=k ugh gksus dh fFkfr esa fudk; ij E4 dk y nkfguh vksj yxsxk blls .J g

ds >ykJd ij igys vf/kdre IkLkZ=k vk;sxkA " " So f *   " 4, f .   = 4, !  *4

*+g

*

* =

.+g

>

vrG f *   " 4, f .   = 4, !  *4 .

 A bl o% + is at ta %& ed $i t& a sp in g an d is mo /i ng to $a d s a fi# ed $a ll $i t& sp ee d / as s&o$n in figue As t&e sping ea%&es t&e $all, it stats %ompessing !&e $o+ done by t&e sping on t&e $all duing t&e po%ess of %ompession is :

,d >ykJd ,d fi!ax ls t.)*k gS rFkk fnEkk;s f-kku.lkj ;g ,d fFkj nh1kj dh vksj / ky ls xfr dj jgk gSA t fi!ax nh1kj rd ig.:rh gS9 ;g laihf)r gksuk i!kj%3k djrh gSA laih)u dh i!f4;k ds nkSjku fi!ax  kjk nh1kj ij fd;k x;k dk;Z gksxk &

Sol.

(A) "* m/ * (B) m/ * (C) Jm/ (D-) 9eo 'k+U;  As po in t of ap pl i%a tio n of fo %e is no t mo /i ng , t&e e foe $o + do ne by t& e fo %e is 9e o

+:fd y dk f4;k fUn. xfr ugh dj jgk gS9 blfy;s y kjk fd;k x;k dk;Z 'k+U; gksxkA

Pa5e No 6 10

C$P)(#(NSIN  A pulse is stated at a time t  1 along t&e 6# die%tion on a long, taut sting !&e s&ape of t&e pulse at t  1 is gi/en by fun%tion f(#) $it& ,d y%h ruh g.bZ jlh esa le; t  1 ij 6# fn'kk esa ,d ian dks 3kstk tkrk gSA le; t  1 ij ian dk vkdkj Qyu f(#) kjk fu%u #dkj fn;k tkrk gS &

 − ? < # ≤ 1 ds fy,  f ( # ) =  1 < # < " ds fy,  vU ; Fkk  

#  ? + " fo  − ? < # ≤ 1  f ( # ) = − # + " fo  1 < # < "  1 ot&e$ise  

#

+" ? − # +" 1

&ee f and # ae in %entimetes !&e linea mass density of t&e sting is 81 gm and it is unde a tension of 84, ;gk: f 1 # lsUBhehBj (%m) esa gSA jlh dk jsEkh; n!";eku Iku71  81 gm gS 1 bls 84 ruk1 esa jEkk x;k gSA 2.

Sol.

!&e s&ape of t&e sting is da$n at t  1 and t&e aea of t&e pulse en%losed by t&e sting and t&e #;a#is is measued It $ill be e7ual to le; t  1 ij ian ds vkdkj dks n'kkZ;k tkrk gSA ian dk
y (% m ) "

3? !&at is a tiangula pulse  Aea of t&e pulse 3.

Sol.

1

# (% m )

"

;g f-k3k.tkdkj iUn gSA

iUn dk


"

 (? F ") 6 (" F ")Q 

8

%m*

* * !&e /eti%al displa%ement of t&e pati%le of t&e sting at #  E %m and t  11" s $ill be (A) 1E8 %m (B) 18 %m (C-) 1*8 %m (D) 9eo #  E %m ij fFkr fUn. dk le; t  11" s ij 0/1kZ/kj f1Fkkiu gksxk (A) 1E8 %m (B) 18 %m (C-) 1*8 %m (D) 'k+U; !

/

µ

&

  "1 ms

Solution of t&e $a/e e7uation t&at gi/es displa%ement of any pie%e of t&e sting at any time

rjax lehdj=k ds gy ls fdlh le; ij )ksjh ds ,d 3kkx ds f1Fkkiu dks Ckr djrs gSA  ( # − /t )  ( # − /t ) + − < ≤ " fo  /t ? # /t  ?  ? +"   y = f ( #, t ) = − ( # − /t ) + " fo  /t < # < /t + " y = f ( #, t ) = − ( # − /t ) + "   1 ot&e$ise 1     /  "111 %ms, t  11" s ds i!;ksx /t  "1 %m as +afd (/t 3 ?) R (#  E %m) R /t Msing

y

/t − ? < # ≤ /t /t

< # < /t + " vU; Fkk

dsfy, dsfy,

ls

" "  (E 3 "1) 6 "  %m  1*8 %m ? ? Pa5e No 6 11

.

Sol.

!&e tans/ese /elo%ity of t&e pati%le at #  ". %m and t  11"8 s $ill be #  ". %m ij fFkr d=k dk le; t  11"8 s ij vu.#Fk 1sx gksxk & (A-) 3*81 %ms (B) 3811 %ms (C) 811 %ms (D) 3"111 %ms ∂y !ans/ese /elo%ity  ∂t at t  11"8 s, /t  "8 %m as fo #  ". %m (/t 3 ?) R # R /t ∂y vu.i!Fk 1sx  ∂t t  11"8 s ij , /t  "8 %m #  ". %m ds fy, (/t 3 ?) R # R /t t&eefoe vr G ∂y / 3  3 *81 %ms ∂t ?

10.

In ea%& situation of %olumn;I, t&e #;%oodinate of a pati%le mo/ing along #;a#is is gi/en in tems of time t (ω is a positi/e %onstant) at%& t&e e7uation of motion gi/en in %olumn; I $it& t&e type of motion gi/en in %olumn; II r%3k;I dh i!7;sd fFkfr esa #;fn'kk esa xfr djrs g., d=k dk le; t ds inks esa #; funsZ'kkad fn;k gSA (ω /kuk7ed fu;rkad gS ) r%3k;I esa nh xbZ xfr ds lehdj=k dks r%3k;II esa xfr ds i!dkj ls l.esfyr dfj, & ColumnI ColumnII (A) sin ωt 3 %os ωt (p) SH . (B) sin ωt (7) Peiodi% (C) sin ωt 6 sin. ωt 6 sin8 ωt () Peiodi% but not SH * * (D) e#p (3 ω t ) (s) 4on peiodi% LrEHk I   LrEHk II (p) ljy vk1rZ xfr (SH) (7) vk1rZ (peiodi%) xfr () vk1$8k xfr ij ljy

(A) sin ωt 3 %os ωt (B) sin. ωt (C) sin ωt 6 sin. ωt 6 sin8 ωt

ugh &ns.

(D) e#p (3 ω* t*) (A) p,7 (B) 7, (C) 7, (D) s

Sol.

(A) #

  "   " sin ωt − %os ωt     *   *   (B) #  sin. ωt %an not be $itten as #  A sin(ω5 t 6 φ) so it is not SH =

* 

(s)

⇒ # 

* sin (ω t 3

vk1rZ xfr

dksbZ vk1rZ xfr ugha π ) is peiodi% $it& SH ?

but peiodi% motion (C) inea %ombination of diffeent peiodi% fun%tion is also peiodi% fun%tion

d* # dt *

is not die%tly popotional to # ie t&is motion is not SH

(D) # %ontinuously de%eases $it& time So # is not peiodi% fun%tion

  "   " π sin ωt − %os ωt   ⇒ #  * sin (ω t 3 ) SH ds lkFk vk1rZ xfr   ? *   *   (B) #  sin. ωt dks as #  A sin(ω5 t 6 φ) ds i esa ugh fyEkk tk ldrk gSA (A) #

=

* 

vrG SH ugh gS ijUr. vk1rZ xfr gSA (C) vk1$f8k Qyuksa dk jsEkh; la;kstu 3kh vk1$f8k Qyu gksrk gSA d* # dt *

lh/ks i ls # ds leku.ikrh ugha gSA vrG ;g xfr

(D) # le;

ds lkFk yxkrkj IkBrk gS vrG

# vk1rZ

SH ugh

gSA

Qyu ugh gSA Pa5e No 6 1

PHYSICS TARGET : JEE (MAIN + ADVANCED) 2015 Syllabus : XI class Syllabus DPP No. : 01 to 04 DPP Syllabus : Thermodynamics, Circular motion, Sound a!e, Pro"ectile motion, S#$, Neton%s la, -riction, Strin5 a!e, 'P(, ;.. , *inematics

DPP No. : 03

&NS'() *(+ - DPP N. 0/ 1.

(A )

2.

(B), (C), (D)

1.

.

(B )

/.

(A )

4.

(A )

.

(B), (C) .

3.

8= G

.

(A) s, (B) p, (C) s, (D) 7

(A), (B), (D)

 A simple pendulum 81 %m long is suspended fom t&e oof of a %at a%%eleating in t&e &oi9ontal die%tion $it& %onstant a%%eleation . g ms* !&e peiod of small os%illations of t&e pendulum about its e7uilibium position is (g  π* ms*) : ,d ljy yksyd ftldh y%kbZ 81 lsehK gS ,d xk)*h dh 2r ls yBdk g.vk gS tks fd


*

(A-) "1 se% (A-) "1 Sol.

(B)

lsd=)

(B)

* se% *

lsd=)

(C) "8. se% (C) "8.

lsd=)

*

(D) "=> se% (D) "=>

lsd=)

it& espe%t to t&e %at, e7uilibium position of t&e pendulum is s&o$n If displa%ed by small angle θ fom t&is position, t&en it $ill e#e%ute SH about t&is e7uilibium position, time peiod of $&i%& is gi/en by :

xk)*h ds lkis
!  *π

O g eff 

<

geff  

g * + ( .g ) *

⇒

.

geff   *g ⇒ !  "1 se%ond  A smoot& $ie is bent into a /eti%al %i%le of adius a A bead P %an slide smoot&ly on t&e $ie !&e %i%le is otated about /eti%al diamete AB as a#is $it& a %onstant speed ω as s&o$n in figue !&e bead P is at est $t t&e $ie in t&e position s&o$n !&en

ω* is e7ual to : Pa5e No 6 1/

,d fdus rkj dks f-k;k ds 0/1kZ/kj 1$8k esa eks)*rs gSA ,d eudk P, tks rkj ij fuk IkLkZ=k ds fQly ldrk gSA f-kku.lkj 0/1kZ/kj ";kl  AB ds lkis
(A) Sol.

*g   a

(B-)

 As < %osθ 

*g a .

 

(C)

g . a

 

(D)

*a g .

a

*a θ  =1@ 4 sin=1@  mg

∴

4 %os=1@  m

ω*a *

$t $ie

∴

tan=1@ 

*g

ω*a

ω*  /.

*g a .

!&e potential enegy of a pati%le /aies $it& # a%%oding to t&e point #  * is a point of :

elation M(#)  # * − ? # !&e

,d d=k dh fFkfrt 0tkZ funs'kkad # ds lkFk fn;s x;s l%a/k gSA t d=k #  * ij gSA r d=k (A-) stable e7uilibium (C) neutal e7uilibium (A-) FkkbZ lk%;k1Fkk

esa gksxk

gksxk (C) 6nklhu lk%;k1Fkk esa gksxk Sol.

M(#)  #* − ? #

(B) unstable e7uilibium (D) none of abo/e (B) vFkkbZ (D)

ls nyrh

lk%;k1Fkk esa

buesa ls dksbZ ugha

M(#)  #  3 ?# L1 *

dM( # ) 1 d# *# 3 ?  1

#*

*

d M d# *

  *  1 ie M is minimum &en%e #  * is a point of stable e7uilibium

Pa5e No 6 14

4.

!$o plane mios ae in%lined at E1@ A ay in%ident on one mio at angle

θ afte efle%tion falls on t&e

θ is: nks lery niZ=k E1@ ds dks=k ij V.ds g., gS ,d fdj=k θ dks=k ij niZ=k ij vkifrr gksrh gS ijk1rZu ds kn n+ljs niZ=k ij fxjrh gS blds kn i!Fke niZ=k ds lekUrj ijk1frZr gksrh gS9 rks dks=k θ gS : se%ond mio and is efle%ted fom t&ee paallel to t&e fist mio

(A-) 81@ .

(B) ?8@

(C) .1@

(D) 88@

 A %ylinde of mass  and adius  is esting on t$o %one edges A and B as s&o$n in figue !&e nomal ea%tion at t&e edges A and B ae : (4egle%t fi%tion)  f-k;k ,1a  n!";eku dk ,d syu f-kku.lkj nks IkLkZ=kfgu fdukjksa  A rFkk B ij jEkk gSA  A rFkk B ij vf3ky%1r i!frf4;k gS &

(A) 4 A 

(B-) 4B 

*4B

(C-) 4 A 

.4 A

g *

(D)

4B



* .g

Sol.

8 Lo e7uilibium 4 A %os =12 6 4 B %os .12  g

and 4a sin =12  4 B sin .12 On sol/ing 4B 

.  4 A < 4 A 

g

* 4 A %os =12 6 4 B %os .12  g

lk%;1Fkk ds fy, rFkk 4a sin =12  4B sin .12 gy djus ij .

4B 

g

. 4 A < 4 A 

*

 An ideal gas undegoes a %y%li% po%ess ab%da $&i%& is s&o$n by pessue; density %u/e vkn'kZ xSl dks 4h; i!4e ab%da ds vu.fn'k ys tk;k tkrk gS tks fd nk Iku71

esa i!nf'kZr gSA

P

14

d

% a b ρ"

ρ*

ρ

(A-) o+ done by t&e gas in t&e po%ess 5b%5 is 9eo (B-) o+ done by t&e gas in t&e po%ess 5%d5 is negati/e (C) Intenal enegy of t&e gas at point 5a5 is geate t&an at state 5%5 (D-) 4et $o+ done by t&e gas in t&e %y%le is negati/e (A-) b% i!4e esa xSl kjk fd;k x;k dk;Z 'k+U; gSA (B-) %d i!4e esa xSl kjk fd;k x;k dk;Z =kk7ed gSA (C) a v1Fkk ij xSl dh vkUrfjd 0tkZ % v1Fkk ls ;knk gSA (D-) xSl kjk 4h; i!4e esa fd;k x;k d.y dk;Z =kk7ed gSA

Pa5e No 6 1

Sol.

ρ 

ρ

⇒

,!

P

=

, ! 1

ρ Slope of t&e %u/e α !empeatue

d

Hen%e %d and ab ae isot&emal po%esses "

a

1

%

ρ ∝

' ie b% and da ae %onstant /olume po%ess (A) and (B) ae tue !emp in %d po%ess is geate t&an ab

Sol.

d ' '* '" K 7 u i/ a le n t P ' d ia g  a m 

4et $o+ done by t&e gas in t&e %y%le is negati/e, as is %lea by t&e P';diagam ρ P , ,! ! = ρ  ⇒ ρ 1 1

14 dk Rky α rkieku vrG %d 1 ab lerkih; #4e gS ρ ∝

d

"

a

'

vFkkZrD b% 1 da le vk;rfud #4e gS (A) 1 (B) l7; gSA %d #4e dk rki ab ls vf/kd gSA #4e esa d.y fd;k x;k dk;Z =kk7ed gS tks 2.

% '

P';14

d '

*

esa r W. ;

14

P'

' "

iLB gSA

 A %a mo/es to$ads a &ill $it& speed / % It blo$s a &on of fe7uen%y f $&i%& is &ead by an obse/e  follo$ing t&e %a $it& speed / 1 !&e speed of sound in ai is /

,d dkj igk)*h dh vksj /% ky ls xfr djrh gSA ;g f vk1$fr dk ,d gkJuZ tkrh gS tks /1 ky ls dkj dk ih2k dj jgs ,d ksrk kjk l.uk tkrk gSA g1k esa /1fu dh ky / gSA (A) t&e $a/elengt& of sound ea%&ing t&e &ill is (B-) t&e $a/elengt& of sound ea%&ing t&e &ill is

/ f 

/ − /C f 

(C-) !&e $a/elengt& of sound of &on die%tly ea%&ing t&e obse/e is (D-) t&e beat fe7uen%y obse/ed by t&e obse/e is (A) igk)*h

(C-) i!s
+

/%

f 

*/ % ( / + / 1 )f  /*

− / %*

ij ig.aus 1kyh /1fu dh rjaxnS/;Z

(B-) igk)*h

/

ij ig.:us 1kyh /1fu dh rjaxnS/;Z

/

gSA

f 

/ − /C f 

gSA

ij lh/ks gkuZ ls ig.:us 1kyh /1fu dh rjaxnS/;Z

kjk l.uh x;h f1ian vk1$fr

*/ % ( / + / 1 )f  /*

− / *%

/

+

/%

f 

gSA

 gSA

Pa5e No 6 1

Sol.

Le7uen%y of &on die%tly &ead by obse/e

/ + /1 / + /%

f 

/ / + /% Le7uen%y of e%&o of &on as &ead by obse/e Le7uen%y of e%&o 

/ / − /%

 / + / 1       /    

f  

L7uen%y of Beats :  (/ 6 /1) f

Sol.

 " "  −   / − / % / + /% 



*/ % ( / + / 1 ) (/ *

− / %* )

i!s


/ + /1 / + /%

f 

/ / + /%

i!s


" " − f1ian dh vk1$f8k :  (/ 6 /1) f   / − /% / + /%  3.



/ / − /%

 / + / 1       /    

f  

*/ % ( / + / 1 ) (/ *

− / *% )

Po$e deli/eed to a body /aies as P  . t* Lind out t&e %&ange in +ineti% enegy of t&e body fom t  * to t  ? se% fdlh 1r. kjk nh xbZ 'kf5r P  . t* kjk ifj1frZr gksrh gS9 rks t  * se% ls t  ? se%

rd 1r. dh xfrt 0tkZ esa ifj1rZu Ckr djksX Sol.

 Applying $o+ enegy t&eoem to body ∆JK  $o+ done by fo%es deli/eing po$e P

1r. ij dk;Z 0tkZ i!es; yxkus ij ∆JK  'kf5r P nsus 1kys yksa kjk fd;k x;k dk;Z ?



?

∫ Pdt   ∫ .t t =*

*

dt   8= G

t =*

&ns. 8= G .

Lou pati%les ae mo/ing $it& diffeent /elo%ities in font of stationay plane mio (lying in y;9 plane)  At t  1, /elo%ity of A is / = Ti  , /elo%ity of B is / = − Ti + . 0T  , /elo%ity of C is / = 8Ti + = 0T , /elo%ity  A

B

C

of D i s / D = .Ti −  0T  A%%eleation of pati%le A is a A = *Ti +  0T and a%%eleation of pati%le C is a = * t 0T  !&e pati%le B and D mo/e $it& unifom /elo%ity (Assume no %ollision to ta+e pla%e till t  * C

se%onds) All 7uantities ae in SI Mnits elati/e /elo%ity of image of ob0e%t A $it& espe%t to ob0e%t A is denoted by ' A 5, A   'elo%ity of images elati/e to %oesponding ob0e%ts ae gi/en in %olumn I and t&ei  /alues ae gi/en in %olumn II at t  * se%ond at%& %olumn I $it& %oesponding /alues in %olumn II fFkj lery niZ=k ds lkeus kj d=k f1f3kUu 1sx ls xfr dj jgs gS TniZ=k y9 ry esa gS@A t  1 le; ij  A dk 1sx / = Ti , B dk 1sx / = −Ti + . 0T  , C dk 1sx / = 8Ti + = 0T , D dk  A

B

C

1sx / D = .Ti −  0T gSA d=k  A dk 71j=k a A = *Ti +  0T vkSj d=k C dk 71j=k a % = *t 0T gSA d=k B 1 D ds 1sx fu;r gS T;g ekfu;s fd t  * lsY rd niZ=k ls dksbZ B55j ugh gksrh gS@A f% (1r.) A ds lkis
Column I LrEHk  I  (B)

'B5, B

 (p) *Ti  (7) − =Ti

(C)

'C5,C

 0  () − "*Ti + ? T

(A) ' A 5, A

&ns. Sol.

Column II LrEHk  II

(D) 'D5,D  (s) − "1 T i (A) s, (B) p, (C) s, (D) 7 T )( * )   8 Ti + * 0 T 7$oderate8 / A = Ti + a t  Ti + ( * Ti +  0

/ A 5

= −8 Ti + * 0T

/ A 5, A  /  A 5 − / A = −"1 Ti

'B

= ( − Ti + . 0T ) , 'B5 = Ti + . 0T so

Lo pati%le C (d=k C ds

d/ y dt

= *t

'B5, B = *Ti

fy,)

⇒ /y 3 =  t*

⇒ /y  = 6 ?  "1

T  so / C5,C = − "1 Ti / C = 8 Ti + "1  0T , / C5 = −8Ti + "1 0

, / C5 = −8Ti + "1 0T  , / C5,C = − "1 Ti / = . Ti −  0T , / = −.Ti −  0T , / D5, D = −=Ti D

D5

Pa5e No 6 13

PHYSICS TARGET : JEE (MAIN + ADVANCED) Syllabus : XI class Syllabus 4.

DPP No. : 01 to 04 DPP Syllabus : Thermodynamics, Circular motion, Sound a!e, Pro"ectile motion, S#$, Neton%s la, -riction, Strin5 a!e, 'P(, ;.. , *inematics

DPP No. : 04 &NS'() *(+ - DPP N. 04  1.  3.

(A) (D)

.

(A)

1.

 A gas undegoes an adiabati% po%ess and an isot&emal po%ess !&e t$o po%esses ae plotted on a P;' diagam !&e esulting %u/es intese%t at a point P !angents ae da$n to t&e t$o %u/es at P !&ese ma+e angles of ".8@ U "*"@ $it& t&e positi/e ';a#is If tan 8N@  8., t&e gas is li+ely to be: ,d xSl ,d HksLe i!4e vkSj ,d lerkih; i!4e ls x.tjrh gSA nksuksa i!4e ds 14 P;' vkjsEk ij Ekhas x;s gSaA ifj=kkeh 14 fUn. P ij i!fr2sn djrs gSaA nksuksa 14ksa ds i'kZ;k P ij Ekhas tkrs gSaA ;s /kuk7ed ' v
(A-) monoatomi% (C) tiatomi% (A-) ,d ijek=k.d (C) f-kijek=k.d

dk fe=k

/.

(A)

4.

(A), (D) .

E1 %m .

(A)

2.

(C)

(B) diatomi% (D) a mi#tue of monoatomi% U diatomi% gases (B) fijek=k.d (D) ,d ijek=k.d 1 fijek=k.d xSlksa

Sol.

7&8 !&e slope of isot&emal %u/e at point of intese%tion is dP P  tan ".82 (") =− d' ' !&e slope of adiabati% %u/e at point of intese%tion is dP γ P   tan "*"@ (*) =− d' ' fom (") and (*) γ  tan 8N2  "==  8. ∴ gas is monoatomi%

.

 A pati%le is po0e%ted fom a point P (*, 1, 1)m $it& a /elo%ity "1 ms ma+ing an angle ?8@ $it& t&e &oi9ontal !&e plane of po0e%tile motion passes t&oug& a &oi9ontal line P $&i%& ma+es an angle of  .E@ $it& positi/e #;a#is, #y plane is &oi9ontal !&e %oodinates of t&e point $&ee t&e pati%le $ill sti+e t&e line P is: (!a+e g  "1 ms *) ,d d=k fUn. P (*, 1, 1)m ls , =, 1)m (C) ("1, >, 1)m (D) (=, "1, 1)m Pa5e No 6 1

Sol.

ange  "1 m Lo point $&ee pati%le sti+es line P

∴

# %oodinate  "1 %os .E2 6 *  "1m y %oodinate  "1 sin .E2  =m 9 %oodinate  1m

gyG ijkl  "1 m P jsEkk ij d=k dh B5dj 1kys fUn. ds fy, ∴

/.

# funsZ'kkad  "1 %os .E2 6 *  "1m y funsZ'kkad  "1 sin .E2  =m 9 funsZ'kkad  1m

 A ay of lig&t is in%ident at an

∠ of .1@ on a plane mio  " Anot&e plane mio  * is in%lined at angle

θ to " &at is t&e /alue of angle θ so t&at lig&t efle%ted fom * is paallel to " ,d i!dk'k fdj=k lery niZ=k " ij .1@ ds dks=k ij vkifrr gksrh gSA ,d n+ljk lery niZ=k *, " ls θ dks=k ukrk gSA dks=k θ dk eku 5;k gks rkfd i!dk'k fdj=k * ls ijk1rZu ds i'krD " ds lekukUrj gksA

(A-) =1@ (C) =E8@

(B) E8@ (D) none of t&ese

bues ls dksbZ ugh

Pa5e No 6 0

4.

 A /aiable fo%e L  "1 t is applied to blo%+ B pla%ed on a smoot& sufa%e !&e %oeffi%ient of fi%tion bet$een A U B is 18 (t is time in se%onds Initial /elo%ities ae 9eo) ,d fdus ry ij jEks >ykJd B ij ,d ifj1rhZ y L  "1 t yxk;k tkrk gSA A  A 1 B ds h IkLkZ=k x.=kkad 18 gSA (t lsd=)* esa le; gS 1 i!7;sd dk i!kjf%3kd 1sx

'k+U; gS@ (A-)

blo%+ A stats sliding on B at t  8 se%onds >ykJd  A, >ykJd B ij t  8 lsd=)* ij fQlyuk i!kj%3k djrk gSA t&e &eat podu%ed due to fi%tion in fist 8 se%onds is ."*8G IkLkZ=k kjk i!Fke 8 lsd=)* esa 67iUu 0Lek ."*8G gSA t&e &eat podu%ed due to fi%tion in fist 8 se%onds is (=*8>) G IkLkZ=k kjk i!Fke 8 lsd=)* esa 67iUu 0Lek (=*8>) G gSA a%%eleation of A at "1 se%onds is 8 ms * "1 1sa lsd=)* esa  A dk 71j=k 8 ms* gSA

(B) (C) (D-)

Sol.

f ma#  µ F .g  18 F .1  "8 4 blo%+ A stats sliding $&en fi%tion fo%e be%omes ma# ie f ma#  "8 at t&at instant (LB D)

bot& $ill mo/e $it& same a%%eleation So "8  .a ⇒ a  8ms * L 3 "8  Ea "1t 3 "8  E F 8 "1t  81 ⇒ t  8 se% o+ done by fi%tion in 8 se%onds  

∫ L ) ds

∫ "1t

) ds

(a 

L m

= "1t = t ) "1

8



∫ "1 t  'dt

(ds  /dt)

1 8



∫ 

"1 t 

1

t* dt *

(' 

∫

adt

∫ 

= tdt =

t* ) *

8



∫ 8t

.

dt

1 8

t?  =*8 × 8 8  8   =*8 − 1Q  ?  ?  1 ? .

A point sou%e S is %enteed in font of a E1 %m $ide plane mio A man stats $al+ing fom t&e sou%e along a line paallel to t&e mio in a single die%tion a#imum distan%e t&at %an be $al+ed by man $it&out losing sig&t of t&e image of t&e sou%e is VVVVV Pa5e No 6 1

,d fUn. l!ksr S ,d E1 %m kS)*s lery niZ=k ds lkeus dsfUn!r gS9 ,d ";f5r ds ,d fn'kk esa9 niZ=k ds lekUrj jsEkk ij l!ksr ls yuk #kj%3k djrk gSA ";f5r  kjk yh xbZ 1g vf/kdreD n+jh ftlls l!ksr dk #frf% ";f5r dh vk:Ekks ls vksVy u gks  VVVVV gksxhA <&ns. 20 cm =

Sol.

 E1 + E1 = E1%m      !&en &e %an see image   * *    E1 + E1 = E1%m      t&en &e %an not loose sig&t of image If man mo/es fom sou%e to point B    * *   Lom figue if man mo/es fom sou%e to point A 

C$P)(#(NSIN  A sinusoidal $a/e is popagating in negati/e #3die%tion in a sting stet%&ed along #;a#is A pati%le of  sting at #  *m is found at its mean position and it is mo/ing in positi/e y die%tion at t  " se% If t&e amplitude of t&e $a/e, t&e $a/elengt& and t&e angula fe7uen%y of t&e $a/e ae 1"mete, π? mete  and ?π adse% espe%ti/ely #3v
Sol.

gy%

!&e e7uation of t&e $a/e is

rjax dk lehdj=k gS &

(A-) y  1" sin (? π(t 3")6 >(# 3 *)) (B) y  1" sin ( (t3")3 (# 3 *)) (C) y  1" sin (? π(t 3")3>(# 3 *)) (D) none of t&ese buesa ls dksbZ ugh !&e e7uation of $a/e mo/ing in negati/e #;die%tion, assuming oigin of position at #  * and oigin of  time (ie initial time) at t  " se% y  1" sin (?πt 6 >#) S&ifting t&e oigin of position to left by *m, t&at is, to #  1 Also s&ifting t&e oigin of time ba%+$ads by " se%, t&at is to t  1 se% y  1" sin (? πt 6 >(# 3 *)Q fFkfr dk e+y fUn.  #  * ij rFkk le; dk e+y fUn. (vFkkZrD #kjf%3kd le;) t  " se% ij ekurs g.,9 =kk7ed #3fn'kk esa xfr djrh g.bZ rjax dk lehdj=k & y  1" sin (?πt 6 >#) fFkfr ds e+y fUn. dks ka;h vksj *m, f1Fkkr djus ij9 vFkkZrD #  1 ds fy,A le; ds e+y fUn. dks 3kh " se%, ih2s f1Fkkr djus ij9 vFkkZrD t  1 se% ds fy, 9 y  1" sin (? πt 6 >(# 3 *)Q

Pa5e No 6 

2.

Sol.

3.

Sol.

!&e speed of pati%le at #  * m and t  "se% is #  * m rFkk t  "se% ij d=k dh ky gSa & (A) 1*π ms (B) 1=π ms (C-) 1?π ms (D) 1  As gi/en t&e pati%le at #  * is at mean position at t  " se% ∴ its /elo%ity /  ω A  ?π F 1"  1? π ms fn;k x;k d=k t  * se% ij #  * ij ek/; fFkfr ij gSA ∴ bldk 1sx /  ω A  ?π F 1"  1? π ms !&e instantaneous po$e tansfe t&oug& #* m and t ""*8 se%, is t  ""*8 se% ij #  * m ij rk7
(D-) 9eo

'k+U;

! se%onds afte t  " se%ond, t&e pati%le is at est at e#teme ?

position Hen%e instantaneous po$e at #  * at t  ""*8 se% is 9eo *π *π " = = se% nksyu dk vk1rZdky !  ω ?π *

blfy;s

t  ""*8 se%,

vFkkZrD

f1jke ij gksxkA blfy;s

t  " se%

ds

#  * ij t  ""*8 se%

! se%onds kn9 ?

d=k je (vfUre) fFkfr ij

ij rk7
Pa5e No 6 /