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8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
1/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn 3> E_]-[ajutiags/Xeysiks
[ajutiags ta Eadn _arl ]nst/Xeysiks
6.(K) Fktiag - rnfktiag pfir, nqufj fgm appasitn.
3.(FCK) Fkt ag twa mibbnrngt ac`nkts efs nqufj dfogitumns efvn appasitn mirnktiags.
;.(K) Barkn cy knijigo ag kefig
B 4 ] + _3
fgm ] 4 _6
B 4 _6+ _3
>.(F) Cate skfjns wijj rnfm 68 lo.
2.(F)
d J x
] fJ
dx
B ] fJ
B J xB
J
?.(C)
Kjnfrjy, 3 6f f 3 6t t
5.(KM)
9.(M) Ib ten skaatnr fkknjnrftns, teng 8b
]atfj barkn ag dfg cy snft,3 3 B G b >88B G 6 ; fgm t t
B 4 >88 G bar 3t
68.(M) [ystnd kfggat rndfig ig nquijicriud.
Mygfdiks ab f Xfrtikjn E_] - 6
_3
_6
]
_6
B
]
_3
68 lo
]
68o]
]
]
]
J
J x x
rapn
]atfj dfss,dB
J x]
f
x
B
f
]Oaigo up
v
lv
do
fkknjnrftiagf6
Kadigo mawg
do
lv
fkknjnrftiagf3
v
Djibt
]
Do
] 4 Do ib fkknjnrftiag 4 8
dfg
G
b>88G
G 4 >88 G
>88fb
o
Mirnktiag ab
datiag
F CB
sdaate
b
B
CG
do
G
FB do
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
2/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn 32 E_]-[ajutiags/Xeysiks
6.(F) Briktiag ag C is upwfrm, ta cfjfgkn wnioet.
;.(M) ]en fgojn ab weike ten cjakl `ust cnoigs ta sjimn is
6tfg
mans gat mnpngm ag ten dfss ab ten cjakl.
=.(FC) Briktiag is tawfrms nfst ib ten kfr fkknjnrftns. Ig rajjigo witeaut fkknjnrftiag, tenrn is ga earizagtfj barkn ag ten kfr.
ga briktiag.
>.(M) ]idn pnriam frn nqufj 6 3
3
z 6 3
2.(K)
f o sig kas f o sig kas
36
3s ft 6t / f
oaigo up kaddigo mawg6
3t t
= o sig kas o sig kas 8 2. tfg
?.(K) Ft tap
3
d
do Gr
3
d
dor
9.(F) is mnkrnfsigo fs ten kfr kjidcs ten crimon.3
d
do kas G r
3
d
G do kasr
G is igkrnfsigo
68.(C)
3
6d
br
3 b df
33
3 3 36 3
b b d fr
3
d
Br
Mygfdiks ab f Xfrtikjn E_] - 3
d
do sig d o kas
oaigo up
do sig
d o kas
kadigo mawg
wftnr
do
G
3
r
Gardfj barkn brad cuklnt
Gv
do
3d
r
b3
b6
kfr
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
3/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn 3? E_]-[ajutiags/Xeysiks
6.(CM) Gnt barkn,3
gntdv
Br
(rfmifjjy)
gnt atenrsB B B
Fs ten pfrtikjn davns ig ten kirkjn,
gntB kefgons mirnktiag
Fs B is f kagstfgt, atenrsB dust kefgon mirnktiag fs wnjj fs dfogitumn.
3.(K) ]4d6o
]/3 4d6o/3
d3,d;fkknjnrftn
3 ;
3 ;
3
3
d d]o
d d
3 ; 6
3 ;
3
3
d d o d o
d d
6 3 ;
= 6 6
d d d
;.(C) do ] df
] do df
] do 6 f o g
=.(C)3
D d
Ddo]
D d
33
Ddo~ do
D
>.(K)
6 3
6 3
3
d d] o
d d]atfj barkn ag pujjny, 6 3
6 3
=
d d oB
d d
6 3 d d d6 3=
d d oB
ddfxB do
2.(C) B kas G
B sig G do b G
doB
sig kas
36
dig doB
Mygfdiks ab f Xfrtikjn E_] - ;
]
d6
d3
d;
]/3
]
do
dfgf
]
d
D
Kefigd3
d6
6 3 d d d
]n
d
f 3 3 ] d o d f
]
d6o
f 6 6 d o ] d f
G
B
b
do
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
4/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn 35 E_]-[ajutiags/Xeysiks
?.(F) 8] kas ]
8] sig do
] do / tfg
5.(FC) >8 i kd / s
b i
frnf ugmnr tenkurvn
dfss
8 8?8 >8
8 8?
.. d / s
.
8 > . d / s
6
8 86
b iff
tidn .
3688 d / s
9.(F) Ft rnst6 3
68 2 ] o ] o
@ust fbtnr crnfligo, 6 368 8 ] o ]
=f4 2o
f4 ;o/3 4 6>d/s3
68.(C)
63
do do
fd
33
;
do dof
d;
3
3
do dof
d
4 3/; 4 o/3
6 ; 3 f f f
6.(K) 6 3
lv lvf o f o
d D
6 3|f | | f |
6
ef
6 3e e
3.(K)
]4do
Mygfdiks ab f Xfrtikjn E_] - =
do
]
]8
F C
X
8.88= 8.8885 8.86
68
B(G)
t
]3
=lo
]6
2lo
68o
=lo
=o
f
d B64 3dod
3d
d
d
do
D
do
lv
d
do
lv
3do
3do
] ]
do
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
5/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn 39 E_]-[ajutiags/Xeysiks
>.(F) b do sig
6838
;8
do G
sig
3d lo
2.(F)
6f o sig 3 f o sig kas
6 3 3t t /
3
6
f t 6 3=f f
;
= tfg
?.(K) 3 G do
6G b
]arqun fcaut K 4 8
6 33 3 6 > G b G .
3 3 6 > b b . do
;
5
dob
3 ; 5 b G /
5.(K)6
;
6 3
dig
doB
;dig
do /b
3 ;/63 > . loB
9.(K)
b 4 68G
do
do sig
sdaate
do sig
b do kas
rauoe
F
=
8 ; C
do
K
G6
G3
b
B
3>lo
G;8G
b
do
Gnt barkn ag cjakl cy igkjign
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
6/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;8 E_]-[ajutiags/Xeysiks
6.(F)
3.(K) Snbnr ta E_]-= [ajutiag Ga 6
;.(C) ; ;] do
6
3 3
3
d d o]
d d
=
;
do
3 65
3;
do
] ] rioet simn oans mawg.
=.(C) Snbnr ta E_] - ; [ajutiag Ga.68
2.(FCKM) [uppasn ten kfr fgm pjfgt efvn ten sfdn fkknjnrftiag, f ig appasitn mirnktiags
]+b4d6f
3 b ] d f
8] ib 6 3d d
Ib 6 3 8 d d ]
?.(F)
68G o
63 68 ] G
638 68 6;8 ] G
38G o
388 6;8 38 38 o f
33 >f . d / s
5.(C) G df
do B
sb G
sdo df
s
of
Mygfdiks ab f Xfrtikjn E_] - >
t3
G
b6do
SF
b6
B
do
G
F
d
3d
]6
]3
];
;d
G f
]
bd6o
d6
K
d3S
]
d3o
X
b
Gf
B4388G
38lo68lo
4 8.6 G
]
68lo
do
63d/s3
G
G
388
38o
f
G
6;8G
fD d
b
G
do
f
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
7/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;6 E_]-[ajutiags/Xeysiks
9.(F) 8 G b do
| G B| do(Gnt barkn cy ten pjfgn)
68.(C) 688od ft rnst 688 ] od o
4 6 G
38838868
6888 6888 ] f
3>f d / s
Fkknjnrftiag ab pujjny X64 >/3 d/s3
6 6>
33
] d o d
6 3 68 > 3d / / 6 628d o
6.(C) Barkn 4 Kefgon ig dadngtud 3tidn
dvt
6;3 68 68 >68
8 86
G
.
3.(F) _n kfg writn
3 8 F C Kf f f
3
F KC
f ff
3
f b
mawg3
f b
ar
6
up3 b f
;.(M) 6 5] G
6
3
;8 ]
tfg]
3 5 ;] G
briktiag 4 3 5 ;] G
=8 5 ; b
; > 8 ;> / .
Mygfdiks ab f Xfrtikjn E_] - 2
b
G
do
X6
X3
3]
d6
]688od
388od
(388o)
]
f
d6o
3]
>/3d/s3
]6
_ 4 5G
_ 4 =8G]3
;8
G
]3
=8b
f
F
C
b
K
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
8/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;3 E_]-[ajutiags/Xeysiks
=.(M) ;? S Do sig b Df
;? ;? ;? do sig b kas S sig df
Xut;?
dob S S df
kas
> >
= ;
do b
S
b S
6> 6>
; > ; >
do doS b
;
>; =
> >
S Do bD
b ddo S
; 3>
6> ; > ?> do Do Do
;
do
> 63 28 do do38
D
ddo
3 36> 6> 3> 38 8 d Dd d Dd
IbD4d
6> 6> 3> 38 8 3
;
>.(M) ? ;
8 =? ;
f . o
2.(C) 6 ; 33 x x x
Mibbnrngtiftn w.r.t. tidn 6 ; 33 8 v v v
6 3;
3
v vv
6 3;
3
f ff
Ft 6t a3
6 68 3 v f d / s
3 3= 8 v d / s f ; 8 3 v d / s3
; 6 f d / s
; > 3 6 > ; v d / s
?.(C) Dfss 4 sjapn ab B f orfpe 46= =
3 >= 8
. lo
5.(K) > ;? >; sig D sig
; =>
> >
DD4 ;.?>lo
9.(F) X G
do G
38 do
X G
68 8 > > G . G
6 > 6 o f
3>f d / s
D
d
;?
Gb
D
S do
f f
C
do
b
;?;?
? ;
F K
C
x6 x3
x;
8 >.
X
G
do
G
68GG
6o
f
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
9/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;; E_]-[ajutiags/Xeysiks
68.(C) sb B G 8 >s .
8 > 28 B . o 8 =s .
;88 G
28 ;88 8 = 288 f .3
6f d / s
6.(K) 38 38o ] f 3?f d / s
28] G
3.(F)
3> 8 > 3 5 . o
C kfggat davn Ga. briktiag cntwnng F fgm C
;.(K) Fkknjnrftiag 4
> ; 6
> ; 6
o
4o/9d/s3
6 9 o ] o /
5
9
o] G
=.(C) Briktiag 4 5 G tawfrms jnbt.
Briktiag 4 3G tawfrms rioet
>.(C) Fkknjnrftiag 4 sjapn 4 33 d / s
3 lf o 8 3l .
2.(C) 63r d3f t d / s
Ft 3>t
33
83
t
4 3m d / s
r tf f 3
3v
r
; |d/ s
Mygfdiks ab f Xfrtikjn E_] - ?
B
G
28lo
B
28o
;88
G
l
G
28o
f
]
daglny
38o
f
3>
3
5
F8.3
8.>
]
; lo
6lo
]
> lo
]
6o
o/9
B6 B3
B6 4 68 GB3 4 3 GB3
tf
rf
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
10/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;= E_]-[ajutiags/Xeysiks
?.(M) dfx] bar ga sjippigo 4 = >s o
4 ;2G
3;2=
= >
f d / s
;2 = Do d
2D lo
5.(F)
9.(F)
99
;
oC o
=
doC do
=62
;
Cd lo
oDfss ab sfgm 4 ?lo
68.(F)
X B do df
B Do Df
XDB
D d
6.(C)
368 33 ;
f d / s
; 2 B f G
Mygfdiks ab f Xfrtikjn E_] - 5
=
>lo
f
8 =. ]
D
;2
Do
=
]
6lo
;?
8 5.
G
;?
]
do
C
9o
o/;
C
do
o/=
C 4 63o
X
d
D
X
do
B
f f
do
B
X 4 68G
3lo;lo
CF
f
B ;lo
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
11/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;> E_]-[ajutiags/Xeysiks
3.(C)
33 ;8
3 3
d sig do] o
d
3 3; ;
3 3
] ]]
;
3
do]
;.(F) ;8 ;8 8 digB do sig kas
;8 ;8 66> dfxB do sig kas G
=.(M) ;? ;? G kas do b sig
;? ;? G sig b kas 43
dv
r
Xut b4DG4 ;G /
= ;
> > ;
GG do
3; = ;
= ; ; = ;
dv do do
r
39 = ;
= ;
v or 5=v d / s
>.(C) 6B / d
2.(K) Sfmifj barkn 43
dv
r4
3= 3
626
G
]fgongtifj barkn 4 ; = 63 G ]atfj barkn 4 3 363 62 4 38 G
68.(K)
3 68 3o f 3
>f d / s
3> 8 > 33
df / d / s tawfrms rioet
>3
3] D
= 5>
]D lo
]
D
d
;8
]
;8
]
]
G
;8
]
do
B
G
;8
do
B
b
B
d 4 68lo
;8
; =/
G
;?
6
;
;?
do
v3/r
D
3]
]
d3d6
d6efs ga fkknjnrftiag
] 4 6o
4 68 G
6o
]
3o
f
>/3D
3]
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
12/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;2 E_]-[ajutiags/Xeysiks
6.(K) Barkn 43 3 6 38
6 >8
dR
t /4 3888 G
3.(M) dfxf ab kfr 4 o
36
3s ft
6t
f
6t
;.(K)
Cnbarn kuttigo
;] do
] do
Fbtnr kuttigo
;] do
8]
>.(C)
3 ] sig B 3
3
33 6
B B]
sig x
f
8 df ] kas
83 3
3
Bf xf .
fd f x
83 3
3
Bxf
d f x
2.(F) 6 3t t ?.(M) Snbnr E_] 6 [ajutiag 9 5.(M) Snbnr E_] 6 [ajutiag - 68
9.(F) Snbnr ta E_] 3 [ajutiag - 6
68.(FKM) 3 G D d o (F)
66 G sig D | f | (K)
3 6 df Df
Fktiag rnfktiag pfir 6 3G G )(M)
Mygfdiks ab f Xfrtikjn E_] - 9
;do
3do
f
f 4 o/3]
3d
]
d
do
ff o
B
]]
ff
f8 d x df8
6
xkas
f
d
D
do
G3
G6
G6
do
f6
8/13/2019 Jee 2014 Booklet2 Hwt Solutions Dynamics of a Particle
13/13
Rimyfdfgmir Kjfssns
RDK/Mygfdiks ab f Xfrtikjn ;? E_]-[ajutiags/Xeysiks
6.(K) 38
8 8>> fv
v d / sf
t .
3=88 d / s
;.(F) Ib 8CGnt barkn 4 do C do
=.(K) 8 ; B do . G
>.(K) 6
3
sjapn 6
sjapn 3
f
f
38 >6
63 ;
/
/ 6 6 6
3 3 3
> ?B d f
/B d f
2.(K)
?.(C) 3] f
; ; o ] f
63] G
5.(K) 3 6 X X
Ad d
9.(F) lf o
43
6 3 68 63 . d / s
v u ft
63 8 6 u d / s R t s
68.(K)
6 3d d
6 3
6 3
3
d d] o
d d
Mygfdiks ab f Xfrtikjn E_] - 68
C
do
>8
>8
68 38 ;8
B(G)
t(s)
3>8
3>8
v
t68
38 38
f63v d / s
d3d6
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