Kinematics - 1
SECTION – I
St r ai ghtObj ect i veType Thi ssect i on cont ai ns8mul t i pl echoi cequest i ons.Each quest i on has4choi ces( A) ,( B) ,( C)and( D) ,outofwhi chONLY ONE i scorr ect .
41.
For part particle icle moving moving alon along g straig straight ht line, line, which which grap graph h will will not represe represent nt acce acceler lerated ated motion motion.. (a)
(b)
(c )
(d)
t 3t + 2t + 1÷ m s = − 3 2 3
42.
2
along straight line motion at time ‘t’ sec. n
(a) t ∈ 1,1 43. 43.
2
1
2
of
particle
moving
which interval of motion particle is in retardation.
(b) t ∈ 1 , 2 sec
(c) t ∈ !2, ∞)"ec
(b) 2
g
(a) cos
−1
−2
2 1-
(c) 3
g
$ pa particle ha has in initial ve velocit
( 3i* + 2k* ) ms 4/.
s ec
position
(d) #one of these
$ part partic icle le is movi moving ng %p with with ballo balloon on with with cons constan tantt accel acceler erat atio ion n (g&') (g&') whic which h starts starts from from rest rest from gro%nd and at hight particle is dropped from balloon, $fter this event find time for which particle will be in air (a)
44.
1
is
(d) 4
g
g
( 2i* + 3 *j ) ms − when it was at origin and has constant acceleration 1
. Find angle made b displacement after 2sec with + plane (b)
π 2 − cos−
1
3
1-
(c) sin −1
1. 1-
(d) sin − 1
3
0wo 0wo parti particle cless were were proe proecte cted d sim%lta sim%ltaneo neo%sl %sl in hori horion ontal tal plane plane with with sam samee veloc velocit it u perpendic%lar to each other. Find time after which their vel ocities maes angle 54 with each other (a)
u g
(b)
u 2 g
(c)
u 3 g
(d)
u 2 g
1
Kinematics - 1
45.
4.
(
$ particle is proected with velocit 5i* + / j
1
from a vertical tower of hight 1m. f the
a6is is vertical %p find time of flight. (a) 1sec (b) 2sec (c) 3sec (d) 4sec 7article proected from tower of height 1m as shown in diagram. Find time after which particle will hit gro%nd
(a) 1 "ec 4'.
+ 'k* ) ms −
(b) 2"ec
(c)3sec
(d) 4sec
$dacent graph is drawn for particle along straight line motion. a 8 $cceleration 9 v8volocit. Find displacement of particle from rest till it ac:%ires velocit 2 ms −1
(a) /m
(b) 5m
(c)m
(d) 'm
SECTION – II
Mul t i pl eCorr ectAnswerType Thi ssect i on cont ai ns4mul t i pl ecor r ectanswer ( s)t ypequest i ons.Eachquest i onhas4choi ces( A) ,( B) ,( C)and( D) ,out ofwhi chONE OR MORE i s/ar ecor r ect .
4-.
$ particle is proected from horiontal gro%nd with speed /ms −1 at /34 with horiontal. Find time after which velocit of particle will be 4/4 with horiontal (a)
2
1 1
sec
(b)
3 1
sec
(c)
/ 1
sec
(d)
1
sec
Kinematics - 1
/.
$ particle proected from horiontal gro%nd at angle ‘ θ ’ with speed ‘%’. n same plane of motion a horiontal acceleration ‘a’ e6ists so that proected particle ret%rns bac to point of proection. Find time of flight (a)
/1.
2u sin θ
3u sin θ
(b)
g
(c)
g
2u cos θ a
(d)
3u cos θ
(
a
)
$ particle is proected from horiontal +; 7lane with velocit u xi* + u y *j + u z k* from origin (<a6is is %pward). Find time when velocit of particle will be at 3 4 with horiontal. (a)
u y
−
ux 2
+u
2 z
3u y
(b)
g /2.
−4
ux 2
+u
2 z
(c)
3u y
+4
3 g
ux 2
+u
2 z
3 g
(d)
u y
+
u x 2 + u z 2 3 g
$ carrom strier is given velocit on carrom based has alwas. Friction ca%ses constant retardation. "trier hits bo%ndr of carrom and comes to rest at point from where it started. 0ae initial velocit direction is positive,choose correct graph descriting motion. (v8velocil, s8displacement, t8time)
(a)
(b)
(c)
(d)
SECTION – III
Li nkedCompr ehensi onType Thi ssect i on cont ai ns2 par agr aphs.Based upon each par agr aph,3 mul t i pl e choi ce quest i onshave t o be answer ed. Each quest i on has4choi ces( A) ,( B) ,( C)and( D)outofwhi chONLY ONE i scorr ect.
Par agr aph f orQuest i onsNos.53to55 0wo particles at 1m high cliff were proected with same speed / 3ms −1 in same vertical plane in a
/3. /4.
time gap. =ne particle is proected horiontall and other at angle 54 with horiontal. "o that the collides in air. Find time interval between proecting particles. (a) 1"ec (b) 2"ec (c) 3"ec (d) 4 "ec 0ae origin at foot of cliff %pword is the 8a6is and horiontal is + > a6is. Find co8ordinates of point of collision (a) (/,/)m
//.
(
)
(b) / 2,/ 2 m
(c)
(/
3, /m
)
(
(d) /,/ 2m
)
Find e:%ation of traector of particle proected horiontall 3
Kinematics - 1
(a) y = −
x 2
(b) y = 1 +
1/
x 2 1/
x (c) y = −1 + ÷ 1/
x (d) y = 1 − ÷ 1/
2
2
Par agraph f orQuest i onsNos.56t o58 $dacent diagram shows at trolle on horiontal a6is + which starts from rest with constant acceleration 1./ms −2i* for given time a particle is proected from origin which hits point 7 of trolle. ?hile coming down and motion is along 4/4 with horiontal. $ll motion is in + plane. <a6is is vertical %p. /5.
/.
Find the time after which stone hits point 7 (a) 1"ec (b) 2"ec (c) 3"ec Find velocit of proection
(
(
(
)
)
−1
(b) 5.2/i* + 3./* ms
)
−1
−1 (d) 3./ i* + *j ms
(a) 5.2/i* + 5.2/ *j ms (c) 3./i* + 5.2/* ms /'.
(d) 4 "ec
(
−1
)
Find velocit of particle near point 7 (a) 3./(i* + *)ms −1
(b) 3./(i* − *)ms −1
(c) 5.2/(i* + *)ms −1
(d) 5.2/(i* − *)ms −1 SECTION – IV
Mat r i xMat ch Type This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, , ! and ", while the statements in Column II are labelled #, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement$s% in Column II . The a##ro#riate bubbles corres#onding to the answers to these questions have to be darkened as illustrated in the &ollowing exam#le' (& the correct matches are A ) #, s and t* ) q and r* ! ) # and q* and " ) s and t* then the correct darkening o& bubbles will look like the &ollowing'
.
4
p
:
r
s
t
$
p
:
r
s
t
@
p
:
r
s
t
A
p
:
r
s
t
B
p
:
r
s
t
Kinematics - 1
/-.
$ ball is allowed free to fall from height ‘’ which rebo%nds bac to ma6im%m height ‘h’(). 0ae %pward as the positive direction and intial position on origin Column I
Column II
$
Bisplacement time graph is
(7)
@
Bistance from starting point verses time graph is
(C)
A
Bistance time graph is
(D)
B
Eelocit verses displacement
(")
(0)
5
Kinematics - 1
5.
0raector of particle in proectile motion is y
=( x−x
2
& ' ) , 6 and are in meter. 7roectile range is
on horiontal plane Column I
Column II
$
$ngle of proection " with horiontal is
(7)
@
$ngle of velocit with horiontal at time 1sec
(C)
A
$ngle of velocit with horiontal at hight 2m from gro%nd is
(D)
B
$ngle of displacement with horiontal when velocit is perpendic%lar to displacement
(")
(0)
6
4
1 ÷ 3
tan −1 4/4
1 ÷ 2
tan −1
#=0 7=""@G
