Xi - Dpp # Mechanics (22.3.2016)

8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

1/12

CLASS XI | 23. 2.2016

PHYSICS

1. A circular portion of diameter R is cut outfrom a uniform circular disc of mass Mand radius R as shown in figure. Themoment of inertia of the remaining(shaded) portion of the disc about anaxis passing through the centre O of thedisc and perpendicular to its plane is

(A)

215

32 MR

(B)

27

16 MR

(C)

213

32 MR

()

23

8 MR

2. A man! standing on a turn"table! isrotating at a certain angular fre#uenc$with his arms outstretched. %e suddenl$folds his arms. &f his moment of inertiawith folded arms is ' of that withoutstretched arms! his rotational *ineticenerg$ will(A) increase b$ ++.+(B) decrease b$ ++.+(C) increase b$ ,() decrease b$ ,

3. Moment of inertia of uniform hori-ontalsolid c$linder of mass M about an axis Mabout an axis passing through its edgeand perpendicular to the axis of thec$linder if its length is times its radiusR is /

(A)

239

4

MR

(B)

239

8

MR

(C)

249

8

MR

()

249

4

MR

4. A uniform rod of length 0 meter is bent

at its mid"point to ma*e 12

o

angle. Thedistance of the centre of mass from thecentre of the rod is(A) +.0 cm (B) ,., cm(C) 0'.' cm () -ero

5. A small ob3ect of uniform densit$ rolls upa cur4ed surface with an initial 4elocit$ 4.&t reaches up to a maximum length

h 5

23

4

v

g

! with respect to the initialposition. The ob3ect is (see figure)

(A) ring (B) solid sphere(C) hollow sphere () disc

6. The trac* shown in figure ends in acircular trac* of radius r with centre at O. A small solid sphere of mass m rollsfrom rest without slipping from a point Aat a height h 5 r from the le4el ground.6hat is the speed of the sphere when it

reaches a point B at height r abo4e thele4el ground7

(A)

10 gr

(B)

50

7 gr

(C)

22

7 gr

() -ero

7. A tube of length 8 is filled completel$with an incompressible li#uid of mass Mand closed at both the ends. The tube isthen rotated in a hori-ontal plane aboutone of its ends with a uniform angular

4elocit$ ω. The force exerted b$ the

li#uid at the other end is

1B/1, TVS Street, Rasipura ! 63"#0$. %aa&&a' ()t.*

+- ###331$6, ai' ipu'se#eeai'.4 1 | P a g e

DPP # PHYSICS

mailto:[email protected]:[email protected]:[email protected]

8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

2/12

CLASS XI | 23. 2.2016

PHYSICS

(A)

2

2

M Lω

(B) Mω,8 (C)

2

4

M Lω

()

2 2

2

M Lω

8. Choose the correct statements from thefollowing.(A) The magnitude of instantaneous

4elocit$ of a particle is e#ual to itsinstantaneous speed

(B) The magnitude of the a4erage4elocit$ in an inter4al is e#ual to itsa4erage in that inter4al.

(C) &t is possible to ha4e a situation inwhich the speed of the particle isne4er -ero but the a4erage speed in

an inter4al is -ero.() &t is possible to ha4e a situation inwhich the speed of particle is ne4er -ero but the a4erage speed is -ero.

9. The numerical ratio of a4erage 4elocit$to a4erage speed is(A) alwa$s less than one(B) alwa$s e#ual to one(C) alwa$s more than one() e#ual to or less than one

10. A car is mo4ing on a road and rain is

falling 4erticall$. 9elect the correctanswer.(A) The rain will stri*e the bac* screen

onl$(B) The rain will stri*e the front screen

onl$(C) The rain will stri*e both the screens() The rain will not stri*e an$ of the

screens

11. 6hich one of the following representsthe time"displacement graph of twoob3ects A and B mo4ing with -ero

relati4e speed7

12. :rom a building two balls A and B arethrown such that A is thrown upwardsand B downwards (both 4erticall$). &f 4 A

a 4B are their respecti4e 4elocities onreaching the ground! then(A) 4 A ; 4B (B) 4 A 5 4B(C) 4 A < 4B() their 4elocities depend on their

masses.

13. A particle has initial 4elocit$

(2 3 )i j+

and

acceleration

(0.3 0.2 )i j+. The magnitude

of 4elocit$ after 02 seconds will be

(A) 1

2 units (B)

2 units

(C) units () 1 units

14. A car! starting from rest! accelerates atthe rate f through a distance 9! thencontinues at constant speed for time t

and then decelerates at the rate

2

f

tocome to rest. &f the total distancetra4ersed is 09! then

(A) 9 5

21

6 ft

(B) 9 5 ft

(C) 9 5

21

4 ft

() none of these

15. An ob3ect! mo4ing with a speed of., m=s! is decelerated at a rate gi4en

b$ /

2.5

dv

vdt = − where 4 is the

instantaneous speed. The time ta*en b$the ob3ect! to come to rest! would be(A) ,s (B) >s(C) ?s () 0s

16. &n 0.2s! a particle goes from

point A and B! mo4ing in a

semicircle of radius 0.2m

(see figure). The magnitude

of the a4erage 4elocit$(A) +.0> m=s

(B) ,.2m=s




8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

3/12

CLASS XI | 23. 2.2016

PHYSICS

(C) 0.2 m=s () -ero

17. A bod$ starts from rest at time t 5 2! theacceleration time graph is shown in the

figure. The maximum 4elocit$ attainedb$ the bod$ will be

(A) 002m=s (B) m=s(C) 2m=s () 2m=s

18. A ball is dropped 4erticall$ from a heightd abo4e the ground. &t hits the groundand bounces up 4erticall$ to a heightd=,. @eglecting subse#uent motion andair resistance! its 4elocit$ 4 4aries withthe height h abo4e the ground as

19. A person tra4els along a straight road for the first half time with a 4elocit$ 40 andthe second half time with a 4elocit$ 4,.

Then the mean 4elocit$

vis gi4en b$

(A)

1 2

2v vv +=

(B)

1 2

2 1 1v v v

= +

(C)

1 2v v v=()

2

1

vv

v=

20. A particle co4ers half of the circle of radius r. Then the displacement anddistance of the particle are respecti4el$

(A) ,πr! 2 (B) ,r! πr

(C)

2

r π

! ,r () πr! r

21. A smooth inclined plane is inclined at an

angle θ with hori-ontal. A bod$ starts

from rest and slides down the inclinedsurface.Then the time ta*en b$ it to reach thebottom is

(A)

2h

g

÷

(B)

2l

g

÷

(C)

1 2

sin

h

g θ

()

( )2sin

h

g θ

22. A food pac*et is released from ahelicopter rising steadil$ at the speed of ,m=sec. After , seconds the 4elocit$ of the pac*et is (g 5 02m=sec,)(A) ,,m=sec (B) ,2m=sec(C) 0?m=sec () none of these

23. The relati4e 4elocit$ AB or BA of twobodies A B ma$ be(0) greater than 4elocit$ of bod$ A(,) greater than 4elocit$ of bod$ B(+) less than the 4elocit$ of bod$ A(>) less than the 4elocit$ of bod$ B(A) (0) and (,) onl$(B) (+) and (>) onl$(C) (0)! (,) and (+) onl$() (0)! (,)! (+) and (>)

24. A balloon starts rising from the ground

with an acceleration of 0., ms",. After ?s! a stone is released from the balloon.The stone will (Ta*ing g 5 02ms",)(A) begin to mo4e down after being

released(B) reach the ground in >s(C) co4er a distance of >2m in reaching

the ground() will ha4e a displacement of 2m.

25. A particle experiences a constantacceleration for ,2 sec after starting

from rest. &f it tra4els a distance s0 in02sec and distance s, in the next 02sec!then




8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

4/12

CLASS XI | 23. 2.2016

PHYSICS

(A) s0 5 s, (B) s0 5

2

3

s

(C) s0 5

2

2

s

() s0 5

2

4

s

26. The 4elocit$ of a bod$ depends on timeaccording to e#uation 4 5 ,2 2.0t,. Thebod$ is undergoing(A) Dniform acceleration(B) Dniform retardation(C) @on uniform acceleration() Eero acceleration

27. To a man wal*ing at the rate of ,*m=h!rain appears to fall 4erticall$. 6hen hedoubles his speed it appears to fall at+2o to the 4ertical. The actual 4elocit$ tothe rain is /(A) , *m=h 4erticall$(B) >*m=h 4erticall$(C) >*m=h! +2o to the 4ertical() >*m=h! 2o to the 4ertical

28. An express train is mo4ing with a4elocit$ 40. &ts dri4er finds another trainis mo4ing on the same trac* in the

direction with 4elocit$ 4,. To escapecollision! dri4er applies a retardation aon the train. The minimum time escapingcollision will be /

(A) t 5

1 2v v

a

−

(B) t 5

2 2

1 2

2

v v−

(C) none () both

29. A bod$ falls freel$ from rest. &t co4ers asmuch distance in the last second of itsmotion as co4ered in the first second.

The bod$ has fallen for a time of (A) +s (B) s(C) 's () none

30. A frictionless wire AB is

fixed on a sphere of

radius R. A 4er$ small

spherical ball slips on

this wire. The time

ta*en b$ this ball to slip

from A to B is /

(A)

2 gR

gcosθ

(B)

2 cos

gR g

θ

(C)

2 R

g

()

gR

gcosθ

31. A particle mo4ing in a straight lineco4ers half the distance with speed of +m=s. The other half of the distanceco4ered in two e#ual time inter4als withspeed of >. m=s and '. m=srespecti4el$. The a4erage speed of theparticle during this motion is(A) >.2m=s (B) .2 m=s(C) . m=s () >.? m=s

32. A stone is dropped from a building of

height h and it reaches after t second onearth. :rom the same building if stonesare thrown (one upward and other downwards) with the same 4elocit$ uand the$ reach the earth surface in t0and t, second respecti4el$ then /

(A) t 5 t0 F t, (B)

1 2

2

t t t

+=

(C)

1 2t t t =() t 5

2 2

1 2t t

33. At t 5 2 and x 5 2! an initiall$ stationar$blue car begins to accelerate at theconstant rate of ,.2 m=s, in the positi4edirection of the x"axis. At t 5 ,s! a redcar tra4elling in an ad3acent lane and inthe same direction! passes x 5 2 with aspeed of ?.2 m=s and a constantacceleration of +.2 m=s,. The time whenred car passes the blue car is /(A) >., s (B) +. s(C) ,.1 s () none of these

34. A stone is thrown 4erticall$ upward. Onits wa$ up it passes point A with speedof 4! and point B +m higher than A! withspeed 4=,. The maximum heightreached b$ stone abo4e point B is /(A) 0m (B) ,m(C) +m () m

35. A bod$ is at rest at x 5 2. At t 5 2! itstarts mo4ing in the positi4e x"directionwith a constant acceleration. At thesame instant another bod$ passes

through x 5 2 mo4ing in the positi4ex"direction with a constant speed. Theposition of the first bod$ is gi4en b$ x0(t)after time t and that of the second bod$




8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

5/12

CLASS XI | 23. 2.2016

PHYSICS

x,(t) after the same time inter4al. 6hichof the following graphs correctl$describes (x0 Fx,) as a function of time t7

36. A bod$ is pro3ected 4erticall$ upwards. &f t0and t, be the times at which it is at height habo4e the pro3ection while ascending anddescending respecti4el$! then h is

(A)

1 2

1

2 gt t

(B) gt0t,(C) ,g t0t, () ,hg

37. To get a resultant displacement of 02cm! two displacement 4ectors oneof magnitude m and another of ?mshould be combined

(a) at an angle 60o (b) perpendicular to each(b) parallel (d) anti"parallel

38. 6hen mass is rotating in a planeabout a fixed point its angular momentum is directed along(a) the axis of rotation(b) line at an angle of >o to the axis of

rotation(c) the radius(d) the tangent to the orbit

39. The rectangular components of force d$ne are

(a) + and > d$ne(b) ,. and , d$ne(c) 0 and , d$ne(d) , and + d$ne

40. &f the magnitudes of 4ectorsA

!B

and

C are 0,! and 0+ units

respecti4el$ andA

B

5C

! the angle

between 4ectorsA

andB

is

(a) π=> (b) π=,

(c) π (d) 2

41. A mos#uito flies from the hole in amos#uito net top corner diametricall$opposite. &f the net is +m x ,m x , m!then the displacement of the mos#uitois

(a)

13m

(b)

17m

(c)

11m(d) none of these

42. &f

A

5

B

C

and the magnitudes of A

!B

and

C are ! > and + units

respecti4el$. The angle betweenA

and

Cis

(a) π=, (b) sin"0(+=>)(c) cos"0(+=) (d) cos"0(>=)

43. The resultant of two e#ual forces is

double of either of the force. The anglebetween them is(a) 2o (b) 2o

(c) 12o (d) 0,2o

44. An aeroplane is mo4ing on a circular path with a speed ,2 *mhr "0 what isthe change in 4elocit$ in half re4olution(a) 2 (b) 0, *mhr "0

(c) ,2 *mhr "0 (d) 22 *mhr "0

45. Maximum and minimum magnitudes of the resultant of two 4ectors of magnitudes G and H are in the ratio+/0. 6hich of the following relations istrue(a) GH 5 0 (b) ,H(c) G 5 H (d) none of these

46. 6hat is the pro3ection ofP

on

Q

.

(a)

Q

.

P

(b)

P̂

.

Q̂

(c)P

.

Q

(d)P

.

Q̂




8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

6/12

CLASS XI | 23. 2.2016

PHYSICS

#". Calculate the angle ! (i) 1 ("eg#ee) (ii) 1$(%inute ! a#c # a#c %in) an" (iii) 1&secn" ! a#c # a#c sec) in #a"ian. 'se360 2π #a". 1 60$ an" 1$ 60&.

(a) (i) 1.700*10+2 #a" (ii)2.90*10+4 #a"(iii) 4.55 * 10+6 #a"

(,) (i) 1.746*10+2 #a" (ii)2.91*10+4 #a"(iii) 4.85 * 10+6 #a"

(c) (i) 1.646*10+2 #a" (ii)1.91*10+4 #a"(iii) 2.85 * 10+6 #a"

(") (i) 1.057*10+2 #a" (ii)1.11*10+4 #a"(iii) 1.4 * 10+6 #a"

#$. -he su% ! the nu%,e#s 436.32 227.2 an"0.301 in a##iate signi!icant !igu#es is(a) 663.821(,) 664(c) 663.8 (") 663.82

#. /ung$s %"ulus ! steel is 1.9 * 10 11

%2. hen e*#esse" in C units ! "nes c%2 it ill ,e eual t (1 105

"ne 1 %2 104 c%2)(a) 1.9 * 1010 (,) 1.9 * 1011

(c) 1.9 * 1012 (") 1.9 * 1013

50. hen 97.52 is "ii"e" , 2.54 the c##ect#esult is

(a) 38.3937 (,) 38.394(c) 38.39 (") 38.4

51. hat is the alue ! (5.0 * 10+6) (5.0*10+8)ith "ue #ega#"s t signi!icant !igu#es(a) 2.50 * 10+13 (,) 25.0 * 10+14

(c) 25 * 10+14 (") 250 * 10+15

52. :i%ensins ! #esistance in an elect#icci#cuit in te#%s ! "i%ensins ! %ass ;! length

8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

7/12

CLASS XI | 23. 2.2016

PHYSICS

(C)

22v

g

(:)

222

v

g

5. Cnsi"e# a , n a t#lle h th#s a ,all ith see" 20 %s at an angle 37

ith #esect t t#lle in "i#ectin ! %tin ! t#lle hich %esh#i@ntall ith see" 10 %s then hatill ,e %a*i%u% "istance t#aelle" ,

,all a#allel t #a"(A) 20.2 % (B) 12 %(C) 31.2 % (:) 62.4 %

60. A a#ticle is #Fecte" u the incline" suchthat its c%nent ! elcit alng theincline is 10 %s. -i%e ! !light is 2 secan" %a*i%u% height a,e the incline is5 %. -hen elcit ! #Fectin ill ,e

(A) 10 %s (B) 102

%s

(C) 55

%s (:) nne

61. A a#ticle P is #Fecte" !#% a int nthe su#!ace ! s%th incline" lane (see

!igu#e). i%ultaneusl anthe# #actice Qis #elease" n thes%th incline" lane!#% the sa%e sitin.P an" Q clli"e n theincline" lane a!te# t 4 secn". -he see" !

#Fectin ! P is

A) 5 %s B) 10 %sC) 15 %s :) 20 %s

62. A a#ticle is #Fecte" !#% a int (0 1)n /+a*is (assu%e / "i#ectin e#ticallua#"s) ai%ing ta#"s a int (4 9). =t!ell n g#un" alng * a*is in 1 sec.A) (3 0) B) (4 0)

C) (2 0) :) (25

0)

63. A stne is #Fecte" !#% a h#i@ntal

lane. =t attains %a*i%u% height HG$ Ist#iEes a statina# s%th all I !alls nthe g#un" e#ticall ,el the %a*i%u%height. Assu%e the cllisin t ,e elastic

the height ! the int n the all he#e ,all ill st#iEe is

A)2

H

B)4

H

C)

3

4

H

:) ne ! these

6#. A a#ticle is #Fecte" !#% a te# as

shn in the !igu#e. -hen the "istance!#% the !t ! the te# he#e it illst#iEe the g#un" ill ,e (taEe g 10%s2)

A) 4003 % B) 50003 %C) 2000 % :) 3000%

65. :istance ,eteen a !#g an" an insect n ah#i@ntal lane is 10 %. ?#g can Fu%

ith a %a*i%u% see" ! 10%s. g 10

%s2. ;ini%u% nu%,e# ! Fu%s #eui#e" , the !#g t catch the insect isA) 5 B) 10C) 100 :) 50

66. A a#ticle sta#ts !#% the #igin at t an" %es in the * lane ith cnstantaccele#atin a in the "i#ectin. =tseuatin ! %tin is ,*2. -he *c%nent ! its elcit is

A) a#ia,le B)

2a

b

(C)

2

a

b

(:)

2

b

a




8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

8/12

CLASS XI | 23. 2.2016

PHYSICS

6". A a#ticle is #Fecte" at an angle J !#%g#un" ith the see" ' (g 10 %s2)A) =! u 10 %s an" J 30 then ti%e !

!light ill ,e 1 sec.

B) =! u 103

%s an" J 60 then ti%e! !light ill ,e 3 sec.

C) =! u 103

%s an" J 60 then a!te# 2 sec elcit ,ec%es e#en"icula# t initial elcit.

:) =! u 10 %s an" J 30 then elcitnee# ,ec%es e#en"icula# t initialelcit "u#ing its !light.

6$. A a#ticle is #Fecte" e#ticall ua#"sith a elcit u !#% a int K. hen it#etu#ns t the int ! #FectinA) =ts ae#age elcit is @e#B) =ts "islace%ent is @e#C) =ts ae#age see" is u2:) =ts ae#age see" is u.

6. A uni!#% sua#e late has as%all iece Q ! an i##egula# shae #e%e" an" glue" t thecent#e ! the late leaing a hle

,ehin" (!igu#e). -he %%ent ! ine#tia a,ut the @+a*is is then(A) Increased (B) decreased(C) the same(D) changed in unpredicted manner

"0. A !#ce

ˆˆ ˆ3 6 F i j k α = + + is acting at a

int

ˆˆ ˆ2 6 12r i j k = − −. -he alue !

!# hich angula# %%entu% a,ut

#igin is cnse#e" is(A)1 (B) +1(C) 2 (:) @e#

"1. A heel ! #a"ius L #lls n theg#un" ith a uni!#% elcit v. -heelcit ! t%st int #elatie t

,tt% %st int is(A) @e# (B) 2v(C) v (:) v2

72. A solid sphere is rolling on a frictionless

surface, shown in figure with a translationalvelocit v m!s" If it is to climb the inclinedsurface, then v should be

(A)

10

7 gh≥

(B)2 gh≥

(C) 2gh (:)

107

gh

"3. A uni!#% #" ! length l an" %ass %is !#ee t #tate in a e#tical lanea,ut A as shn in !igu#e. -he #"initiall in h#i@ntal sitin is#elease". -he initial angula# accele#atin ! the #" is

(A)

3

2

g

l (B)

3 g

l

(C)2

g

l (:)

2 g

l

"#. A a#ticle e#!#%s uni!#% ci#cula# %tin ith an angula# %%entu%

8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

9/12

CLASS XI | 23. 2.2016

PHYSICS

t#uehich canst theheel$s

#tatin inne %inuteul" ,e

(A)15

N mπ

−

(B)18

N mπ

−

(C)

2

15 N m

π −

(:)12

N mπ

−

"$. A uni!#% #" ! length l an" %ass %is !#ee t #tate in a e#tical lanea,ut A ?igu#e. -he #" initiall inh#i@ntal sitin is #elease". -heinitial angula# accele#atin ! the #" is(;= ! the #"a,ut A is

2

3

ml

)(A)%gl 2 (B) 3g2 l (C) 2 l 3 g (:) 3 g2 l 2

". -he #ati ! the #a"ii ! g#atin ! aci#cula# "isc a,ut a tangential a*is inthe lane ! the "isc an" ! a ci#cula# #ing ! the sa%e #a"ius a,ut atangential a*is in the lane ! the #ingis

(A)5 A 6

(B)1 2

(C)2 A 3

(:) 2 1

$0. -h#ee i"entical #"s each ! length

8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

10/12

8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

11/12

CLASS XI | 23. 2.2016

PHYSICS

(A) 2 u cs θ (B) u cs θ(C) 2 u cs θ (:) u cs θ

#. A int P %es in cunte#+clcEise"i#ectin n a ci#cula# ath as shn in!igu#e. -he %e%ent ! HP$ is such that issees ut a length s t3 5S he#e s isin %et#es an" t is in secn"s. -he #a"ius ! the ath is 20%. -he accele#atin ! HP$hent 2 s is nea#l

(A) 12 %s2 (B) 7.2 %s2

(C) 14 %s2 (:) 13 %s2

5. -he ulles an" st#ings shn in !igu#ea#e s%th an" ! negligi,le %ass. ?# thesste% t #e%ain in euili,#iu% the angleθ shul" ,e

(A) 0 (B) 30

(C) 45 (:) 60

6. - %asses ; an" ;2 a#e Fine"tgethe# , %eans ! light ine*tensi,lest#ing asse" e# a !#ictinless ulle asshn in !igu#e. hen the ,igge# %ass is#elease" the s%all ne ill ascen" ith anaccele#atin !

(A)

3

g

(B)3

2

g

(C) g (:)

2

g

". A ,lcE ! %ass m is in cntact ith theca#t C as shn in !igu#e.

-he ce!!icient ! static !#ictin ,eteenthe ,lcE an" the ca#t is µ. -heaccele#atin a ! the ca#t that ill #eentthe ,lcE !#% !alling satis!ies

(A) a T

mg

µ

(B) a T

g

m µ

(C) a

g

µ ≥

(:) a U

g

µ

$. An insect c#als u a he%ishe#icalsu#!ace e# sll !igu#e. the ce!!icient! !#ictin ,eteen the insect an" thesu#!ace is 13. =! the line Fining the cent#e! the he%ishe#icalsu#!ace t the insect

%aEes an angle α iththe e#tical the %a*.

ssi,le alue ! α isgien ,(A) ct α 3 (B) sec α 3(C) csec α 3 (:) ne

.




8/17/2019 Xi - Dpp # Mechanics (22.3.2016)

12/12

CLASS XI | 23. 2.2016

PHYSICS

100.


+- ###331$6 ai' ipu'se#eeai' 4 12 | P a g e

Documents

Xi - Dpp # Mechanics (22.3.2016)