Topper’s Package Physics - XI Permutation and ......2020/07/06 · Topper’s Package Physics -...

Topper’s Package Physics - XI Permutation and CombinationsKinematics

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1. VECTORS1. Which of the following is not essential for the

three vectors to produce zero resultant?(a) They should lie in the same plane(b) It should be possible to represent them

by the three sides of triangle taken in thesame order

(c) They should act along the sides of aparallelogram

(d) The resultant of any two vectors shouldbe equal and opposite to the third vector

2. Which of the following vectors is perpendicularto ˆ ˆcos sini P j Q ?(a) ˆ ˆsin cosi P j Q (b) ˆ ˆsin cosi Q j P (c) ˆ ˆcos sini P j Q (d) ˆ ˆcos sini Q j P

3. Given that .0RQP

Two out of the threevectors are equal in magnitude. Themagnitude of the third vector is 2 timesthat of the either of the other two. Which ofthe following can be the angles between thesevectors?(a) 45°, 45°, 90° (b) 45°, 90°, 135°(c) 90°, 135°, 135° (d) 30°, 60°, 90°

4. What is the value of ( ) ( )P Q P Q

?(a) 0 (b) 2 2P Q(c) 2 2 2P Q PQ (d) none of these

5. Given that kbj8.0i4.0 is unit vector.What is the value of b?(a) 0.2 (b) 2.0(c) 0.8 (d) 8.0

6. QP

is unit vector along X-axis. If kjiP

then what is Q

?(a) kj (b) kj(c) kji (d) kji

7. Given that

P. Q O. Also P R 0. Whatis the angle between Q

and R

?

(a) 0° (b) 90°(c) 135° (d) 180°

8. What is the projection of k4i3 on the Yaxis?(a) 3 (b) 4(c) 5 (d) None of these

9. The angle between vectors )ji( and )kj( is:(a) 90° (b) 180°(c) 0° (d) 60°

10. Three forces P, Q, R are acting at a point ina plane. The angles between P & Q and Q &R are 150° and 120° respectively, then forequilibrium, forces P, Q, R are in the ratio:-(a) 1 : 2 : 3 (b) 3:2:1(c) 3 : 2 : 1 (d) 1/23 : 2 :1

11. The resultant of two vectors P and Q is R. IfQ is doubled then the new resultant vectoris perpendicular to ‘P’. The R equals to:-

(a)

PQ2

QP 22

(b) Q

(c) QP

(d) QPQP

12. Two forces each numerically equal to 10 dynesare acting as shown in the following figure,then the resultant is:(a) 10 dynes

10 dynes60°

10 dy

nes

(b) 20 dynes(c) dynes310(d) 5 dynes

13. What is the vector component of

?jialongj4i3

(a) )ij(21

(b) )ij(23

(c) )ij(25

(d)7 ˆ ˆ( j i)2

KINEMATICS Unit 2


14

14. If CBA

and A + B = C, then the anglebetween BandA

is

(a) 0 (b) /4(c) /2 (d)

15. What is the value of ?BABA

(a) 0 (b) 2 2A B(c) 2 2 2A B AB (d) None of these

16. The resultant of .RisBA 1

On reversing the

vector ,B

the resultant becomes .R 2

What is

the value of ?RR 22

21

(a) 2 2A B (b) 2 2A B

(c) 2 22( )A B (d) 2 22( )A B

17. A vector of length l is turned through the angle about its tail. What is the change in theposition vector of its head ?

(a) cos2

l

(b) 2 sin2

l

(c) 2 cos2

l

(d) sin2

l

18. If the sum of two unit vectors is a unit vector,then the magnitude of their difference is:(a) 2 (b) 3(c) 1/ 2 (d) 5

19. Which of the sets given below may representthe magnitudes of three vectors adding to zero?(a) 2, 4, 8 (b) 4, 8, 16(c) 1, 2, 1 (d) 0.5, 1, 2

20. The area of the parallelogram whose sidesrepresented by the vectors j k 3 and i j k 2 is(a) 61 sq. unit (b) 59 sq. unit(c) 49 sq. unit (d) 52 sq. unit

2. DISTANCE & DISPLACEMENT21. A player completes a circular path of radius

R in 40 seconds. Its displacement at the endof 2 min and 20 sec will be(a) zero (b) 2R(c) 2R (d) 7R

22. A cyclist starts from centre O of a circular parkof radius one kilometer, reaches the edge P

of the park, then cycles along thecircumference and returns to the centrealong QO as shown in the figure. If the roundtrip takes ten minutes, the net displacementand average speed of the cyclist in metre andkilometre per hour is

O P

Q

(a) 0, 1 (b) 4 , 0

2

(c) 421.4,

2 (d) 0, 21.4

23. A wheel of radius 1 m rolls foward half arevolution on a horizontal ground. Themagnitude of the displacement of the pointof the wheel initially in contact with theground is(a) 2 (b) 2(c) 2 4 (d)

24. All the graphs of are intended to representthe same motion. Of them does notincorrectly. Pick it up Position

(a) (b)

(c) (d)

3. UNIFORM & NON-UNIFORM MOTION25. A particle is moving eastwards with a velocity

of 5 m/s. In 10 sec, the velocity changes to5 m/s northwards. The average accelerationin this time is(a) zero

(b) 21 /2

m s towards N–W


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(c) 21 /2

m s towards N E

(d) 21 /2

m s towards N–W

26. A person travelling on a straight line moveswith a uniform velocity 1v for some time andwith uniform velocity 2v for the next equaltime. The average velocity v is given by

(a) 1 22

v vv

(b) 1 2v v v

(c)1 2

2 1 1v v v (d)

1 2

1 1 1v v v

27. A particle, starting from rest, moves with auniform acceleration and covers x meters inthe first 5 second. The same particle will coverthe following distance in the next 5 seconds.(a) x metre (b) 2x metre(c) 3x metre (d) 4x metre

28. Three identical particles are at the verticesof an equilateral triangle of side a, and allmoving with uniform instantaneous speed uin such a manner that the first iscontinuously moving towards second, thesecond towards third and the third towards thefirst. After how much time the three will meettogether ?

(a)au (b)

2au

(c)23au (d) 3

au

29. A car travels first 1/3 of its total distance ofjourney with speed 1v and the rest 2/3 of itsjourney with speed 2v , then the average speedis

(a) 1 2

1 2

32

v vv v

(b) 1 2

1 2

22

v vv v

(c) 1 22

v v(c) 1 2

1 2

3v vv v

30. A motorist starting a car from rest acceleratesuniformly to a speed of v m/s in 9 seconds.He maintains this speed for another 50seconds and then applies the brakes anddecelerates uniformly to rest. His decelerationis numerically equal to three times hisprevious acceleration. Then the time duringwhich the deceleration takes place is(a) 3 s (b) 9 s

(c) 27 s (d) 6 s

31. The acceleration of a particle as a functionof time is given by 21.5 0.15 ( / )a t t m s .The particle starts motion from rest at timet = 0 sec. Then the maximum velocity in theforward direction is(a) 10 m/s (b) 25 m/s(c) 50 m/s (d) none of these

32. The length of seconds hand in a watch is 1cm. The change in velocity of its tip in 15seconds is

(a) zero (b) /sec(30 2)

cm

(c) /sec30

cm(d)

( 2) /sec30

cm

33. A car accelerates from rest at a constant rate for some time after which is deceleratesat a constant rate to come to rest. If thetotal time elapsed is t, the maximum velocityacquired by the car is given by

(a)2 2

t

(b)2 2

t

(c) t (d) t

34. A particle travels 10 m in first 5 sec and 10

m in next 3 sec. Assuming constantacceleration/deceleration, what is thedistance travelled in the next 2 s?(a) 8.3 m (b) 9.3 m(c) 6.2 m (d) 5.8 m

35. A balloon starts rising from the ground withan acceleration of 1.25 m/s2. After 8 s, astone is released from the balloon. The stonewill(a) cover a distance of 40 m(b) have a displacement of 50 m(c) reach the ground in 4 s(d) begin to move down after being released

36. The displacement of a particle moving in astraight line at any instant of time t isS = t3 – 6t2 + 3t + 4 meter. The velocity of theparticle, when its acceleration is zero, will be(a) 3 m/s (b) – 12 m/s(c) 42 m/s (d) – 9 m/s

37. The deceleration experienced by a movingboat, after its engine is cut off, is given by

3dv kvdt

, where k is a constant. If 0v is themagnitude of the velocity at cut-off, the


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magnitude of the velocity at a time t after thecut-off is

(a) 0202 1

v

v kt (b) 0

ktv e

(c) 02

v(d) 0v

38. A rifle bullet loses 1/20 of its velocity inpassing through a wooden plank. The leastnumber of planks required to stop the bullet is(a) 5 (b) 10(c) 11 (d) 20

39. The velocity of a particle is v = v0 + gt + ft2.If its position is 0x at 0t , then itsdispalcement after unit time (t = 1) is

(a) 0 2gv f (b) 0 2 3v g f

(c) 0 2 3g fv (d) 0v g f

40. A small block slides, without friction, down aninclined plane starting from rest. Let Sn bethe distance travelled from 1t n to t n .

Then 1

n

n

SS

is

(a) 2 1nn (b)

2 12 – 1nn

(c)

2 12 1nn (d)

22 1

nn

41. A particle moves in xy plane. The positionvector of particle at any time t is

2ˆ ˆ(2 ) (2 )r t i t j m

. The rate of charge of at time t = 2 second (where is the anglewhich its velocity vector makes with positivex-axis) is

(a)2 /sec

17rad (b)

1 /sec14

rad

(c)4 /sec7

rad (d)6 /sec5

rad

42. Consider a collection of large number ofparticles each with speed v. The direction ofvelocity is randomly distributed in thecollection. The magnitude of relative velocitybetween a pair of particles averaged over allthe pairs is(a) zero (b) greater than v(c) less than v (d) v

43. Two cars start off to race with velocities 4 m/s and 2 m/s and travel in straight line withuniform accelerations 1 m/s2 and 2 m/s2

respectively. If they reach the final point atthe same instant, then the length of the pathis(a) 30m (b) 32 m(c) 20 m (d) 24 m

44. Two particles start moving from the samepoint along the same straight line. The firstmoves with constant velocity v and the secondwith constant acceleration a. During the timethat elapses before the second catches thefirst, the greatest distance between theparticles is

(a)2v

a(b)

2

2va

(c)22v

a(d)

2

4va

45. A point mass starts moving in straight linewith constant acceleration a from rest at t =0. At time t = 2s, the acceleration changesthe sign, remaining the same in magnitude.The mass returns to the initial position attime t = t0 after start of motion. Here, t0 is

(a) 4s (b) (4 2 2)s

(c) (2 2 2)s (d) (4 4 2)s

46. A particle moves in space along the path3 2z ax by in such a way that

dx dycdt dt

,

where a, b and c are constants. Theacceleration of the particle is

(a) 2 2 ˆ(6 2 )ac x bc k (b) 2 2 ˆ(6 6 )ax by k

(c) 2 2 ˆ(4 3 )bc x ac k (d) 2 ˆ( )bc x by k

47. A rigid rod leans against a vertical wall (y-axis) as shown in figure. The other end of therod is on the horizontal floor. Point A is pusheddownwards with constant velocity. Path of thecentre of the rod is


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x

yA

(a) a straight line passing through origin

(b) a straight line not passing through origin(c) a circle of radius l/2 and centre at origin(d) a circle of radius l/2 but centre not at

origin

48. Four rods each of length l have been hingedto form a rhombus. Vertex A is fixed to rigidsupport, vertex C is being moved along thex-axis with a constant velocity v as shown inthe figure. The rate at which vertex B isapproaching the x-axis at the moment therhombus is in the form of a square is

v xA C

D

B

(a)4v

(b) 3v

(c) 2v

(d) 2v

49. A particle starts from the origin of co-ordinates at time 0t and moves in the xyplane with a constant acceleration in they-direction. Its equation of motion is 2y x .Its velocity component in the x-direction is

(a) variable (b)2

(c) 2 (d) 2

50. A horizontal wind is blowing with a velocityv towards north-east. A man starts runningtowards north with acceleration a. The timeafter which man will feel the wind blowingtowards east is(a)

va (b)

2va

(c) 2v

a (d)2va

51. Velocity-time equation a particle moving in astraight line is v = 2t – 4 for t 2s and v = 4– 2t for t > 2s. The distance travelled by the

particle in the time interval from t = 0 to t =4s is (Here, t is in second and v in m/s)(a) 12m (b) 16m(c) 4m (d) 8m

52. Starting from rest a particle moves in astraight line with acceleration a = {2 + |t – 2|}m/s2. Velocity of particle at the end of 4s willbe(a) 16 m/s (b) 20 m/s(c) 8 m/s (d) 4 m/s

4. MOTION UNDER GRAVITY53. A stone thrown upward with a speed u from

the top of the tower reaches the ground withthe velocity 3u. The height of the tower is :

(a)23u

g (b)24u

g

(c)26u

g (d)29u

g

54. A man in a balloon rising vertically with anacceleration of 4.9 m/sec2 releases a ball 2seconds after the balloon is let go from theground. The greatest height above the groundreached by the ball is :(a) 14.7 m (b) 19.6 m(c) 9.8 m (d) 24.5 m

55. A ball is released from rest at the top of asmooth inclined plane, and at the sameinstant ball Y is projected upward from the footof the plane with such a velocity that theymeet half way up the plane. Then the velocityof projection of the second ball is

2

1

h l

(a) gh (b) 2gh

(c) 2gh

(d) None of these

56. A body is released from the top of a tower ofheight h metres. It takes t seconds to reachthe ground. Where is the body at the time t/2 sec? (Neglect air resistance)(a) at h/2 metres from the ground(b) at h/4 metres from the ground


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(c) depends upon the mass and volume of ball(d) at 3h/4 metres from the ground

57. A body is released from the great height andfalls freely towards the earth. Another bodyis released from the same height one secondlater. Then, the separation between the twobodies, two seconds after release of the secondbody is(a) 4.9 m (b) 9.8 m(c) 19.6 m (d) 24.5

58. Which of the following statement is wrongabout a ball thrown vertically up(a) it is moving with a constant acceleration(b) it has the same position at two different

times(c) the angle between velocity and

acceleration changes during motion(before falling back on the ground)

(d) the linear momentum is conserved59. From the top of the building a ball is thrown

straight upward with an initial speed and atthe same time another ball is thrown straightdownward with the same initial speed.Neglecting air resistance, which statementis correct ?(a) Ball second reaches the ground first(b) Both the balls hit the ground with the

same speed(c) Both balls experience the same

acceleration(d) all of the above

60. Two identical objects are released from A. Theobject 1 falls vertically downward and theobject 2 slides down on frictionless surface AC.Then the ratio of time taken by them to reachthe bottom of the inclined plane is(a) 1 : 1

(b) 1 : 21

2 A

B C 30° (c) 2 : 1(d) 1: 2

61. B1, B2 and B3 are three balloons ascendingwith velocities V, 2V and 3V respectively. Ifa bomb is dropped from each when they areat the same height, then(a) bomb from B1 reaches ground first(b) bomb from B2 reaches ground first(c) bomb from B3 reaches ground first(d) they reach the ground simultaneously

62. A particle is dropped from a height d. It travels

(7/16)d distance in the last second of itsjourney. If g = 10 m/s2, then the height d is(a) 122.5 m (b) 125 m(c) 80 m d) 40 m

63. A particle thrown up vertically reaches itshighest point in time t1 and returns to theground in further time t2. The air resistanceexerts a constant force on the particle oppositeto its direction of motion(a) t1 > t2(b) t1 = t2(c) t1< t2(d) may be (a) or (c) depending on the ratio

of the force of air resistance to the weightof the particle

64. A particle is projected vertically upwards froma points A on the ground. It takes time t1 toreach a point B, but it still continues to moveup. If it takes further t2 time to reach theground from point B. Then the velocity ofprojection is

(a) 1 21 ( )2

g t t (b) g (t1 + t2)

(c) 21 2

1 ( )8

g t t (d) 1 212

gt t

65. A ball is dropped from the roof of a tower ofheight h. The total distance covered by it inthe last second of its motion is equal to thedistance covered by it in first three seconds.The value of h in metres is: (g = 10 m/s2)(a) 125 (b) 200(c) 100 (d) 80

66. Two stones are thrown up simultaneouslyfrom the edge of a cliff with initial speeds vand 2v. The relative position of the secondstone with respect to first varies with timetill both the stones strike the ground as(a) linearly(b) first linearly then parabolically(c) parabolically(d) first parabolically then linearly(assume that the first stone comes to restafter striking the ground)

67. From a tower of height H, a particle is thrownvertically upwards with a speed u. The timetaken by the particle, to hit the ground, is ntimes that taken by it to reach the highestpoint of its path. The relation between H, uand n is:

(a) 2 22gH n u (b) 2 2( 2)gH n u(c) 22 ( 2)gH nu n (d) 2( 2)gH n u


19

68. A stone is dropped from a building of heighth and it reaches after t seconds on earth. Fromthe same building if two stones are thrown(one upwards and other downwards) with thesame velocity u and they reach the earthsurface after t1 and t2 seconds respectively,then

(a) t = t1 – t2 (b)

1 22

t tt

(c) 1 2t t t (d) 1 2t t t

69. A ball is projected upwards from a height habove the surface of the earth with velocityv. The time at which the ball strikes theground is

(a) 2

2hgv

g (b)

21 1v hg g

(c)

2

21 1 ghvg v

(d)

2 21 gv vg h

70. A man throws a ball with the same speedvertically upwards one after the other at aninterval of 2 seconds. What should be the speedof the throw so that more than two balls are inthe sky at any time (Given g = 9.8 m/s2)(a) At least 0.8 m/s(b) Any speed less than 19.6 m/s(c) Only with speed 19.6 m/s(d) More than 19.6 m/s.

71. At a metro station, a girl walks up stationaryescalator in time t1. If she remains stationaryoan the escalator, then the escalator take herup in time t2. The time taken by her to walkup on the moving escalator will be(a) (t1 + t2)/2 (b) t1t2/(t1 – t2)(c) t1t2/(t2 + t1) (d) t1 – t2

72. Four marbles are dropped from the top of atower one after the other with an interval ofone second. The first one reaches the groundafter 4 seconds. When the first one reachesthe ground the distance between the first andsecond, the second and the third and the thirdand forth will be respectively(a) 35, 25 and 15 m (b) 30, 20 and 10 m(c) 20, 10 and 5 m (d) 40, 30 and 20 m

73. The displacement x of a particle with varieswith time t, x = ae–t + be–bt, where a, b, and are positive constants. The velocity ofthe particle will(a) Go on decreasing with time(b) Be independent of and (c) Drop at zero when =

(d) Go on increasing with time

5. GRAPHS

74 For the motion along x-axis shown in figure,the instantaneous velocity of the object atpoint A is(a) 1.5 m/s

(b) 0 m/s

A 15

5 0

10 20 t, sec

x, m 30

(c) 0.25 m/s(d) none of these

75. An object is thrown upward with a velocity u,then its displacement time graph is

(a) st

(b) s

t

(c) s t (d) s

t

76. The following figures show velocity v versustime t curves. But only some of these can berealised physically. These are

(i)

V

t (ii)

V

t

(iii)

V

t (iv)

V

t

(a) (i), (ii) and (iv) only

(b) (i), (ii) and (iii) only

(c) (ii) and (iv) only

(d) all of these

77. An object is projected upward with a velocityV from the surface of earth. The velocity-time


20

graph is illustrated by

(a)0

V

t

+

– (b)

V

t 0

+

–

(c)

V

t 0

+

– (d)

V

t 0

+

–

78. In the following velocity-time graph of body,the distance and displacement travelled bythe body in5 seconds, (in meters) will be

V (m/s)

t (sec)

5 4 2 0

20

40

– 40

– 20

1 3

(a) 70, 110 (b) 110, 70(c) 40, 70 (d) 90, 50

79. The displacement-time graphs of two particlesP and Q are as shown in the figure. The ratioof their velocities VP and VQ will be

Q

P

t

x

30°60°

(a) 1 : 3 (b) 1: 3(c) 1 : 2 (d) 3 :1

80. A particle thrown down from the top of a towertakes time t1 to reach the ground. It takestime t2 if thrown from the same point withthe same speed in the upward direction. Thetime it will take to fall freely to the groundfrom the top of the tower will be(a) t1t2 (b) (t1t2)1/2

(c) (t1t2)1/3 (d) (t1t2)1/4

81. A ball is dropped vertically from a height dabove the ground. It hits the ground and

bounces up vertically to a height d/2.Neglecting subsequent motion and airresistance, its velocity v varies with theheight h above the ground as

(a)h

v

Od

(b) h

v

Od

(c)h

v

O d(d)

h

v

O d

82. A body starts from rest at time t = 0. Theacceleration time graph is shown in thefigure. The maximum velocity attained by thebody will be

Otime (sec)

acceleration

(m/s2)10

11

(a) 110 /m s (b) 55 m/s(c) 650 m/s (d) 550 m/s

83. One stone is dropped from a tower from restand simultaneously another stone is projectedvertically upwards from the tower with someinitial velocity. The graph of the distance(s)between the two stones varies with time (t)as: (before either stone hits the ground)

(a)t

s

(b)t

s

(c)t

s

(d)t

s

84. Acceleration (a) displacement (s) graph of aparticle moving in a straight line is as shownin the figure. The initial velocity of theparticle is zero. The v-s graph of the particlewould be


21

a

s

(a)

v

s(b)

v

s

(c)

v

s(d)

v

s

85. Which graph corresponds to an object movingwith a constant negative acceleration and apositive velocity?

(a) (b)

(c) (d)

86. Two stones are thrown up simultaneouslyfrom the edge of a cliff 240 m high with initialspeed of 10 m/s and 40 m/s respectively.Which of the following graph best representsthe time variation of relative position of thesecond stone with respect to the first?(Assume stones do not rebound after hittingthe ground and neglect air resistance, takeg = 10 m/s2) (The figures are schematic andnot drawn to scale)

(a) (b)

(c) (d)

87. If a body moving in a circular path maintainsconstant speed of 10 ms–1, then which of thefollowing correctly describes relation betweenacceleration and radius ?

(a) (b)

(c) (d)

88. Two stones are thrown up simultaneouslyfrom the edge of a cliff 240 m high with initialspeed of 10 m/s and 40 m/s. respectively.Which of the following graph best representsthe time variation of relative position of thesecond stone with respect to the first (Assumestones do not rebound after hitting the groupand neglect air resistance, take g = 10 m/s2). (The figures are schematic and not drawnto scale)

(a) (b)

(c) (d)

89. Given below are four curves describingvariation of velocity with time of a particle.Which one of these describe the motion of aparticle initially in positive direction withconstant negative acceleration

v

t(W) (X)

tO

v

(Y)t

O

v

(Z)

tO

v

(a) (W) (b) (X)(c) (Y) (d) (Z)

90. The displacement of a particle as a functionof time is shown in the figure. The figureshows that


22

0 2 3 41

1

2Di

spla

cem

ent

Time in second(a) The particle starts with certain velocity

but the motion is retarded and finally theparticle stops.

(b) The velocity of the particle is constantthroughout

(c) The acceleration of the particle isconstant throughout

(d) The particle starts with constant velocity,then motion is accelerated with finallythe particle moves with another constantvelocity

91. Figure shows the distance time graph of themotion of a car. It follows from the graph thatthe car is

(a) at rest(b) in uniform motion(c) In non-uniform motion(d) Uniformly accelerated

92. Which of the following graphs can not possiblerepresent one dimensional motion of aparticle

(a) I and II (b) II and III(c) II and IV (d) All four

93. Which of the following velocity-time graphsshows a realistic situation for body in motion

(a) (b)

(c) (d)

94. Velocity-time (v – t) graph for a moving objectis shown in the figure. Total displacement ofthe object during the time interval whenthere is non-zero acceleration and retardationis

(a) 60 m (b) 50 m(c) 30 m (d) 90 m

95. The dispalcement time graph of movingparticle is shown in figure. The instantaneousvelocity of the particle is negative at the point

(a) D (b) F

(c) C (d) E

96. An object is moving a uniform accelerationwhich is parallel to its instantaneous directionof motion. The displacement(s) - velocity (v)graph of this object is

(a) (b)


23

(c) (d)

97. v - t graph for a particle is as shown. Thedistance travelled in the first 4s is

(a) 12 m (b) 16 m(c) 20 m (d) 24 m

98. The given graph shows the variation ofvelocity displacement. Which one of the graphgiven below correctly represents the variationof acceleration with dispalcement

(a) (b)

(c) (d)

99. A body is a set at x = 0. At t = 0, it startsmoving in the positive x-direction with aconstant acceleration. At the same instantanother body passes through x = 0 moving inthe positive x-direction with a constant speed.The position of the first body is given by x1(t)after time ‘t’ and that of the second body x2(t)after the same time interval. Which of thefollowing graphs correctly describes (x1 – x2)as net function of time ‘t’

(a) (b)

(c) (d)

6. RELATIVE VELOCITY100. A 120 m long train is moving in a direction

with speed 20 m/s. A train B moving with 30m/s in the opposite direction and 130 m longcrosses the first train in a time.(a) 6 s (b) 5 s(c) 38s (d) None of these

101. A 210 m long train is moving due north ata speed of 25 m/s. A small bird if flyind duesouth a little above the train with speed 5 m/s. The time taken by the bird to cross thetrain is(a) 6 s (b) 7 s(c) 9 s (b) 10 s

102. A police jeep is chasing with velocity of 45km/h a thief in another jeep moving withvelocity 153 km/h. Police fires a bullet withmuzzle velocity of 180 m/s. The velocity withwhich it will strike the car of the thief is(a) 150 m/s (b) 27 m/s(c) 450 m/s (d) 250 m/s

103. The distance between two particles movingtowards each other is decreasing at the rateof 6 m/sec. If these particles travel with samespeeds and in the same direction, then theseparation increases at the rate of 4 m/sec.The particles have speeds as(a) 5 m/sec., 1 m/sec(b) 4 m/sec, 1 m/sec(c) 4 m/sec, 2 m/sec(d) 5 m/sec, 2 m/sec

104. A train is moving towards east and a car isalong north, both with same speed. Theobserved direction of car to the passenger inthe train is(a) East-north direction(b) North-west direction(c) South-east direction(d) None of these

105. Particle A moves along X-axis with a uniform


24

velocity of magnitude 10 m/s. Particle Bmoves with uniform velocity 20 m/s along adirection making an angle of 60° with thepositive direction of X-axis as shown in figure.The relative velocity of B with respect to thatof A is

(a) 10 m/s(b) 10 3 m/s along Y-axis (perpendicular to

X-axis)(c) 10 5 along the bisection of the velocity

of A and B(d) 30 m/s along negative X-axis.

106. Two cars A and B are travelling in the samedirection with velocities v1 and v2 (v1 > v2).when the car A is at a distance d ahead ofthe car B, the driver of the car A applied thebrake produding a unifrom retardation a.There will be no collision when

(a)2

1 2( )2

v vd

a

(b)2 21 22

v vd

a

(c)2

1 2( )2

v vd

a

(d)2 21 22

v vd

a

107. A boat crosses a river from port A to B, whichare just on the opposite side. The speed ofthe water is Vw and that of boat is VB relativeto still water. Assume VB = 2Vw. What is thetime taken by the boat, if it has to cross riverdirectly on the AB line = D units

(a) 23B

DV

(b) 32 B

DV

(c)2B

DV

(d) 2B

DV

108. In the figure, one car is at rest and velocity

of light from head light is c, then velocity oflight from head light for the moving car atvelocity v, would be

(a) c + v (b) c – v(c) c v (d) c

109. Two trains A and B each of the length 400m are moving in two parallel tracks in thesame direction (with A ahead of B) with samespeed 72 km/h. The driver of B decides toovertake A and accelerates by 1 m/s2. If after50 s, B just brushes past A, calculate theoriginal distance between A and B(a) 750 m (b) 1000 m(c) 1250 m (d) 2250 m

7. PROJECTILE MOTION

110. In a projectile motion the velocity(a) is always perpendicular to the

acceleration(b) is never perpendicular to the acceleration(c) is perpendicular to the acceleration for

one instant only(d) is perpendicular to the acceleration for

two instants

111. Two bullets are fired simultaneously,horizontally and with different speeds from thesame place. Which bullet will hit the groundfirst?(a) the faster one(b) the slower one(c) both will reach simultaneously(d) depends on the masses

112. An aeroplane flying at a constant speedreleases a bomb. As the bomb drops away fromthe aeroplane,


25

(a) it will always be vertically below theaeroplane

(b) it will always be vertically below theaeroplane only if the aeroplane was flyinghorizontally

(c) it will always be vertically below theaeroplane only if the aeroplane was flyingat an angle of 45° to the horizontal

(d) it will gradually fall behind the aeroplaneif the aeroplane was flying horizontally

113. An aeroplane is flying with a horizontalvelocity of 60 km/hr at a height of 490 m.A bomb is dropped from the aeroplane. Howfar the aeroplane must be, from the enemyspot, so that it may directly hit the target.

(a) 5003 m (b) 5

3 m

(c) 503 m (d) 5 m

114. The time of flight of a projectile is 10 second.The maximum height reached by it will be(g =10 m/s2)(a) 25 m (b) 50 m(c) 82 m (d) 125 m

115. A particle is projected from point O withvelocity u in a direction making an angle with the horizontal. At any instant its positionis at point P at right angles to the initialdirection of projection. Time at whcih velocityare

90°u

v

P

100

90

(a)tanug

(b)

cotug

(c)cosecu

g

(d)secug

116. A particle of mass 100 g is fired with a velocity20 ms–1 making an angle of 30° with thehorizontal. When it rises to the highest pointof its path, then the change in its momentum

is

(a) 13 seckg m (b) 11 sec2

kg m

(c) 12 seckg m (d) 11 seckg m

117. A particle P is at the origin and startswith velocity j4i2 (m/s) and constantacceleration 2ˆ ˆ3 5 /i j m s . After it hastravelled for 2 seconds, its distance from theorigin is(a) 10 m (b) 10.2 m(c) 9.8 m (d) 11.7 m

118. A projectile is thrown with a velocity of10 2 /m s at an angle of 45° with horizontal.The interval between the moment when speedis 125 /m s is 2( 10 / )g m s(a) 1.0s (b) 1.5s(c) 2.0 s (d) 0.5 s

119. The height y and the distance x along thehorizontal plane of projection on a certainplanet (with no surrounding atmosphere) aregiven by y = 8t – 5t2 metre and x = 6t meterwhere t is in seconds. The velocity ofprojection is(a) 8 m/s (b) 6 m/s(c) 10 m/s (d) data in sufficient

120. A particle is projected from the ground withan initial velocity of 20 m/s at an angle of30° with horizontal. The magnitude of changein velocity in a time interval from t = 0 tot = 0.5s is : (g = 10 m/s2)(a) 5 m/s (b) 2.5 m/s(c) 2 m/s (d) 4 m/s

121. A ball is projected upwards from the foot ofa tower. The ball crosses the top of the towertwice after an interval of 6s and the ballreaches the ground after 12s. The height ofthe tower is (g = 10 m/s2)(a) 120 m (b) 135 m(c) 175 m (d) 80 m

122. A particle of mass m is projected from theground with initial linear momentum p(magnitude) such that to have maximumpossible range. Its minimum kinetic energywill be

(a)2

2pm (b)

2

4pm


26

(c)2p

m(d) none of these

123. The trajectory of a projectile in a vertical planeis y = ax – bx2, where a and b are constantsand x and y are respectively horizontal andvertical distances of the projectile from thepoint of projection. The maximum heightattained by the particle and the angle ofprojection from the horizontal are

(a)2

1, tan ( )2b ba

(b)2

1, tan (2 )a ab

(c)2

1, tan ( )4a a

b (d)

212 , tan ( )a a

b

124. A particle is projected from the ground withan initial speed of v at an angle withhorizontal. The average velocity of the particlebetween its point of projection and highestpoint of trajectory is

(a) 21 2cos2v

(b) 21 cos2v

(c) 21 3cos2v

(d) cosv

125. Two particles A and B are projectedsimultaneously from a point situated on ahorizontal plane. The particle A is projectedvertically up with a velocity Av while theparticle B is projected up at an angle of 30°with horizontal with a velocity Bv . After 5sthe particles were observed moving mutuallyperpendicular to each other. The velocity ofprojection of the particle Av and Bvrespectively are(a) 150 , 100 /ms m s

(b) 1 1100 , 50ms ms

(c) Av can have any value, 1100ms

(d) none of these

126. A projectile is fired at an angle of 30° to thehorizontal such that the vertical componentof its initial velocity is 80 m/s. Its time offlight is T. Its velocity at T = T/4 has amagnitude of nearly(a) 200 m/s (b) 300 m/s(c) 72 m/s (d) 100 m/s

127. Ratio of minimum kinetic energies of twoprojectiles of same mass is 4 : 1. The ratioof the maximum height attained by them isalso 4 : 1. The ratio of their ranges would be

(a) 16 : 1 (b) 4 : 1(c) 8 : 1 (d) 2 : 1

128. A particle is projected from the ground at anangle of 60° with horizontal with speed u =20 m/s. The radius of curvature of the pathof the particle, when its velocity makes anangle of 30° with horizontal is (g = 10 m/s2)(a) 10.6 m (b) 12.8 m(c) 15.4 m (d) 24.2 m

129. A bullet is to be fired with a speed of 2000ms–1 to hit a target 200 m away on a levelground. If g = 10 ms–2, the gun should beaimed(a) Directly at the target(b) 5 cm below the target(c) 5 cm above the target(d) 2 cm above the target

130. A larger number of bullets are fired in alldirections with the same speed v. What is themaximum area on the ground on which thesebullets will spread

(a)2v

g (b)

4

2vg

(c)4

22

vg

(d)2

22

vg

131. From the top of a tower, 80 m high from theground, a stone is thrown in the horizontaldirection with a velocity of 8 ms–1. The stonereaches the ground after a time t and fallsat a distance of d from the foot of the tower.Assume g = 10 ms–2, the time t and distanced are given respectively by(a) 6s, 64m (b) 6s, 48m(c) 4s, 32m (d) 4s, 16m

132. The relation between the time of flight of aprojectile, Tf and the time to reach themaximum height tm is

(a) Tf = 2 tm (b) Tf = tm

(c)2m

ft

T (d) 2 ( )f mT t

133. A ball is projected with kinetic energy E atan angle of 45° to the horizontal. At thehighest point during the flight, its kineticenergy will be(a) zero (b) E/2(c) E/2 (d) E


27

134. A ball is thrown from a point with a speed v0at an angle of projection . From the samepoint and at the same instant a person startsrunning with a constant speed v0/2 to catchthe ball. Will the person be able to catch theball? If yes, what should be the angle ofprojection(a) Yes, 60° (b) Yes, 30°(c) No (d) Yes, 45°

135. A projectile is fired with initial velocity u atsome angle has a range R. If the initialvelocity be doubled at the same angle ofprojection, then the range will be(a) 2R (b) R/2(c) R (d) 4R

136. If a body A of mass M is thrown with velocityV at an angle of 30° to the horizontal andanother body B of the same mass is thrownwith the same speed at angle of 60° to thehorizontal. The ratio of horizontal range of Ato B will be(a) 1 : 3 (b) 1 : 1(c) 1 : 3 (d) 3 : 1

137. The angle of projection at which the horizontalrange and maximum height of projectile areequal is(a) 45°(b) = tan–1(2.5)(c) = tan–1(4)(d) 60°

138. Ratio between maximum range and square oftime flight in projectile motion is(a) 10 : 49 (b) 40 : 10(c) 98 : 10 (d) 10 : 98

139. The coordinates of a moving particle at anytime t are given x = t3 asnd y = t3. The speedof the particle at time t is given by

(a) 2 2 (b) 2 23t

(c) 2 2 23t (d) 2 2 2t

140. A projectile moves from the ground such thatits horizontal displace is x = Kt and verticaldisplacement is y = Kt(1 – t), where K and

are constants and t is time. Find out totaltime of flight (T) and maximum heightattained (Ymax) is

(a) max,2KT Y (b)

max1 2, KT Y (c) max

1 ,6KT Y

(d) max1 ,

4KT Y

141. A body is projected vertically upwards at timet = 0 and it is seen at a height H at instantst1 and t2 seconds during its flight. Themaximum height attained is (g isacceleration due to gravity)

(a)2

2 1( )8

g t t(b)

21 2( )

4g t t

(c)2

1 2( )8

g t t(d)

22 1( )

4g t t

142. A particle of mass m is projected from theground with an initial speed u0 at an angle with the horizontal. At the highest point of itstrajectory, it makes a completely inelasticcollision with another identical particle,which has thrown vertically upward from theground with the same initial speed u0. Theangle that the composite system makes withthe horizontal immediately after the collisionis

(a) 4 (b) 4

a

(c) 4a (d) 2

143. A stone projected with a velocity u at an angle with the horizontal reaches maximumheight H1. When it is projected with velocity

u at an angle 2

with the horizontal, it

reaches maximum height H2. The relationbetween the horizontal range R of theprojectile, H1 and H2 is

(a) 1 24R H H (b) R = 4(H1 – H2)

(c) R = 4(H1 + H2) (d)2122

HR

H


28

144. For a given velocity, a projectile has the samerange R for two angles of projection it t1 andt2 are the same times of flight in the twocases then

(a) t1t2 R2 (b) t1t2 R

(c) 1 21t tR

(d) 1 2 21t t

R

145. Figure shows four paths for a kicked football.Ignoring the effects of air on the flight, rankthe paths according to intial horizontalvelocity component, highest first

(a) 1, 2, 3, 4 (b) 2, 3, 4, 1(c) 3, 4, 1, 2 (d) 4, 3, 2, 1

8. INTEGER TYPE QUESTIONS146. A man walking with a speed of 3 km/h finds

the rain drops falling vertically downwards.When the man increases his speed to 6 km/h he find that the rain drops are fallingmaking an angle of 30o with the vertical. Findthe speed of the rain drops (in km/h)

147. Six Particles are situated at the corners of aregular hexagon. These particles startmoving with equal speed of 10 m/s in such away that velocity of any one particle is directedtowards the next particle. Find the rate (inm/s) at which length of a side of the hexagonis decreasing.

148. A boy standing on the top of a tower of height54 ft throws a packet with a speed of 20 ft/sdirectly aiming towards his friend standingon the ground at a distance of 72 ft from thefoot of the tower. The packet falls short of theperson on the ground by x × 16/3 ft. The valueof x is.

149. Two particles are simultaneously thrown fromthe roofs of two high buildings as shown infigure. Their velocities are vA = 2 m/s and vB= 14 m/s respectively. Calculate theminimum distance between the particles inthe process of their motion. Also find the timewhen they are at closest distance.

20m

22m

11m

45o

45o

A

B

150. A ball is projected from ground with speed103 m/s at angle 60o from the horizontal.After how much time (in s) its velocity makesangle 60o with the vertical (Take g = 10 m/s2)

151. Figure shows a ring of radius 2 m and a rod oflength l. The rod is moving with velocity 4m/s perpendicular to its length. Find theangular speed (in rad/s) of point intersectionA w.r.t. O at the instant when = 30o.

O

A

v

152. Two balls are projected from a point in twomutually perpendicular vertical planes. Speedof projection of both the balls is 400 m/s. Angleof projection with horizontal is 53o for boththe balls. After how much time (in s) theirvelocities will be at angle 60o from eachother? (Take g = 10 m/s2).

153. Acceleration (a) of a particle moving along xaxis is given by a = 8 – 4x. Velocity of theparticle at x = 0 is zero. Find the speed of theparticle at x = 2.


29

1. VECTORS1. c 2. b 3. c 4. d 5. b6. b 7. b 8. b 9. d 10. d11. b 12. c 13. d 14. a 15. a16. c 17. b 18. b 19. c 20. b

2. DISTANCE AND DISPLACEMENT21. b 22. d 23. c 24. d

3 UNIFORM & NON UNIFORM MOTION25. b 26. a 27. c 28. c 29. a30. a 31. b 32. d 33. d 34. a35. c 36. d 37. a 38. c 39. c40. c 41. a 42. b 43. d 44. b45. c 46. a 47. c 48. c 49. d50. c 51. d 52. d

4. MOTION UNDER GRAVITY53. b 54. a 55. a 56. b 57. d58. d 59. d 60. a 61. c 62. c63. d 64. a 65. a 66. b 67. c68. d 69. c 70. c 71. c 72. a

5. GRAPHS73. d 74. a 75. c 76. c 77. b78. a 79. a 80. b 81. b 82. b83. c 84. c 85. a 86. a 87. c88. c 89. c 90. d 91. d 92. b93. b 94. d 95. d 96. b 97. a98. a

6. RELATIVE VELOCITY99. d 100. b 101. b 102. a 103. a104. b 105. b 106. c 107. a 108. b

7. PROJECTILE MOTION109. C 110. c 111. b 112. a 113. a114. d 115. c 116. d 117. b 118. a119. c 120. a 121. b 122. a 123. c124 c 125. c 126. c 127. b 128. b129. c 130. b 131. c 132. a 133. b134. a 135. d 136. b 137. c 138. c139. b 140. a 141. c 142. c 143. a144. b 145. d

8. INTEGER TYPE QUESTION146. (6) 147. (5) 148. (9) 149. (6)150. (1) 151. (4) 152. (8) 153. (4)

Topper’s Package Physics - XI Permutation and ......2020/07/06 · Topper’s Package Physics -...

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