Topper’s Package Physics - XI Permutation and ...€¦ · 15/7/2020 · Topper’s Package Physics - XI Permutation and CombinationsWork, Power and Energy 44 1. WORK 1. A particle

Topper’s Package Physics - XI Permutation and CombinationsWork, Power and Energy

44

1. WORK

1. A particle of mass m moves in a circular pathof radius r under the action of a force 2/mv r .The work done during its motion over half ofthe circumference of the circular path will be

(a)2mv r

r

(b)2

2mv rr

(c)2

(2 )/ mvrr

(d) zero

2. A force of 800 N is applied to a car to bring it torest in a distance of 450 m. Then, the workdone in stopping the car is(a) zero (b) 36 k J(c) – 360 k J (d) none of these

3. A force F x acts on a particle in thex-direction, where and are constants. Thework done in moving the particle from 0x tox d is(a) d (b) ( )d d

(c) 212

d d (d) zero

4. A force ˆ ˆ(3 4 )F x i j

newton (where x is inmt.) acts on a particle which moves from aposition (2 , 3 )m m to (3 , 0 )m m . Then, the workdone is(a) 7.5 J (b) – 12 J(c) – 4.5 J (d) + 4.5 J

5. The equation of motion of a body of mass 3 kg.

is 3

3tx meter. The work done by the body in

3 seconds will be(a) 12.5 joule (b) 121.5 joule(c) 0.125 joule (d) zero

6. A plot of velocity versus time is shown in fig. Asingle force acts on the body. The correctstatement is

A B

C

D

O

v

t

(a) in moving from C to D, work done by theforce on the body is positive

(b) in moving from B to C, work done by theforce on the body is positive

(c) in moving from A to B, the body does workon the system

(d) in moving from O to A, work is done by thebody and is negative

7. A ball is released from the top of a tower. Theratio of work done by the force of gravity in firstsecond and third second of the motion is(a) 1 : 2 : 3 (b) 1 : 4 : 16(c) 1 : 3 : 5 (d) 1 : 9 : 15

8. A force ˆ ˆ ˆ6 2 3F i j k

acts on a particle anddisplaces it through ˆ ˆ ˆ2 3s i j x k

. The

value of x for zero work done is(a) 0.05 (b) – 2(c) 2 (d) 6

9. N similar slabs of cubical shape of edge b arelying on ground. Density of material of slabis D. Work done to arrange them one over theother is(a) 2 2 2( 1 )N b Dg (b) 4( 1)N b Dg

(c) 2 41 ( )2

N N b Dg (d) 2 4( )N N b Dg

10. Force acting on a particle is ˆ ˆ(2 3 )i j N . Workdone by this force is zero, when a particle ismoved on the line 3y + kx = 5. Here value of kis(a) 2 (b) 4(c) 6 (d) 8

11. v-t graph of an object of mass 1 kg is is shown.Select the wrong statement

WORK, POWER ANDENERGY

Unit 4


45

10 20 30

10

20v(m/s)

t(m/s)

(a) Work done on the object in 30s is zero(b) Work done on the object is zero(c) The average velocity of the object is zero(d) The average force on the object is zero

12. The force required to stretch a spring varieswith the distance as shown in the figure. If theexperiment is performed with the above springof half the length, the line OA will

AF

XO

(a) shift towards F-axis(b) shift towards X-axis(c) remain as it is(d) becomes double in length

13. A vertical spring of force constant 100 N/mis attached with a hanging mass of 10 kg.Now an external force is applied on the massso that the spring is stretched by additional2m. The work done by the force F is : (g =10 m/s2)(a) 200 J (b) 400 J(c) 450 J (d) 600 J

14. A body is acted upon by a force which isinversely proportional to the distance coveredx. The work done by the force will beproportional to :(a) x (b) x2

(c) x3/2 (d) None of the above

15. When a rubber-band is stretched by a distancex, it exerts restoring force of magnitude F =ax + bx2 where a and b are constants. Thework done in stretching the unstretchedrubber-band by L is:

(a) aL2 + bL3 (b) 2 31 ( )2

aL aL

(c) 2 3

2 3aL bL (d)

2 312 2 3

aL bL

16. If W1, W2 and W3 represent the work done inmoving a particle from A to B along three

different paths 1, 2 and 3 respectively (asshown) in the gravitational field of a point massm, find the correct relation between W1, W2and W3 .

m

B

A

12

3

(a) W1 > W2 > W3 (b) W1 = W2 = W3(c) W1 < W2 < W3 (d) W2 > W1 > W3

17. The work done by a force 3ˆ( 6 )F x i N in

displacing a particle from x = 4m to x = –2mis(a) +360J (b) 240J(c) –240J (d) –360J

18. The potential energy of a conservative systemis given by V(x) = (x2 – 3x) joule. Then itsequilibrium position is at(a) x = 1.5 m (b) x = 2 m(c) x = 2.5 m (d) x = 3 m

19. A force ˆ ˆ( )F K yi xj (where K is a positive

constant) acts on a particle moving in the xyplane. Starting from the origin, the particle istaken along the positive x-axis to the point (a,0) and then parallel to the y-axis to the point(a, a). The total work done by the force F onthe particle is :(a) – 2 Ka2 (b) 2 Ka2

(c) – Ka2 (d) Ka2

20. The work done on a particle of mass m by a

force ˆ ˆ2 2 3/2 2 2 3/2+

( + ) ( + )x yK i j

x y x y

(K

being a constant of appropriate dimensions,when the particle is taken from the point (a,0) to the point (0, a) along a circular path ofradius a about the origin in the x-y plane is

(a) 2Ka (b) K

a

(c) 2K

a (d) 0


46

21. The potential energy of a certain spring whenstretched through a distance ‘S’ is 10 joule.The amount of work (in joule) that must bedone on this spring to stretch it through anadditional distance ‘S’ will be(a) 30 (b) 40(c) 10 (d) 20

22. A particle in a certain conservative force fieldhas a potential energy given by

20xyUz

.The force exerted on it is

(a) 220 2020ˆ ˆ ˆy xyxi j kz z z

(b) 220 2020ˆ ˆ ˆy xyxi j kz z z

(c) 220 2020ˆ ˆ ˆy xyxi j kz z z

(d) 220 2020ˆ ˆ ˆy xyxi j kz z z

23. A pointer reading v/s load graph for a springbalance is as given in the figure. The springconstant is

(a) 0.1 kg/cm (b) 5 kg/cm(c) 0.3 kg/cm (d) 1 kg/cm

24. A particle is acted upon by a force F whichvaries with position x as shown in figure. Ifthe particle at x = 0 has kinetic energy of25 J, then the kinetic energy of the particleat x = 16 m is

(a) 45 J (b) 30 J

(c) 70 J (d) 135 J

25. A block of mass M is attached to the lowerend of a vertical spring. The spring is hungfrom a ceiling and has force constant valuek. The mass is released from rest with thespring initially unstretched. The maximumextension produced in the length of the springwill be(a) 1 Mg/k (b) 2 Mg/k(c) 4 Mg/k (d) Mg/2k

26. A time dependent F = 6t acts on a particleof mass 1kg. If the particle starts from rest,the work done by the force during the first1 sec. will be(a) 18 J (b) 4.5 J(c) 22 J (d) 9 J

27. A body of mass m = 10–2kg is moving inmedium and experience a frictional force F= –kv2. Its initial speed is v0 = 10ms–1. If after

10s, its energy is 20

18

mv , the value of k willbe(a) 10–1Kgm–1s–1 (b) 10–3Kgm–1

(c) 10–3Kgs–1 (d) 10–4Kgm–1

28. Consider a drop of rain water having mass1 g falling from a height of 1 km. It hits theground with a speed of 50 m/s. Take ‘g’constant with a value 10 m/s2. The work doneby the (i) gravitational force and the (ii)resistive force of air is(a) (i) –10 J (ii) –8.25 J(b) (i) 1.25 J (ii) –8.25 J(c) (i) 100 J (ii) 8.75 J(d) (i) 10 J (ii) –8.75 J

2. CONSERVATION OF ENERGY

29. A block of mass m slides on a horizontalfrictionless table-top with a constant speed v.It is brought momentarily to rest bycompressing a spring of spring constant k, inits path. Then, the maximum distance d, bywhich the spring is compressed, is


47

m

v

(a)2

2v

g (b) 22 /mv k

(c) 2 /mv k (d) 2/k mv

30. A body of mass 2 kg slides down a curved trackwhich is quadrant of a circle of radius 1 metre(figure). All the surfaces are frictionless. If thebody starts from rest, its speed at the bottomof the track is

1m

1m

(a) 4.43 m/sec (b) 2 m/sec(c) 0.5 m/sec (d) 19.6 m/sec

31. A long spring is stretched by 2 cm. Its potentialenergy is u. If the spring is stretched by 10cm. The potential energy in it will be(a) u / 25 (b) u / 5(c) 5 u (d) 25 u

32. A car is moving along a straight horizontal roadwith a speed 0v . If the coefficient of frictionbetween tyres and the road is µ. The shortestdistance in which the car can be stopped is

(a)20

2vµg (b)

0vµg

(c)2

0vµg

(d)20vµ

33. Before a rubber ball bounces off from the floor,the ball is in contact with the floor for a fractionof second. Which of the following statementsare correct(a) conservation of energy is not valid during

this period(b) conservation of energy is system valid

during this period(c) as ball is compressed, kinetic energy is

converted to compressed potential energy

(d) none of these

34. A block of mass 2 kg slides down a curved trackthat is one quarter of a circle of radius 1 m. Itsspeed at the bottom is 4 m/s. Work done byfrictional force is (take 210 /g m s )

1m

1m

(a) – 4 J (b) 8 J(c) – 8 J (d) 20 J

35. A block slides down an inclined plane of slopeof angle with a constant velocity v. It is thenprojected up the plane with an initial velocityu. The distance upto which it will rise beforecoming to rest is

(a)2

4 sinu

g (b) 4 sinu

g

(c)2 sin4

ug

(d)

sin4

ug

36. A sphere is suspended by a thread of length l.What minimum horizontal velocity has to beimparted the ball for it to reach the height ofthe suspensions?

(a) g l (b) 2 g l

(c) g (d) 2g

37. The potential energy of a 1 kg particle free tomove along the x-axis is given by

4 2( )

4 2x xU x J

The total mechanical energy of the particle is2J . Then, the maximum speed (in /m s ) is(a) 2 (b) 3/ 2(c) 2 (d) 1/ 2

38. An ideal spring with spring constant k is hungfrom the ceiling and a block of mass M isattached to its lower end. The mass is releasedwith the spring initially unstretched. Then themaximum extension in the spring is

(a)4Mg

k (b)2Mg

k

(c)Mgk (d)

2Mg

k


48

39. A 0.5 kg ball is thrown vertically up with 14m/s. It attains a height of 8m. The energydissipated by air drag acting on the ball duringascent is(a) 9.8J (b) 4.9J(c) 10J (d) 19.6J

40. A long spring, when stretched by x cm has apotential energy U. On increasing the lengthof spring by stretching to nx cm , the potentialenergy stored in the spring will be(a) /U n (b) nU(c) 2n U (d) 2/U n

41. Velocity - time graph of a particle moving in astraight line is as shown in the figure. Mass ofthe particle is 2 kg. Work done by all the forcesacting on the particle in time interval between

0t to 10 sect is

t (sec)10

–20

10

O

v m s( / )

(a) 300J (b) 300J

(c) 400J (d) 400J

42. A particle is released from a height H. Atcertain height its kinetic energy is two timesits potential energy. Height and speed of particleat that instant are

(a) , 23 3H gH

(b) ,3 3H gH

(c)2 2,3 3H gH

(d) , 23H gH

43. Two particles 1 and 2 are allowed to descend ontwo frictionless chords OP and OQ. The ratio ofthe speeds of the particles 1 and 2 respectivelywhen they reach on the circumference is

1

2

P

O

Q

60°

(a)14

(b)12

(c) 1 (d)1

2 2

44. The ratio of momentum and kinetic energy ofparticle is inversely proportional to the time.Then this is the case of a(a) uniformly accelerated motion(b) uniform motion(c) uniformly retarded motion(d) simple harmonic motion

45. A uniform flexible chain of mass m and length2l hangs in equilibrium over a smoothhorizontal pin of negligible diameter. One endof the chain is given a small verticaldisplacement so that the chain slips over thepin. The speed of chain when it leaves pin is

(a) 2gl (b) gl

(c) 4gl (d) 3gl

46. A particle is released from the top of twoinclined rough surfaces of height h each. Theangle of inclination of the two planes are 30°and 60° respectively. All other factors (e.g.,coefficient of friction, mass of block etc.) aresame in both the cases. Let K1 and K2 be thekinetic energies of the particle at the bottomof the plane in two cases. Then(a) K1 = K2 (b) 1 2K K(c) 1 2K K (d) data insufficient

47. The potential energy of a particle of mass m is

given by 212

U k x for 0x and 0U for

0x . If total mechanical energy of the particle

is E. Then its speed at 2Exk

is

(a) zero (b)2Em

(c)Em

(d) 2Em

48. Percentage change in K.E. of a particle is 300%.Then percentage change in its linearmomentum will be(a) 100% (b) 150%(c) 300% (d) 50%


49

49. Kinetic energy k of a particle of mass m movingalong a straight line depends upon distance sas k = as2. The force acting on the particle is(a) 2as (b) 2mas(c) 2a (d) 2as

50. When a body of mass M slides down an inclinedplane of inclination , through a distance S, thechange in kinetic energy is:(a) μMgcosθS(b) μMgsin θS(c) (μ θ – θ)SMg cos sin(d) MgS(sinθ–μcosθ)

51. A heavy weight is suspended from a spring is E.If the weight is raised till the spring comes toits unstretched position and the work done indoing so is W. Then gain in gravitatio potentialenergy of the weight will be:(a) W + E (b) W – E(c) W (d) E

52. A person trying to loss weight by burning fatlifts a mass of 10 kg upto a height of 1 m 100times. Assume that the potential energy losleach time he lowers the mass is dissipated.How much fat will he lose up considering thework done only when the weight is lifted up?Fat supplies 3.8 107 J of energy per kg whichis converted to mechaincal energy with a 20%efficiency rate. Take g = 9.8 ms–2

(a) 9.89 10–3 kg (b) 1.289 10–3 kg(c) 2.45 10–3 kg (d) 6.45 10–3 kg

53. A point particle of mass m, moves along theuniformly rough track PQR as shown in thefigure. The coefficient of friction, between theparticle and the rough track equals . Theparticle is released, from rest, from the pointP and it comes to rest at a point R. Theenergies, lost by the ball, over the parts PQand QR, of the track, are equal to each other,and no energy is lost when particle changesdirection from PQ to QR. The values of thecoefficient of frictionand the distance x (=QR),are, respectively close to :

(a) 0.2 and 6.5 m (b) 0.2 and 3.5 m(c) 0.29 and 3.5 m (d) 0.29 and 6.5 m

54. A time dependent force F = 6t acts on a particleof mass 1 kg. If the particle starts from rest,the work done by the force during the first 1sec will be(a) 4.5 J (b) 2.4 J(c) 9 J (d) 18 J

55. Velocity-time graph for a body of mass 10 kg isshown in figure. Work-done on the body in firsttwo seconds of the motion is

(a) – 9300 J (b) 12000 J(c) – 4500 J (d) – 12000 J

56. A particle is moving in a circle of radius r underthe action of a force 2F r which is directedtowards centre of the circle. Total mechanicalenergy (kinetic energy + potential energy) ofthe particle is (take potential energy = 0 forr = 0)

(a) 3r (b) 313

r

(c) 343

r (d) 356

r

57. Two bodies of masses m1 and m2 have equalkinetic energies. If p1 and p2 are theirrespective momentum, then ratio p1 : p2 isequal to(a) m1 : m2 (b) m2 : m1

(c) 1 2:m m (d) 2 21 2:m m

58. A toy car of mass 5 kg moves up a ramp underthe influence of force F plotted againstdisplacement x. the maximum height attainedis given by

x = 0 x = 11m

10080604020

0 2 4 6 8 1012 x

F(N)


50

(a) ymax = 20 m (b) ymax = 15 m(c) ymax = 11 m (d) ymax = 5 m

59. A particle of mass m at rest is acted upon bya force F for a time t. Its kinetic energy afteran interval t is

(a)2 2F tm

(b)2 2

2F t

m

(c)2 2

3F t

m(d) 2

Ftm

60. A compressed spring of spring constant kreleases a ball of mass m. If the height of springis h and the spring is compressed through adistance x, the horizontal distance covered byball to reach ground is

m

h

(a) x khmg (b)

xkhmg

(c)2khxmg (d)

mgx kh

61. A vertical spring with force constant K is fixedon a table. A ball of mass m at a height h abovethe free upper end of the spring falls verticallyon the spring so that the spring is compressedby a distance d. The net work done in theprocess is

(a) 21( )2

mg h d Kd (b) 21( )2

mg h d Kd

(c) 21( )2

mg h d Kd (d) 21( )2

mg h d Kd

62. Two inclined frictionless tracks, one gradualand the other steep meet at A from where

two stones are allowed to slide down from rest,one on each track as shown in figure. Whichof the following statement is correct

(a) Both the stones reach the bottom at thesame time but not with the same speed.

(b) Both the stones reach the bottom with thesame speed and stone I reaches thebottom earlier than stone II.

(c) Both the stones reach the bottom with thesame speed and stone II reaches thebottom earlier than stone I

(d) Both the stones reach the bottom atdifferent times and with different speeds

63. The potential energy function for a particle

executing linear SHM is given by 21( )2

V x kx

where k is the force constant of the oscillator(Fig.). For k = 0.5 N/m, the graph of V(x) versusx is shown in the figure. A particle of totalenergy E turns back when it reaches x = ±xm.If V and K indicate the PE and KE, respectivelyof the particle at x = +xm, then which of thefollowing is correct

(a) V = O, K = E (b) V = E, K = O(c) V < E, K = O (d) V = O, K < E

64. In a shotput event an athlete throws theshotput of mass 10kg with an initial speed of1ms–1 at 45° from a height 1.5m aboveground. Assuming air resistance to benegligible and acceleration due to gravity tobe 10 ms–2, the kinetic energy of the shotputwhen it just reaches the ground will be(a) 2.5 J (b) 5.0 J(c) 52.5 J (d) 155.0 J

65. A spherical ball of mass 20 kg is stationary at


51

the top of a hill of height 100 m. If slides downa smooth surface to the ground, then climbsup another hill of height 30 m and finallyslides down to a horizontal base at a heightof 20 m above the ground. The velocityattained by the ball is(a) 10 m/s (b) 10 30 /m s(c) 40 m/s (d) 20 m/s

66. A particle free to move along the x-axis haspotential energy given by

2

( ) [1 exp(– )]xU x k e for – x + wherek is a positive constant of appropriatedimensions. Then(a) at points away from the origin, the particle

is in unstable equilibrium(b) for any finite non-zero value of x, there

is a force directed away from the origin(c) if its total mechanical energy is k/2, it has

its minimum kinetic energy at theorigin.

(d) for small displacements from x = 0, themotion is simple harmonic.

67. Two identical cylindrical vessels with theirbases at same level each contains a liquidof density . The height of the liquid in onevessel is h1 and that in the other vessel ish2. the area of either base is A. The workdone by gravity in equalizing the levels whenthe two vessels are connected, is(a) (h1 – h2)g (b) (h1 – h2) Ag

(c) 21 2

1 ( )2

h h gA (d) 21 2

1 ( )4

h h gA

68. The potential energy function for the forcebetween two atoms in a diatomic molecule isapproximately given by

12 6( ) a bU xx x

where a and b are constants and x is thedistance between the atoms. If thedissociation energy of the molecule isD = [U(x = ) – Uat equilibrium], D is

(a)2

6ba

(b)2

2ba

(c)2

12b

a (d)2

4ba

69. Two plates each of the mass m are connectedby a massless spring as shown. A weight Wis put on the upper plate which compresses

the spring further. When W is removed, theentire assembly jumps up. The minimumweight W needed for the assembly to jump upwhen the weight is removed is just more than

(a) mg (b) 2mg(c) 3mg (d) 4mg

70. Figure below shows a small mass connectedto s string, which is attached to a vertical post.If the ball is released when the string ishorizontal as shown, the magnitude of thetotal acceleration (including radial andtangential) of the mass as a function of theangle is

(a) g sin (b) 23cos 1g

(c) g cos (d) 23sin 1g

71. A particle is acted upon by a force given byF = –x3 – x4 where and are positiveconstants. At the point x = 0, the particle is(a) In stable equilibrium(b) In unstable equilibrium(c) In neutral equilibrium(d) Not in equilibrium

72. A body moves in a circular orbit of radius Runder the action of a central force. Potentialdue to the central force is given by V(r) = kr(k is a positive constant). Period of revolutionof the body is proportional to

(a) 12R (b) 1

2R

(c) 32R

(d) 52R

73. A particle with total mechanical energy,


52

which is small and negative, is under theinfluence of a one dimensional potential U(x)= (x4/4 – x2/2)J where x is in meters. At timet = 0s it is at x = –0.5m. Then at a later timeit can be found(a) Anywhere on the x axis(b) Between x = –1.0m to x = 1.0m(c) Between x = –1.0m to x = 0.0m(d) Between x = 0.0m to x = 1.0m

74. A uniform thin rod of length 2L and mass mlies on a horizontal table. A horizontal impulseJ is given to the rod at one end. There is nofriction. The total K.E. of the rod just after theimpulse will be

(a)2

2Jm

(b)2J

m(c)

22Jm

(d)26J

m

75. A particle is placed at the origin and a forceF = kx, is acting on it (where k is positiveconstant). If U(0) = 0, the graph of U(x) versusx will be (where U is the potential energyfunction)

(a) (b)

(c) (d)

76. Consider a rubber ball freely falling from aheight h = 4.9 m onto a horizontal elastic plate.Assume that the duration of collision isnegligible and the collision with the plate istotally elastic. Then the velocity as a functionof time and the height as a function of timewill be

(a)

(b)

(c)

(d)

77. A particle, which is constrained to move alongthe x - axis, is subjected to a force in the samedirection which varies with the distance x ofthe particle from the origin as F(x) = – kx +ax3. Here k and a are postive constants. Forx 0,the functional form of the potentialenergy U(x) of the particle is

(a) (b)

(c) (d)

78. A tennis ball is dropped on a horizontal smoothsurface. It bounces back to its original positionafter hitting the surface. The force on the ballduring the collision is proportional to thelength of compression of the ball. Which oneof the following sketches describes thevariation of its kinetic energy K with time tmost appropriately? The figures are onlyillustrative and not to the scale.

(a)K

t

(b)

K

t

(c)K

t

(d)

K

t

79. Which of the diagrams shown in figurerepresents variation of total mechanicalenergy of a pendulum oscillating in air as


53

function of time

(a) (b)

(c) (d)

80. Which of the diagrams shown in figure mostclosely shows the variation in kinetic energyof the earth as it moves once around the sunin its elliptical orbit

(a) (b)

(c) (d)

81. A raindrop falling from a height h aboveground, attains a near terminal velocity whenit has fallen through a height (3/4)h. Whichof the diagrams shown in figure correctlyshows the change in kinetic and potentialenergy of the drop during its fall up to theground

(a) (b)

(c) (d)

82. Two rectangular blocks A and B of masses 2kgand 3kg respectively are connected by aspring of spring constant 10.8 Nm–1 and areplaced on a frictionless horizontal surface. Theblock A was given an initial velocity of 0.15ms–1 in the direction shown in the figure. Themaximum compression of the spring during

the motion is

(a) 0.01 m (b) 0.02 m(c) 0.06 m (d) 0.03 m

3. POWER

83. A body is moved along a straight line by amachine delivering constant power. Thedistance moved by the body in time t isproportional to

(a) 1/2t (b) 3/4t

(c) 3/2t (d) 2t84. A constant force of 3.0 N accelerates a

stationary object of mass 0.15 kg through adisplacement of 20 metre. Then the averagepower delivered is(a) zero watt (b) 60.0 W(c) 42.5 W (d) 36.2 W

85. The power of a water pump is 2 kW. If210 /g m s . The amount of water it can raise

in one minute to a height of 10 m is(a) 2000 litre (b) 1000 litre(c) 1200 litre (d) 100 litre

86. Power applied to a particle varies with time asP = (3t

2 – 2t + 1) watt, where t is in second.

Find the change in its kinetic energy betweent = 2 sec and t = 4 sec(a) 32 J (b) 46J(c) 61 J (d) 102 J

87. A wind-powered generator converts wind energyinto electric energy. Assume that the generatorconverts a fixed fraction of the wind energyintercepted by its blocks into electrical energy.For wind speed v, the electrical power outputwill be proportional to(a) v (b) 2v(c) 3v (d) 4v

88. A force F acting an a body depends on itsdisplacement s as 1/3F s . The powerdelivered by F will depend on displacement as(a) 2/3s (b) 5/3s

(c) 1/2s (d) 0s


54

89. A constant power P is applied to a particle ofmass m. The distance travelled by the particlewhen its velocity increases from 1v to 2v is(neglect friction)

(a) 2 22 1

3 ( )P v vm

(b) 2 1( )3m v vP

(c) 3 32 1( )

3m v vP

(d) 2 22 1( )

3m v vP

90. A body is moved from rest along a straight lineby a machine delivering constant power. Theratio of displacement and velocity (s/v)( varieswith time t as

(a)s v/

t

(b)s v/

t

(c)s v/

t

(d)s v/

t

91. A block of mass m slides down a rough inclinedplane of inclination with horizontal with zeroinitial velocity. The coefficient of frictionbetween the block and the plane is µ with

1tan ( )µ . Rate of work done by the force offriction at time t is(a) 2 sinµmg t (b) 2 (sin cos )µmg t µ (c) 2 cos (sin cos )µmg t µ (d) 2 cosµmg t

92. A car of weight W is on an inclined road thatrises by 100 m over a distnace of 1 km and

applies a constant frictional force 20W

on the car.While moving uphill on the road at a speed of10 m s–1, the car needs power P. If it needs

power 2P

while moving downhill at speed v thenvalue of v is(a) 20 m s–1 (b) 5 ms–1

(c) 15 ms–1 (d) 10 ms–1

93. A partcile of mass M is moving in a circle offixed radius R in such a way that its centripetalacceleration at time t is given by n2Rt2 where nis a constant. The power delivered to theparticle by the force acting on it, is

(a) 2 2 212

Mn R t (b) Mn2R2t

(c) MnR2t2 (d) MnR2t

94. A particle of mass m moving in the x directionwith speed 2v is hit by another particle of mass2m moving in the y-direction with speed v. Ifthe collision is perfectly ineleastic, thepercentage loss in the energy during thecollision is close to(a) 56% (b) 62%(c) 44% (d) 50%

95. A body of mass m, accelerates uniformly fromrest to v1 in time t1. As a function of timet, the instantaneous power delivered to thebody is

(a) 1

1

mv tt (b)

21

1

mv tt

(c)2

1

1

mv tt (d)

2121

mv tt

96. A car of mass m starts from rest andaccelerates so that instantaneous powerdelivered to the car has a constant magnitudeP0. The instantaneous velocity of this car isproportional to(a) t2P0 (b) t1/2

(c) t–1/2 (d)tm

97. A force of ˆ ˆ ˆ2 3 4i j k N acts on a body for 4second, produces a displacement of

ˆ ˆ ˆ(3 4 5 )i j k m . The power used is(a) 9.5 W (b) 7.5 W(c) 6.5 W (d) 4.5 W

98. A particle of mass M starting from restundergoes uniform acceleration. If the speedacquired in time T is V, the power deliveredto the particle is

(a)2MV

T(b)

2

212

MVT

(c)2

2MVT

(d)21

2MV

T99. A motor of power p0 is used to deliver water

at a certain rate through a given horizontalpipe. To increase the rate of flow of waterthrough the same pipe n times, the power ofthe motor is increased to p1. The ratio of p1to p0 is(a) n : 1 (b) n2 : 1(c) n3 : 1 (d) n4 : 1

100. A car of mass ‘m’ is driven with acceleration‘a’ along a straight level road against aconstant external resistive force ‘R’. When thevelocity of the car is ‘V’, the rate at which


55

the engine of the car is doing work will be(a) RV (b) maV(c) (R + ma)V (d) (ma – R)V

101. A body is moving uni-directionally under theinfluence of a source of constant powersupplying energy. Which of the diagramsshown in figure correctly shown thedisplacement-time curve for its motion

(a) (b)

(c) (d)

102. A pump motor is used to deliver water at acertain rate from a given pipe. To obtain twiceas much water from the same pipe in thesame time, power of the motor has to beincreased to(a) 16 times (b) 4 times(c) 8 times (d) 2 times

103. A particle of mass m is driven by a machinethat delivers a constant power k watts. If theparticle starts from rest the force on theparticle at time ‘t’ is(a) 1/2mkt (b) 1/22mkt

(c) 1/212

mkt (d) 1/22

mkt

104. A particle of mass ‘m’ is moving in circularpath of constant radius ‘r ’ such thatcentripetal acceleration is varying with time‘t’ as K2rt2 where K is a constant. The powerdelivered to the particle by the force actingon it is(a) m2K2r2t2 (b) mK2r2t(c) mK2rt2 (d) mKr2t

4. INTEGER TYPE QUESTIONS105. The velocity of a particle moving along a line

varies with distance as v = a x where a is aconstant. The work done by all forces when theparticle moves from x = 0 to x = l is 0, what is

the value of 28

ma l

.

106. A force F = Kx2 acts on a particle at an angle of60o with the x-axis. The work done in displacing

the particle from x1 to x2 will be 2 1( )K x x ,

then what is the value of + ?

107. A uniform spring is kept on a horizontalfrictionless floor such that one end is fixed to avertical wall and other end is free. Mass of thespring is m. At the instant shown in figurevelocity of free end is v and length of the springis L. Assuming that speed varies linearly fromzero to v, the kinetic energy of the spring will

be 1

mv2, what is the value of .

vL

108. An explosion breaks a rock into three parts ina horizontal plane. The of them go off at rightangles to each other. The first part of mass 1kg moves with a speed of 12 ms–1 and secondpart of mass 2 kg moves with 8 ms–1 speed. Ifthe third part lies off which 4 ms–1 speed, thenits mass (kg) is

109. A light inextensible string that goes over asmooth fixed pulley as shown in the figureconnects two blocks of masses 0.36 kg and 0.72kg. Taking g = 10 m/s2, find the work done (injoules) by the string on the block of mass 0.36kg during the first second after the system isreleased from rest.

110. Three objects A, B and C are kept in a straightline on a frictionless horizontal surface. Thesehave masses m, 2m and m, respectively. Theobject A moves towards B with a speed 9 m/sand makes an elastic collision with it. Thereafter, B makes completely inelastic collisionwith C. All motions occur on the same straightline. Find the final speed (in m/s) of the objectC.

m 2 m mA B C


56

111. A block of mass 0.18 kg is attached to a springof force-constant 2 N/m. The coefficient offriction between the block and the floor is 0.1.Initially the block is at rest and the spring isun-stretched. An impulse is given to the blockas shown in the figure. The block slides adistance of 0.06 m and comes to rest for thefirst time. The initial velocity of the block inm/s is V = N/10. Then N is

112. A particle of mass 0.2 kg is moving in onedimension under a force that delivers aconstant power 0.5 W to the particle. If theinitial speed (in ms–1) of the particle is zero,the speed (in ms–1) after 5 s is


57

T1 WORK1. d 2. c 3. c 4. c 5. b6. a 7. c 8. c 9. c 10. a11. c 12. a 13. d 14. d 15. c16. b 17. a 18. a 19. c 20. d21. a 22. c 23. a 24. a 25. b26. b 27. d 28. d

T2 CONSERVATION OF ENERGY29. c 30. a 31. d 32. a 33. b34. a 35. a 36. d 37. b 38. b39. a 40. c 41. a 42. a 43. b44. a 45. b 46. c 47. b 48. a49. a 50. d 51. a 52. b 53. c54. a 55. c 56. b 57. c 58. c59. b 60. c 61. b 62. c 63. b64. d 65. c 66. d 67. d 68. d69. b 70. d 71. c 72. a 73. b74. a 75. a 76. c 77. d 78. b79. c 80. d 81. b 82. c

T3 POWER83. c 84. c 85. c 86. b 87. c88. a 89. c 90. a 91. c 92. c93. b 94. a 95. d 96. b 97. a98. d 99. c 100. c 101. b 102. c103. b 104. b

T4 INTEGER QUESTIONS105. (4) 106. (9) 107. (6) 108. (5) 109. (8)110. (4) 111. (4) 112. (5)

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Topper’s Package Physics - XI Permutation and ...€¦ · 15/7/2020 · Topper’s Package Physics - XI Permutation and CombinationsWork, Power and Energy 44 1. WORK 1. A particle