Question Bank for JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति Self Evaluation Test - Work, Energy and Power

1)

A ball whose kinetic energy is E, is projected at an angle of \[45{}^\circ \] to the horizontal. The kinetic energy of the ball at the highest point of its flight will be

A)

E

B)

\[E/\sqrt{2}\]

C)

\[E/2\]

D)

zero

View Solution

2)

A load hangs from a travelling crane, moving horizontally with velocity v. If the load is not to swing more than 4 m horizontally, when the crane is stopped suddenly, what is the maximum allowable speed of the crane?

A)

4.05 m/s

B)

4.00 m/s

C)

3.00 m/s

D)

3.50 m/s

View Solution

3)

A 10 kg block is pulled in the vertical plane along a frictionless surface in the form of an arc of a circle of radius 10 m. The applied force is of 200 N as shown in figure. If the block had started from rest at A, the velocity at B would be

A)

1.7 m/s

B)

17 m/s

C)

27 m/s

D)

34 m/s

View Solution

4)

Calculate the work done on the tool by \[\vec{F}\left( 11.25\hat{i}+11.25\hat{j} \right)N\] if the tool is first moved out along the x-axis to the point \[x=3.00m,\] \[y=0\] and then moved parallel to the y-axis to\[x=3.00m,\]\[y=3.00\text{ }m\].

A)

67.5 J

B)

85 J

C)

102 J

D)

7.5 J

View Solution

5)

A force F acting on an object varies with distance x as shown here. The force is in N and x in m. The work done by the force in moving the object from \[x=0\] to \[x=6\] m is

A)

18.0 J

B)

13.5 J

C)

9.0 J

D)

4.5 J

View Solution

6)

A particle describe a horizontal circle of radius 0.5 m with uniform speed. The centripetal force acting is 10 N. The work done in describing a semicircle is

A)

zero

B)

5J

C)

\[5\pi J\]

D)

\[10\,\pi J\]

View Solution

7)

A force F acts on a particle such that its position x changes as shown in the figure. The work done by the particle as it moves from \[x=0\] to 20 m is

A)

37.5 J

B)

10 J

C)

45 J

D)

22.5 J

View Solution

8)

Two identical beads of \[m=100\] gram are connected by an inextensible massless string can slide along the two arms AC and BC of a rigid smooth wire frame in a vertical plane. If the system is released from rest, the kinetic energy of the first particle when they have moved by a distance of 0.1 m is\[8 \times {{10}^{-3}}J\]. Find the value of \[\operatorname{x}.\left( g=10m/{{s}^{2}} \right)~~~~~~\]

A)

8

B)

6

C)

9

D)

11

View Solution

9)

A cord is used to lower vertically a block of mass M, a distance d at a constant downward acceleration of\[g/4\]. The work done by the cord on the block is

A)

\[Mg\frac{d}{4}\]

B)

\[3Mg\frac{d}{4}\]

C)

\[-3Mg\frac{d}{4}\]

D)

\[Mgd\]

View Solution

10)

A spring of spring constant \[5\times 103 N/m\] is stretched initially by 5 cm from the upstretched position. Then the work required to stretch it further by another 5 cm is

A)

18.75 J

B)

25.00 J

C)

6.25 J

D)

12.50 J

View Solution

11)

A uniform force of \[\left( 3\hat{i}+\hat{k} \right)\] newton acts on a article of mass 2 kg. The particle is displaced from position \[\left( 2\hat{i}+\hat{k} \right)\] meter to position \[\left( 4\hat{i}+3\hat{j}-\hat{k} \right)\] meter. The work done by the force on the particle is

A)

6 J

B)

13 J

C)

15 J

D)

9 J

View Solution

12)

The position of a particle of mass 4 g, acted upon by a constant force is given by\[\operatorname{x} = 4{{t}^{2}} + t\], where x is in metre and t in second. The work done during the first 2 seconds is

A)

\[128mJ\]

B)

\[512mJ\]

C)

\[576mJ\]

D)

\[144mJ\]

View Solution

13)

A body moves a distance of 10 m along a straight line under the action of a force of 5 newtons. If the work done is 25 joules, the angle which the force makes with the direction of motion of body is

A)

\[0{}^\circ \]

B)

\[30{}^\circ \]

C)

\[60{}^\circ \]

D)

\[90{}^\circ \]

View Solution

14)

A block of mass m is suspended by a light thread from a lift. The lift is moving upward with uniform velocity v. From the frame of lift, the work done by tension on the block in t seconds will be

A)

\[-mgvt\]

B)

\[0\]

C)

\[\frac{mgvt}{2}\]

D)

\[mgvt\]

View Solution

15)

The work done by a force\[\vec{F}=\left( -6{{x}^{3}}\hat{i} \right)N,\]in displacing a particle from \[x=4\text{ }m\text{ }to\text{ }x=-2\]m is

A)

\[360J\]

B)

\[240J\]

C)

\[-240J\]

D)

\[-360J\]

View Solution

16)

Work done by static friction on an object

A)

May be positive

B)

must be negative

C)

Must be zero

D)

None of these

View Solution

17)

A particle is placed at the origin and a force \[F=kx\] is acting on it (where k is positive constant). If\[U(0)=0\], the graph of \[U(x)\]versus x will be (where U is the potential energy function)

A)

B)

C)

D)

View Solution

18)

Calculate the K.E and RE. of the ball half way up, when a ball of mass 0.1 kg is thrown vertically upwards with an initial speed of \[20\text{ }m{{s}^{-1}}\].

A)

\[10\text{ }J,\text{ }20\text{ }J\]

B)

\[10\,J,\text{ }10\,J\]

C)

\[15\text{ }J,\text{ }8\text{ }J\]

D)

\[8\,J,16\,J\]

View Solution

19)

At time \[t=0s\] particle starts moving along the x-axis. If its kinetic energy increases uniformly with time f, the net force acting on it must be proportional to

A)

\[\sqrt{t}\]

B)

constant

C)

\[t\]

D)

\[\frac{1}{\sqrt{t}}\]

View Solution

20)

Two bodies of masses 4 kg and 5 kg are moving with equal momentum. Then the ratio of their respective kinetic energies is

A)

\[4:5\]

B)

\[2:1\]

C)

\[1:3\]

D)

\[5:4\]

View Solution

21)

A rod of mass m and length (is made to stand at an angle of \[60{}^\circ \] with the vertical. Potential energy of the rod in this position is

A)

\[mg\,\ell \]

B)

\[\frac{mg\,\ell }{2}\]

C)

\[\frac{mg\,\ell }{3}\]

D)

\[\frac{mg\,\ell }{4}\]

View Solution

22)

A 2 kg block slides on a horizontal floor with a speed of4m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000 N/m. The spring compresses by Critical Thinking

A)

8.5 cm

B)

5.5 cm

C)

2.5 cm

D)

11.0 cm

View Solution

23)

The potential energy of a conservative system is given by\[\operatorname{U} = a{{y}^{2}}-by\], where y represents the position of the particle and a as well as b are constants. What is the force acting on the system?

A)

\[-ay\]

B)

\[-by\]

C)

\[2ay-b\]

D)

\[\operatorname{b}-2ay\]

View Solution

24)

A block of mass \[m=0.1\] kg is connected to a spring of unknown spring constant k. It is compressed to a distance \[\left( \frac{x}{2} \right)\] from its equilibrium position and released from rest. After approaching half the distance from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity\[3m{{s}^{-1}}\]. The total initial energy of the spring is

A)

\[0.3\text{ }J\]

B)

\[0.6\text{ }J\]

C)

\[0.8\text{ }J\]

D)

\[1.5\text{ }J\]

View Solution

25)

A block of 1 kg is kept on a rough surface of an elevator moving up with constant velocity of 5m/s. In 10 seconds work done by normal reaction (the block does not slide on the inclined surface)

(i) from ground frame is 320 J

(ii) is equal to work done by friction force in elevator frame

(iii) is equal to work done by friction in ground frame of the three statements given above, the one that is true is given by the choice

A)

Only (i)

B)

(ii) and (iii)

C)

(i) and (ii)

D)

only (iii)

View Solution

26)

300 J of work is done in sliding a 2 kg block up an inclined plane of height 10m. Taking\[g=10m/{{s}^{2}}\], work done against friction is

A)

100J

B)

zero

C)

1000J

D)

200J

View Solution

27)

A force acts on a 30gm particle in such a way that the position of the particle as a function of time is given by\[x=3t-4{{t}^{2}}+{{t}^{3}}\], where x is in metres and t is in seconds. The work done during the first 4 seconds is

A)

576mJ

B)

450mJ

C)

490mJ

D)

530mJ

View Solution

28)

A man starts walking from a point on the surface of earth (assumed smooth) and reaches diagonally opposite point. What is the work done by him?

A)

Zero

B)

Positive

C)

Negative

D)

Nothing can be said

View Solution

29)

The components of a force acting on a particle are varying according to the graphs shown. When the particles move from (0,5,6) to (2,10,0) then the work done by this force is

A)

192J

B)

\[\frac{400}{3}J\]

C)

\[\frac{287}{2}J\]

D)

None of these

View Solution

30)

A force \[\operatorname{F}=- K \left( y\hat{i} + x\hat{j} \right)\] (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken 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 on the particle is

A)

\[- 2K{{a}^{2}}\]

B)

\[2K{{a}^{2}}\]

C)

\[- K{{a}^{2}}\]

D)

\[K{{a}^{2}}\]

View Solution

31)

A block of mass 1 kg is pulled along the curve path ACB by a tangential force as shown in figure. The work done by the frictional force when the block moves from A to B is

A)

5 J

B)

10 J

C)

20 J

D)

None of these

View Solution

32)

If stretch in a spring of force constant k is tripled then the ratio of elastic potential energy in the two cases will be

A)

9:1

B)

1:6

C)

3:1

D)

1:3

View Solution

33)

One man takes 1 min. to raise a box to a height of 1 metre and another man takes 1/2 min. to do so. The energy of the

A)

Two is different

B)

two is same

C)

first is more

D)

second is more

View Solution

34)

If the momentum of a body is increased by 50%, then the percentage increase in its kinetic energy

A)

50%

B)

100%

C)

125%

D)

200%

View Solution

35)

A ball dropped from a height of 2m reaches to a height of 1.5m before hitting the ground. Then the percentage of potential energy lost is

A)

25

B)

30

C)

50

D)

100

View Solution

36)

A body starts from rest and acquires a velocity V in time T. The work done on the body in time t will be proportional to

A)

\[\frac{V}{T}t\]

B)

\[\frac{{{V}^{2}}}{T}{{t}^{2}}\]

C)

\[\frac{{{V}^{2}}}{{{T}^{2}}}t\]

D)

\[\frac{{{V}^{2}}}{{{T}^{2}}}{{t}^{2}}\]

View Solution

37)

Four particles given, have same momentum. Which has maximum kinetic energy

A)

Proton

B)

Electron

C)

Deutron

D)

a-particles

View Solution

38)

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be

A)

\[\sqrt{2}m/s\]

B)

\[\left( \sqrt{2}-1 \right)m/s\]

C)

\[\frac{1}{\left( \sqrt{2}-1 \right)}m/s\]

D)

View Solution

39)

A steel ball of mass 5g is thrown downward with velocity 10 m/s from height 19.5 m. It penetrates sand by 50 cm. The change in mechanical energy will be

A)

1 J

B)

1.25 J

C)

1.5 J

D)

1.75 J

View Solution

40)

The figure gives the potential energy function U(x) for a system in which a particle is in one- dimensional motion. In which region the magnitude of the force on the particle is greatest:

A)

OA

B)

AB

C)

BC

D)

CD

View Solution

41)

A ball is allowed to fall from a height of 10 m. If there is 40% loss of energy due to air friction, then velocity of the ball when it hit the ground is

A)

\[\sqrt{190}m/s\]

B)

\[\sqrt{180}m/s\]

C)

\[\sqrt{150}m/s\]

D)

\[\sqrt{120}m/s\]

View Solution

42)

A body falls freely under gravity. Its velocity is v when it has lost potential energy equal to U. What is the mass of the body?

A)

\[{{\operatorname{U}}^{2}}/{{v}^{2}}\]

B)

\[2{{\operatorname{U}}^{2}}/{{v}^{2}}\]

C)

\[2\operatorname{U}/{{v}^{2}}\]

D)

\[\operatorname{U}/{{v}^{2}}\]

View Solution

43)

When a body is projected vertically up from the ground with certain velocity, its potential energy and kinetic energy at a point A are in the ratio 2 : 3. If the same body is projected with double the previous velocity, then at the same point A the ratio of its potential energy to kinetic energy is

A)

9 : 1

B)

2 : 9

C)

1 : 9

D)

9 : 2

View Solution

44)

A uniform chain of length 2 m and mass 0.1 kg overhangs a smooth table with its two third part lying on the table. Find the kinetic energy of the chain as it completely slips- off the table.

A)

\[\frac{8}{9}J\]

B)

\[\frac{12}{5}J\]

C)

\[\frac{3}{7}J\]

D)

\[\frac{11}{3}J\]

View Solution

45)

A 1 kg particle at a height of 8m has a speed of 1 Om/s down a fixed incline making an angle \[53{}^\circ \] with horizontal as shown in figure. It slides on a horizontal section of length 10 m at ground level and then up a fixed incline making an angle \[37{}^\circ \] with horizontal. All surfaces have\[{{\mu }_{k}} = 0.5\]. How far (in meters) from point 0 (bottom of right inclined plane), along the incline making an angle \[37{}^\circ \] with horizontal, does the particle first come to rest?

A)

1m

B)

0.5m

C)

2m

D)

5m

View Solution

46)

A man places a chain of mass m and length L on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is

A)

\[-mg\frac{L}{2}\]

B)

\[-\frac{mg\,L}{4}\]

C)

\[-\frac{3mg\,L}{8}\]

D)

\[-\frac{mg\,L}{8}\]

View Solution

47)

. A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to \[8\times 1{{0}^{-4}}J\]by the end of the second revolution after the beginning of the motion?

A)

\[0.1 m/{{s}^{2}}\]

B)

\[0.15 m/{{s}^{2}}\]

C)

\[0.18 m/{{s}^{2}}\]

D)

\[0.2 m/{{s}^{2}}\]

View Solution

48)

A variable force P is maintained tangent to a frictionless cylindrical surface of radius a as shown in figure. By slowly varying this force, a block of weight W is moved and the spring to which it is stretched from position 1 to position 2. The work done by the force P is

A)

\[\operatorname{W} a sin \theta \]

B)

\[\frac{1}{2} k{{a}^{2}} {{\theta }^{2}}\]

C)

\[\operatorname{W}\,a\,sin \theta + k\,{{a}^{2}}{{\theta }^{2}}\]

D)

\[\operatorname{W}\,a\,sin \theta +\frac{1}{2} k\,{{a}^{2}}{{\theta }^{2}}\]

View Solution

49)

A straight bar, of mass 15 kg and length 2 m, at rest on a frictionless horizontal surface, receives an instantaneous impulse of 7.5 Ns perpendicular to the bar. If the impulse is applied at the mid-point of the bar, the energy transferred is

A)

3.2 J

B)

1.9J

C)

3.8 J

D)

2.5 J

View Solution

50)

A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as\[\operatorname{F}\left( x \right)=-\operatorname{kx}+a{{x}^{3}}\]. Here k and a are positive constants. For\[x\ge 0\], the functional form of the potential energy U(x) of the particle is

A)

B)

C)

D)

View Solution

51)

Two blocks of masses m and M are joined with an ideal spring of spring constant k and kept on a rough surface as shown. The spring is initially unstretched and the coefficient of friction between the blocks and the horizontal surface is u. What should be the maximum speed of the block of mass M such that the smaller block does not move?

A)

\[\mu g\sqrt{\frac{Mm}{\left( M+m \right)k}}\]

B)

\[\mu g\sqrt{\frac{\left( M+m \right)k}{Mm}}\]

C)

\[\mu g\sqrt{\frac{\left( 2M+m \right)m}{kM}}\]

D)

None of these

View Solution

52)

Two blocks of masses \[{{m}_{1}}=10\,kg\,\,and\,\,{{m}_{2}}=20\,\,kg\] are connected by a spring of stiffness\[k=200N/m\]. The coefficient of friction between the blocks ' and the fixed horizontal surface is\[\mu = 0.1\]. Find the minimum constant horizontal force F (in newtons) to be applied to m, in order to slide the mass my \[\left[ Take g = 10 m/{{s}^{2}} \right]\]

A)

\[\mu {{m}_{1}}g+\frac{\mu {{m}_{2}}g}{2}\]

B)

\[\mu {{m}_{1}}g+\mu {{m}_{2}}g\]

C)

\[\mu {{m}_{1}}g+\frac{\mu {{m}_{2}}g}{2}\]

D)

\[\frac{\mu {{m}_{1}}g+\mu {{m}_{2}}g}{2}\]

View Solution

53)

Two objects each of mass m are connected with a uniform rope having same mass m and length \[\ell =10/3\] m are shown in the figure. The rope can slide on a frictionless pulley which is fixed to the edge of the table. Initially 1/3 of the rope hangs vertically. Friction is negligible everywhere.

If the system is released from rest and object on the right hand side descend further by a distance of 1/3, what would be the speed of the object (in m/s)?

A)

2.12 m/s

B)

3.33 m/s

C)

0.33 m/s

D)

4.12 m/s

View Solution

54)

A bead of mass m is sliding down the fixed inclined rod without friction. It is connected to a point P on the horizontal surface with a light spring of spring constant k. The bead is initially released from rest and the spring is initially unstressed and vertical. The bead just stops at the bottom of the inclined rod. Find the angle which the inclined rod makes with horizontal.

A)

\[{{\cot }^{-1}}\left( 1+\sqrt{\frac{2mg}{kh}} \right)\]

B)

\[ta{{n}^{-1}}\left( 1+\sqrt{\frac{2mg}{kh}} \right)\]

C)

\[{{\cot }^{-1}}\left( 1+\sqrt{\frac{mg}{kh}} \right)\]

D)

\[ta{{n}^{-1}}\left( 1+\sqrt{\frac{mg}{kh}} \right)\]

View Solution

55)

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function of time is given by

A)

\[\frac{m{{v}^{2}}}{{{T}^{2}}}.{{t}^{2}}\]

B)

\[\frac{m{{v}^{2}}}{{{T}^{2}}}.t\]

C)

\[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}.{{t}^{2}}\]

D)

\[\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}.t\]

View Solution

56)

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude pg. The instantaneous velocity of this car is proportiourl to:

A)

\[{{\operatorname{t}}^{2}}{{p}_{o}}\]

B)

\[{{\operatorname{t}}^{1/2}}\]

C)

\[{{\operatorname{t}}^{-1/2}}\]

D)

\[\frac{t}{\sqrt{m}}\]

View Solution

57)

How much water, a pump of 2 kW can raise in one minute to a height of 10 m, take\[\operatorname{g} = 10 m/{{s}^{2}}\]?

A)

1000

B)

1200

C)

100

D)

2000

View Solution

58)

In figure, a block having a mass of 5 kg is released from rest, where the spring acting on the body are horizontal and have a tension of 50 N. The force constant of each spring is, \[k=500\text{ }N/m\]. The velocity of the block after it has descended by 0.3m.

A)

0

B)

I m/s

C)

2 m/s

D)

none

View Solution

59)

The engine of a vehicle delivers constant power. If the vehicle is moving up the inclined plane then, its velocity,

A)

Must remain constant

B)

Must increase

C)

Must decrease

D)

May increase, decrease or remain same.

View Solution

60)

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time 'f' is proportional to

A)

\[{{t}^{3/4}}\]

B)

\[{{t}^{3/2}}\]

C)

\[{{t}^{1/4}}\]

D)

\[{{t}^{1/2}}\]

View Solution

61)

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

A)

At the highest position of the body

B)

At the instant just before the body hits the earth

C)

It remains constant all through

D)

At the instant just after the body is projected

View Solution

62)

A body of mass 10 kg moves with a velocity v of 2m/s along a circular path of radius 8 m. The power produced by the body will be

A)

10J/s

B)

98J/s

C)

49J/s

D)

zero

View Solution

63)

A constant power P is applied to a car starting from rest. If v is the velocity of the car at time t, then

A)

\[v\propto t\]

B)

\[v\propto \frac{1}{t}\]

C)

\[v\propto \sqrt{t}\]

D)

\[v\propto \frac{1}{\sqrt{t}}\]

View Solution

64)

If two persons A and B take 2 seconds and 4 seconds respectively to lift an object to the same height h, then the ratio of their powers is

A)

1:2

B)

1:1

C)

2:1

D)

1:3

View Solution

65)

A 10 H.P. motor pumps out water from a well of depth 20 m and fills a water tank of volume 2380 litres at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is \[\left( g= 10m{{s}^{-2}} \right)\]

A)

5 minutes

B)

10 minutes

C)

15 minutes

D)

20 minutes

View Solution

66)

If a machine gun fires n bullets per second each with kinetic energy K, then the power of the machine gun is

A)

\[{{\operatorname{nK}}^{2}}\]

B)

\[\frac{K}{n}\]

C)

\[{{\operatorname{n}}^{2}}K\]

D)

\[\operatorname{nK}\]

View Solution

67)

A ring of mass m can slide over a smooth vertical rod as shown in figure. The ring is connected to a spring of force constant\[k=4mg\text{ }I\text{ }R\], where 2 R is the natural length of the spring. The other end of spring is fixed to the ground at a horizontal distance 2 R from the base of the rod. If the mass is released at a height 1.5 R, then the velocity of the ring as it reaches the ground is Critical Thinking

A)

\[\sqrt{gR}\]

B)

\[2\sqrt{gR}\]

C)

\[\sqrt{2gR}\]

D)

\[\sqrt{3gR}\]

View Solution

68)

An engineer claims to have made an engine delivering 10kW power with fuel consumption of 1 g/s. The calorific value of fuel is 2 kcal/g. This claim is

A)

Valid

B)

Invalid

C)

Depends on engine design

D)

Dependent on load

View Solution

69)

A force applied by an engine of a train of mass \[2.05\times 1{{0}^{6}} kg\]changes its velocity from 5m/s to 25 m/s in 5 minutes. The power of the engine is

A)

1.025 MW

B)

2.05 MW

C)

5 MW

D)

6 MW

View Solution

70)

A 10 m long iron chain of linear mass density \[0.8 kg {{m}^{-1}}\] is hanging freely from a rigid support. If\[\operatorname{g}~=10 m{{s}^{-2}}\], then the power required to left the chain up to the point of support in 10 second

A)

10 W

B)

20 W

C)

30 W

D)

40 W

View Solution

71)

The net power of all the forces acting on a particle (P) versus time curve is shown. Work done upon the particle from A to B

A)

Increases

B)

Decreases

C)

First increases then

D)

First decreases then

View Solution

72)

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy For wind speed v, the electrical power output will be proportional to

A)

v

B)

\[{{v}^{2}}\]

C)

\[{{v}^{3}}\]

D)

\[{{v}^{4}}\]

View Solution

73)

A body of mass 1 kg begins to move under the action of a time dependent force\[\vec{F}=\left( 2t\hat{i}+3{{t}^{2}}\hat{j} \right]) N,\], where \[\hat{i} and \hat{j}\]are unit vectors alogn x and y axis. What power will be developed by the force at the time t?

A)

\[\left( 2{{t}^{2}}+3{{t}^{3}} \right)W\]

B)

\[\left( 2{{t}^{2}}+4{{t}^{4}} \right)W\]

C)

\[\left( 2{{t}^{3}}+3{{t}^{4}} \right)W\]

D)

\[\left( 2{{t}^{3}}+3{{t}^{5}} \right)W\]

View Solution

74)

The energy content of gasoline is\[3.6\times 1{{0}^{7}}J/L\]. A motor with an efficiency of 20% is needed at fall output power of 45 kW for 50.0 minutes. How many litres of gasoline are required to operate the motor for this amount of time?

A)

0.31 L

B)

0.38 L

C)

1.6 L

D)

19 L

View Solution

75)

An escalator has 2400 W of power available to move passengers from the first floor of a mall to the second, 6.0 m vertically. If the average mass of the passengers is 65 kg, what is the maximum number of passengers that can be carried to the second floor in 1.0 minute?

A)

4

B)

5

C)

22

D)

37

View Solution

76)

An iron ball of mass m, suspended by a light inextensible string of length from a fixed point, 0, is shifted by an angle \[{{\theta }_{0}}\] as shown so as to strike the vertical wall perpendicularly. The ' maximum angle made by the string with vertical after the first collision, if e is the coefficient of restitution, is

A)

\[{{\sin }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\]

B)

\[{{\cos }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\]

C)

\[{{\tan }^{-1}}\left\{ 1-{{e}^{2}}\left( 1-\cos {{\theta }_{0}} \right) \right\}\]

D)

Zero

View Solution

77)

Mass \[{{m}_{1}}\] strikes m which is at rest. The ratio of masses for which they will collide again (collision between ball and wall are elastic, coefficient of restitution between \[{{\operatorname{m}}_{1}} and {{m}_{2}}\]is e and all the surfaces are smooth.)

A)

\[<\frac{e}{2+e}\]

B)

\[>\frac{2e}{2+e}\]

C)

\[\ge \frac{e}{2\left( 2+e \right)}\]

D)

None of the above

View Solution

78)

Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be

A)

\[\frac{u}{12}\left( \hat{i}+\sqrt{3}\hat{j} \right)\]

B)

\[\frac{u}{12}\left( \hat{i}-\sqrt{3}\hat{j} \right)\]

C)

\[\frac{u}{12}\left( -\hat{i}+\sqrt{3}\hat{j} \right)\]

D)

\[\frac{u}{12}\left( -\hat{i}-\sqrt{3}\hat{j} \right)\]

View Solution

79)

Two small bodies of masses 'm' and '2m' are placed in a fixed smooth horizontal circular hollow tube of mean radius 'r' as shown. The mass 'm' is moving with speed 'u' and the mass '2m' is stationary. After their first collision, the time elapsed for next collision is [ coefficient of restitution e = 1/2 ]

A)

\[\frac{2\pi r}{u}\]

B)

\[\frac{4\pi r}{u}\]

C)

\[\frac{3\pi r}{u}\]

D)

\[\frac{12\pi r}{u}\]

View Solution

80)

A block lying on a smooth surface with spring connected to it is pulled by an external force as shown. Initially the velocity of ends A and B of the spring are 4 m/s and 2 m/s respectively. If the energy of the spring is increasing at the rate of 20 J/sec, then the stretch in the spring is Critical Thinking

A)

1.0 cm

B)

2.0 cm

C)

10 cm

D)

2.0 cm

View Solution

81)

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 Km and applies a constant frictional force \[\frac{W}{20}\] on the car. While moving uphill on the road at a speed of\[10\text{ }m{{s}^{-1}}\], the car needs power P. If it needs power \[\frac{P}{2}\] while moving downhill at speed v then value of v is:

A)

\[20m{{s}^{-1}}\]

B)

\[5m{{s}^{-1}}\]

C)

\[15m{{s}^{-1}}\]

D)

\[10m{{s}^{-1}}\]

View Solution

82)

A block of mass \[m=1\text{ }kg\]is moving with a constant acceleration \[a=1\text{ }m/{{s}^{2}}\]on a rough horizontal plane. The coefficient of friction between the block and plane is\[u=0.1\]. The initial velocity of block is zero at\[t=0\]. The power delivered by the external agent at a time t = 2 sec from the beginning is equal to \[\left( Takeg= 10m/{{s}^{2}} \right)\]

A)

1 watt

B)

2 watt

C)

3 watt

D)

4 watt

View Solution

83)

A ball of mass m hits the floor making an angle 9 as shown in the figure. Ife is the coefficient of restitution, then which relation is true, for the velocity component before and after collision?

A)

\[{{V}^{1}}\sin \theta '=V\,sin\theta \]

B)

\[{{V}^{1}}\sin \theta '=-\,sin\theta \]

C)

\[{{V}^{1}}\cos \theta '=V\,\cos \theta \]

D)

\[{{V}^{1}}\cos \theta '=-V\,\cos \theta \]

View Solution

84)

A rubber ball is dropped from a height of 5m on a plane, where the acceleration due to gravity is not shown. On bouncing it rises 1.Sm. The ball loses its velocity on bouncing by a factor of

A)

\[\frac{16}{25}\]

B)

\[\frac{2}{5}\]

C)

\[\frac{3}{5}\]

D)

\[\frac{9}{25}\]

View Solution

85)

A ball of mass m moving with a constant velocity strikes against a ball of same mass at rest. If e= coefficient of restitution, then what will be the ratio of velocity of two balls after collision?

A)

\[\frac{1-e}{1+e}\]

B)

\[\frac{e-1}{e+1}\]

C)

\[\frac{1+e}{1-e}\]

D)

\[\frac{2+e}{e-1}\]

View Solution

86)

The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is

A)

\[\frac{k{{L}^{2}}}{2M}\]

B)

\[\sqrt{Mk}L\]

C)

\[\frac{M{{L}^{2}}}{k}\]

D)

zero

View Solution

87)

An object of mass 2.0 kg makes an elastic collision with another object of mass M at rest and continues to move in the original direction but with one-fourth of its original speed. What is the value of M?

A)

0.75kg

B)

1.0kg

C)

1.2kg

D)

None of these

View Solution

88)

A bullet of mass 20g and moving with 600 m/s collides with a block of mass 4 kg hanging with the string. What is velocity of bullet when it comes out of block, if block rises to height 0.2 m after collision?

A)

200mA

B)

150 m/s

C)

400 m/s

D)

300 m7s

View Solution

89)

A block of mass 0.50 kg is moving with a speed of \[2.00\text{ }m{{s}^{-1}}\] on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

A)

0.16 J

B)

1.00 J

C)

0.67 J

D)

0.34 J

View Solution

90)

The heart of man pumps 5 liters of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be \[13.6\times 1{{0}^{3}}kg/{{m}^{3}}\]and \[\operatorname{g} = 10m/{{s}^{2}}\]then the power of heart in watt is:

A)

2.35

B)

3.0

C)

1.50

D)

1.70

View Solution

91)

An engine is hauling a train of mass M kg on a level track at a constant speed v m/s. The resistance due to friction is\[fN/kg\]. What extra power must the engine develop to maintain the speed up a gradient of h in s :

A)

\[\frac{mghv}{s}\]

B)

\[\frac{mghs}{v}\]

C)

\[Mghvs\]

D)

zero

View Solution

92)

An electric pump is used to fill an overhead tank of capacity \[9{{m}^{3}}\] kept at a height of 10m above the ground. If the pump takes 5 minutes to fill the tank by consuming 10 kW power the efficiency of the pump should be \[\left( g = 10 m{{s}^{-2}} \right)\]

A)

60%

B)

40%

C)

20%

D)

30%

View Solution

93)

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of energy. How much power is generated by the turbine?\[\left( g = 10 m/{{s}^{2}} \right)\]

A)

8.1 k W

B)

10.2 kW

C)

12.3 k W

D)

7.0 kW

View Solution

94)

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration \[{{a}_{c}}\] is varying with time t as \[{{a}_{c}}={{k}^{2}}r{{t}^{2}}\] where k is a constant. The power delivered to the particles by the force acting on it is

A)

\[2\pi m{{k}^{2}}{{r}^{2}}t\]

B)

\[m{{k}^{2}}{{r}^{2}}t\]

C)

\[\frac{\left( m{{k}^{4}}{{r}^{2}}{{t}^{5}} \right)}{3}\]

D)

zero

View Solution

95)

A uniform rope of linear mass density 'k and length (. is coiled on a smooth horizontal surface. One end is pulled up with constant velocity v. Then the average power applied by the external agent in pulling the entire rope just off the horizontal surface is

A)

\[\frac{1}{2}\lambda \ell {{v}^{2}}+\frac{\lambda {{\ell }^{2}}g}{2}\]

B)

\[\lambda \ell gv\]

C)

\[\frac{1}{2}\lambda {{v}^{3}}+\frac{\lambda \ell vg}{2}\]

D)

\[\lambda \ell vg+\frac{1}{2}\lambda {{v}^{3}}\]

View Solution

96)

A particle fells from a height A on a fixed horizontal plane and rebounds. If e is the coefficient of restitution, the total distance travelled by the particle before it stops rebounding is

A)

\[\frac{h}{2}\frac{\left[ 1-{{e}^{2}} \right]}{\left[ 1+{{e}^{2}} \right]}\]

B)

\[\frac{h\left[ 1-{{e}^{2}} \right]}{\left[ 1+{{e}^{2}} \right]}\]

C)

\[\frac{h}{2}\frac{\left[ 1+{{e}^{2}} \right]}{\left[ 1-{{e}^{2}} \right]}\]

D)

\[\frac{h\left[ 1+{{e}^{2}} \right]}{\left[ 1-{{e}^{2}} \right]}\]

View Solution

97)

A collision occurs between two identical balls of mass m each, moving with velocity\[{{\overrightarrow{\mu }}_{1}}\,and\,{{\overrightarrow{\mu }}_{2}}\]. If the collision is head on and the energy lost in the collision is \[\Delta E=\frac{3}{16}{{({{\vec{u}}_{1}}-{{\vec{u}}_{2}})}^{2}}\] then the coefficient of restitution is

A)

0.25

B)

0.75

C)

0.5

D)

0.9

View Solution

98)

A massive disc of radius R is moved with a constant velocity m on a frictionless table. Another small disc collides with it elastically with a speed of\[{{v}_{0}}= 0.3 m/s\], the velocities of the discs being parallel. The distance (/shown in the figure is equal to R/2, friction between the discs is negligible. For which u (in m/s) will the small disc move perpendicularly to its original motion after the collision?

A)

0.1

B)

0.5

C)

1.0

D)

0.01

View Solution

99)

A shell is fired from a cannon with a velocity v (m/sec.) at an angle 9 with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed (in m/sec.) of the other piece immediately after the explosion is

A)

\[3\,v\,cos\text{ }\theta \]

B)

\[2\,v\,cos\text{ }\theta \]

C)

\[\frac{3}{2}\,v\,cos\text{ }\theta \]

D)

\[\sqrt{\frac{3}{2}}\,v\,cos\text{ }\theta \]

View Solution

100)

An object of mass m is projected vertically upwards with a speed of \[{{v}_{0}}\]At the same moment another object of mass M, which is initially above the projected one, is dropped from a height of h. The two point like objects collide completely in elastically, and they stick to each other. Find kinetic energy (in J) of combined mass just before it hits the ground.\[(Given : m = 1 kg, {{v}_{0}}= 20 m/s,\] \[M=3 kg, h=20m,g= 10m/{{s}^{2}})\]

A)

550 J

B)

650 J

C)

450 J

D)

250 J

View Solution

JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति Question Bank

done Self Evaluation Test - Work, Energy and Power Total Questions - 100

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Self Evaluation Test - Work, Energy and Power

Self Evaluation Test - Work, Energy and Power Total Questions - 100