Work, power & energy Questions and Answers

diment mass m kg moving in one time t in second by the equa Comprehension Type s in first six seconds is 4 36 m vi then the particle is taken fr the origin in the x y plane 4 zero IX From the graph choose the correct statements N 20 10 0 10 20 B C D 10 20 30 40 50 I HE F 60 70 cm G X 25 Find the work done at the end of displacement 20 cm 1 2 J 2 7 J 3 5 J LEVEL 126 Find the work done at the end of displacement 40cm 1 4 J 2 7 J 3 6 J 27 Find the work done at the end of displacement 60cm 1 6 J 2 7 J 3 5 J Matrix Match Type 4 9 J 4 9 J 4 8 J Column II

16 The ball of mass m is thrown with speed Vo The ball strikes the block of mass 2m and sticks to it Find the maximum compression of spring gh migh M M ih Igh m w Smooth m 1 Vo3K No 3k 2m 3 Vo K k 2m k mmmm m 2 Voy2k 3m 4 Vok city at JI 21 The graph of force in figure A body of m s at x 0 Find th 10 m F N 10 N 12 N 1 436 J 3 484 J A partial

41 Six charges are placed at the vertices of a regular hexagon as shown in the figure The electric field on the line passing through point O and perpendicular to the plane of the figure at a distance of x a from O is 0 Qa TREX 20 Qa TEX 3 Q 30a TEX Q 4 zero 1 400 2 20 WIN ZAS NM2

A body of mass 2 kg falls from a height of 20 m What is the loss in potential energy 1 400 J 2 300 J 3 200 J 4 100 J

Illustration 16 Force between the atoms of a diatomic molecule has its origin in the interaction the nuclei present in each atom This force is conservative and associated potential energy U r is to ac approximation represented by the Lennard Jones potential function U r U 9 A97 a r F Here r is the distance between the two atoms and U and a are positive constants Develop express he associated force and find the equilibrium separation between the atoms dU 1 Using equation F we obtain the expression for the force dr 6U a 2 a 13 12 L At equilibrium force must be zero Therefore the equilibrium separation is r 2 a

Two discs A and B are mounted co axially on a vertical axle The discs have moments of inertia I and 21 respectively about the common axis Disc A is imparted an initial angular velocity 2w using the entire potential energy of a spring compressed by a distance X Disc B is imparted an angular velocity w by a spring having the same spring constant and com pressed by a distance x Both the discs rotate in the clockwise direction i The ratio A 2 X1 x2 is 1 LC

A particle moves in the X Y plane under the influence of a force such that its is linear momentum P t A i cos kt j sin kt where A and k are constants The angle between the force and the momentum is UPSEAT 2000 IIT JEE 2007 a 0 c 45 b 30 d 90

4 A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v If the collision is perfectly inelastic the percentage loss in the energy during the collision is close to a 44 56 b 50 d 62

In an XY horizontal plane a force field F 40 N m yi x is present where x and y are the coordinates of any point on the plane A smooth rod AB is fixed in the plane as shown in the figure A particle of mass 5 kg is to be released with a velocity in this force field such that it reaches to point B Find the minimum velocity that must be imparted along the rod at A such that it reaches to B A 1 m s C 3 m s B 2 m s D 4 m s avi A 0 1 Y m 45 B 1 0 X m I is as shown in the fig

A pendulum consisting of a massless string of length 20 cm and a tiny bob of mass 100 g is set up as a conical pendulum Its bob now performs 75 rpm Calculate kinetic energy and increase in

41 The terminal potential difference across A and B in the circuit shown is 1 E Ir 3 E E www B r 2 E Ir 4 Zero

A 1 0 hp motor pumps out water from a well of depth 20 m and fills a water tank of volume 2238 73 liters at a height of 10 m from the ground The running time of the motor to fill the empty water tank is g 10m s see W 1 5 minutes 2 10 minutes All

A ball with mass mis attached to the end of a rod of mass M and length I The other end of the rod is pivoted so that the ball can move in a vertical circle The rod is held in the horizontal position as shown in the figure and then given just enough a downward push so that the ball swings down and just reaches the vertical upward position having zero speed there Now answer the following questions 3 The change in potential energy of the system ball rod is M a mgl b M m gl c mgl 2 the d M m 2 OL gl

Find the acceleration of block of mass m Assume pulleys are massless and frictionless A g 3 B 2g 3 C g 2 D None of these m MAUER 2m

Block A shown in figure can slide over fixed rigid frictionless wire of quarter circular shape String connected to A and B is massless and inextensible System is released from rest when 0 0 Determine the ratio k MA MB approximate integer value for which the system will come to rest again when 0 30 MA BIN

43 A ball is released from the top of a high building from rest The average power delivered to the ball by the gravity in first second and third second of motion is 1 1 6 8 3 1 1 1 2 2 4 8 4 1 3 5

7 A force F k yi x where k is constant acts on a particle moving in the xy plane Starting from origin the particle is taken along y axis to the point 0 a The work done by agent applying the force F on the particle is 1 k x y 3 ky 2 Zero 4 kx

2 An object of mass 500g initially at rest acted upon by a variable force whose X component varies with x in the manner shown The velocities of the object at point X 8 m and X 12 m would be the respective values of nearly m a F N 20 10 10t 20 25 F 4 5 8 10 12 at 1 18 m s and 24 4 m s 2 23 m s and 24 4 m s 23 m s and 20 6 m s 2 mvxx 2 1 3 mu 1 1 x m x 2 1x3x v q Jas vod V sim

Two plates of masses m and m are connected by a spring whose spring constant is k What force should be applied to the upper plate front to raise the lower one after the force is removed Neglect the mass of the spring a g m m c gm m 2 b b gm1m d g m m

In a certain field the potential energy is U ax bx where a and b constants The particle is in stable equilibrium at x equal to 1 Zero 3 2a 3b 2 4 a 3b 2a b

4 The potential energy between two atoms in a where a and b are positive constants and x is the distance between the atoms The atom is in stable equilibrium when a molecule is given by U x 1 X 2 X 3 x 0 LAY 2a b 11a 5b 1 6 1 6 a 1 6 12 b 6 X

A quarter horse power motor runs at a speed of 600 rpm Assuming 40 efficiency the wor done by the motor in one rotation will be a 7 46 J b 7400 J d 74 6 J c 7 46 erg e 746 J

An engine can pull 4 coaches at a maximum speed of 20 m s Mass of the engine is twice the mass of every coach Assuming resistive forces to be proportional to the weight approximate maximum speeds of the engine when it pulls 12 and 6 coaches are A 8 5 m s and 15 m s respectively C 8 5 m s and 13 m s respectively B 6 5 m s and 8 m s respectively D 10 5 m s and 15 m s respectively

Figure function of x for a particle moving along the x axis M abcd astel Consider the following statements A a c and d are points of equilibrium B a is a point of stable equilibrium C b is a stable equilibrium point Correct statements are only A 2 only A and B 3 only C

A particle suspended by a light inextensible thread of length is projected horizontally from its lowest position with velocity 4g The particle will leave the circular path at a height from its lowest position 1 3 3 1 2 4 3 2 51 3 4 21

ustration 33 44 A 30000 kg air plane takes off at a speed of 50 m s and 5 min later it is at an elevation of 3 km v ALLEN a speed of 100 m s What average power is required during this 5 min if 40 percent of the power is use Illustra in overcoming dissipative forces on nerov sur

17 During the rocket propulsion gases ejecting with velocity 1 km s relative to rocket The rate of fuel m consumption is kg s where m is the 10 instantaneous mass of the rocket If air resistance varies according to equation f 0 15 mv then terminal veloicty of the rocket is 1 300 m s Ons iro 3 7 92 km s 2 600 m s 4 11 2 km s

A force F 31 ci 2k acting on a particle causes a displacement d 41 2j 3k If the work c is 6J then the value of c is a 12 46 b 0 d 1

A thin circular rod is supported by a hinge at A Attached to point A is a spring of spring constant k and natural length equal to arc length AB A bead of mass m not attached to the spring can slide without friction along the rod The bead is released at rest making an angle 0 with the vertical A For the bead to complete the vertical circle k 2mg Re2 D k B B For all the values of k normal will remain radially inwards for the complete motion C Tangential acceleration of block is maximum at point B mg 2D D Normal force on the bead at point B just after loosing contact with spring is N 19 9 and 0 60 1 cos 0 mg for

A particle A of mass kg is moving in the positive x direction Its initial position is x 0 initial 10 7 velocity is 1 m s The velocity at x 10m is use the graph given Power in watts 4

m Two objects A and B of mass m are connected with a uniform rope of length A 1 0 3 m and mass m as shown in the figure The rope can slide in a tube which forms a quarter of a circle and which is fixed to the edge of the table Initially 1 3 of the rope hangs vertically Friction is negligible If the system is released from rest and B descends a distance of 1 3 what is the speed in m s of B Hoonch gris m B

acts on a particle moving in the x y 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 forces F on the particle is a 2 Kq c Ka b 2 Ka d Ka

A uniform chain of length L and mass M is lying 5 on a smooth table and one third of its length is hanging vertically down over the edge of the table If g is acceleration due to gravity work required to pull the hanging part on to the table is 2 3 1 MgL MgL 3 MgL 9 4 MgL 18

A block of mass m is kept in an elevator which starts moving downward with an acceleration a as shown in figure The block is observed by two observers A and B for a time interval to 2 A mg t The observer B finds that the work done by gravity is 1 B mg t 2 A zero A A A mat2 2 DgS V 8 The observer B finds that work done by normal reaction N is 2 B Na t 2 Na 1 2 According to observer B the net work done on the block is 1 2 B ma t 0 fa B b 0 According to the observer A A the work done by gravity is zero C the work done by pseudo force is zero C mga t 2 0 C A C mga t2 g b AC 2800 Ov 1 D mga t D None of these 1 2 D mga t slount or lannon adi bail B the work done by normal reaction is zero D all the above

23 Potential difference across the terminals of the battery shown in the figure is 10 V 1 8 V 2 10 V 3 5 V 4 0 V r 19 www www 40 No current short circuit As AV

a A point mass m is connected with ideal inextensible string of length and other end of string is tied at point O as shown in the figure The string is made horizontal and mass is released from point A to perform vertical circular motion There is a nail at point N such that ON r Find the value of r so that mass m is able to just perform complete vertical circular motion about point N O F g 4 2 3 0 B l

34 Which of the following represents loudness versus intensity of sound graph ort 3 1 L L 1 2 4 L L A metal wire of linear mass dopl stretched with I I 1 9

A body dropped from a height h reaches the ground with a speed gh Th work done by the air friction is ifadta fello gh fold D D PRE A mgh 0 25 mgh B 0 5 mgh 0 125 mgh

m we can calculate tensions T and Illustrations tion 16 A block of mass 25 kg is raised in two different ways by a 50 kg man as shown in fig What is the action in the two cases If the floor yields to a normal force of 700 N which mode should the man adopt to lift the block without the yielding of the floor 50 kg block m 25 kg mg Mg mg b mward direction reaction being equal on he downw

II A rocket of total mass 3180 kg is traveling in outer space with a velocity of 115 m s To alter its course by 35 0 its rockets can be fired briefly in a direction perpendicular to its original motion If the rocket gases are expelled at a speed of 1750 m s how much mass must be expelled

A 100W bulb B and two 60W bulbs B B are connected to a 250V source Now W W2 W3 ar the output powers of the bulbs B B2 B3 respectively then B B 000 THE 250V A W W W B B W W W3 C W W W D W W W

ch the following items Column I A Work done by all the forces B Work done by internal conservative forces C Work done by external forces Column II Change in mechanical energy q Change in kinetic energy r P Negative of change in potential energy

7K The tractor is moving with velocity of 6 km hr Mass of belt is 720 gm KE of belt is di 1 4 J 2 1 J 3 2 J 4 6 J

To maintain a rotor at a uniform angular speed of 200 rad s an engine needs to transmit a torque of 180 Nm What is the power required by the engine Note uniform angular velocity in the absence of fric tion implies zero torque In practice applied torque is needed to counter frictional torque Assume that the engine is 100 efficient NCERT 36 kW

41 A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1 05 kJ of energy The initial velocity of the shell is a 40 m s c 100 m s b 120 m s d 80 m s

1 A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s It collides with a horizontal spring of force constant 200 N m The maximum compression produced in the spring will be 1 0 7 m 3 0 5 m 2 0 2 m 4 0 6 m

insulating A cone made of material has a total charge Q spread uniformly over its sloping surface Calculate the energy required to take a test charge q from infinity to B

2 An engine pumps water through a hose pipe W passes through the pipe and leaves it with a veloc of 2 m s The mass per unit length of water in t pipe is 100 kg m What is the power of the eng 1 800 W 2 400 W 3 200 W

1 Work done by the force F x yi N in displacing a body from 0 0 m to 1 2 m is 1 8 J 3 2 J 2 1 J ON TUM 4 Zero

g 10 m s The displacement x of a body of mass 1 kg on smooth horizontal surface as a function of time t is given by where x is in metres and t is in seconds Find the work done by the external agent for the first one FR X 3 second 11