Work, power & energy Questions and Answers

8 An old pinball game machine starts play with a handle pulled back a distance x to compress a spring with a metal ball at rest on the end When the spring is released the ball is sent forward with a significant speed into the pinball machine For this problem the ball reaches a top speed of 4 5 m s when the spring uncoils If the spring constant is 220 N m and the mass of the metal ball is 82 g determine the distance by which the spring was compressed Express your final answer in centimeters Jual 16 0

1 1 2 2 5 6 3 4 3 4 5 8 Blackened metal foil receives heat from a heated sphere placed at a distance r from it It is found that foil receive power P If the temperature and the distance of the sphere are doubled then the power received by the foil will be 1 P 2 2P 3 8P 4 4P in it takes 4 minutes in cooling from 61 C to 59 C The time tak A L

In millikan oil drop experiment a charged drop fall with a terminal velocity V If an electric field E applied vertically upwards it moves with termina velocity 2V in upward direction If electric fiel reduces to E 2 then its terminal velocity will be V A 2 C 3V B V D 2V

If we shift a body in equilibrium from A to C in a gravitational field via path AC or ABC by force F Then af 2 at C and B A The work done by the force for both paths will be same a fan and jai qui q B W W AC C W W AC D None of these Your Answer A ABC ABC

Body A of mass 4 m moving with speed u collides with another body B of mass 2m at rest The collision is head NEET 201 and elastic in nature After the collision the fraction of energy lost by the colliding body A is 1 5 9 2 1 9 3 8 9 4 4 9

A ball impinges directly on a similar ball at rest The first ball is brought to rest by the impact If half of the kinetic energy is lost by impact the value of coefficient of restitution is AIIMS 2017 1 1 2 2 2 3 m Cur 3 4 3 2

Two identical balls A and B having velocities of 0 5 ms and 0 3 ms respectively collide elastically in one dimension The velocities of B and A after the collision respectively will be NEET 2016 2 0 5 ms and 0 3 ms 1 0 5 ms and 0 3 ms 3 0 3 ms and 0 5 ms 4 0 3 ms and 0 5 ms having mass Am The lighter block com

A 50 g bullet moving with velocity 10 m s strikes a block of mass 950 g at rest and gets embedded into it The loss in kinetic energy will be RPMT 2009 1 100 2 95 3 5 4 50 hall of mass m moying with the velocity v collides haed on with another ball of mass mat rest If the coefficient CRPMT2014

Morning breakfast gives 5000 cal to a 60 kg person The efficiency of person is 30 The height upto which the person can climb up by using energy obtained from breakfast is 1 5 m 2 10 5 m 3 15 m 4 16 5 m

22 Small identical balls are attached at each end of a spring of force constant k 200 N m and relaxed length 1 20 cm Unknown amount of charges are gradually transferred to the balls in unequal amounts until the spring length becomes twice of its relaxed length What amount of work must be done by an external agency in slowly compressing the spring back to its relaxed length a 8 J c 16 J b 12 J d 20 J

Zero Marks 0 In all other cases sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre What is the ratio of the magnitude of the electric field at a distance 2R from the magnitude of the electric field at a distance of R 2 from the centre ie Er 2R Er R 2

1 10 2 eV An energy of 24 6 eV is required to remove one of the electrons from a neutral helium atom The energy In required to remove both the electrons from a neutral helium atom is 1 38 2 2 49 2 3 51 8 4 79 0

4 Have speeds varying from zero up to 50 of the X rays coming from a Coolidge tube is able to pass through a 0 1 mm thick aluminum foil The potential difference between the target and the filament is increased The thickness of aluminimum foil which will allow 50 c the X ray to pass through will be 1 zero 2 0 1 mm 3 0 1 mm 4 0 1 mm antiol as a function of frequency of incident radiation is plotted for two different photo elect

A block of mass m is moving with initial velocity on horizontal frictionless surface Find the minimum value of velocity v so that the block will complete the vertical circle 1 5Rg m V R 2 3Rg

Figure shows the intensity wavelength relations of X rays coming from two different Coolidge tubes The solid curve represents the relation for the tube A in which the potential difference between the target and the filament is V and the atomic number of the target material is Z These quantities are V and Z for the other tube Then A B 1 V V Z ZB Intensity K Wavelength 2 V V Z Z 3 V V Z Z 4 V V Z Z A

In Bohr s model of hydrogen atom the centripetal force is provided by the Coulomb attraction between the proton and the electron If a is the radius of the ground state orbit m is the mass and e the charge of an electron and is the vacuum permittivity the speed of the electron is 1 zero 2 e e 4 m 3 4ream 4KE a m e ound state to a higher energy state its orbital spe

A block placed under the head of the claw hammer as shown greatly facilitates the extraction of the nail If a 50 lb pull on the handle is required to pull the nail calculate the tension T in the nail The contacting surfaces at A are sufficiently rough to prevent slipping Select one a T 250 lb b T 150 lb c T 100 lb d T 200 lb 50 lb 20 F 2 1 8 TH

A body of mass m accelerates uniformly from rest to v in time t The instantaneous power delivered to the body an function of time t is AIEEE 200 1 my t t Y2 myt t 3 my t 1 4 myt 4 Dow delivered to

P Q A particle of mass m is driven by a machine that delivers a constant power k watts If the particle starts from rest the FE and and F force on the particle at time t is Basic NEET 2015 1 2mkt 1 2 2 mkt 1 2 3 mk 2 1 2 4 mkt 1 2

1 200 J 3 A vertical spring with force constant k is fixed on a table All ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d The net work done in the process is AIPMT 2007 1 mg h d k kd 3 mg h d kd kd 2 mg h d 4 mg h d kd to rest after attaining a height of

during the time the particle goes up is 1 0 5 J 2 1 25 J A particle is projected at 60 to the horizontal with 1 K 2 zero AIEEE 2008 An athlete in the olympic games covers a distance of 100 m in 10 s His kinetic energy can be estimated to be in the 3 1 25 J 4 0 5 J a kinetic energy K The kinetic energy at the highest point is AIEEE 2007 3 K 4 4 K 2

1 8 J 2 11 J A bullet of mass 10 g moving horizontally with a celocity of 400 ms strikes a wood block of mass 2 kg which suspended by light inextensible string of length 5 m As a result the centre of gravity of the block found to rise a vert INEET 20 distance of 10 cm The speed of the bullet after it emerges out horizontally from the block will be 1 100 ms 2 80 ms 3 120 ms 4 160 ms falling from a height of 1 km It hit the ground with a speed of 50

1 E 2 2 2E 3 E 4 A stone projected vertically up with a velocity u reaches a maximum height h When it is at a height 3h 4 from the ground the ratio of KE and PE at that point is consider PE 0 at the point of projectory 1 1 1 2 1 2 3 1 3 4 3 1 10cpring is stretched by 2 cm it stores 100 J of energy If it is stretched further by 2 cm the stored energy will

The potential energy for a force field F is given by U x y sin x y Magnitude of the force acting on the particle Telegrali of mass m at 1 1 is Para pifferentiates 2 2 3 4 0 of work done in carrying a body from P to Q from

53 2 2 2 1 1 For the path PQR in a conservative force field fig the amount of work done in carrying a body from P to Q from Q to R are 5 J 2 J respectively The work done in carrying the body from P to R will be 1 7 J R 2 3J 3 21 J 4 zero moving in a potential region given by U K x y z The force acting on the particle is given by

x Figure shows a particle sliding on a frictionless track which terminates in a straight horizontal section If the particle farts slipping from the point A how far away from the track will the particle hit the ground Paper moren 1 0m 1 At a horizontal distance of 1 m from the end of the track 2 At a horizontal distance of 2 m from the end of the track 3 At a horizontal distance of 3 m from the end of the track 4 Insufficient information To 5m

A body of mass m kg initially at rest attains a velocity of v m sec in time t under the action of a constant force F T power supplied to the mass is 1 mv t 2 mv t 3 Fv 4 Fv 2

produced will be heat 1 350 cal The amount of work done 1 5 000 J 2 150 cal 3 60 cal 4 6 cal in pumping water out of a cubical vessel of height 1 m is nearly Take g 10 m s 2 10 000 J 3 5 J 4 10 J S fm 10 m

The kinetic energy K of a particle moving in a straight line depends upon the distance s as K as The force acting on the particle is Look 1 2as 2 2mas 3 2a 4 as on loading then the energy stored by the spring is T is the tension in the spring and K is forc

When a man walks on a horizontal surface with constant velocity work done by G 1 friction is zero 2 contact force is non zero 3 gravity is non zero 4 None of these dieplacement of the body in metre is a function of time as follows

Two springs of spring constants 1500 N m and 3000 N m respectively are stretched with the same force They will have potential energy in the ratio 1 4 1 2 1 4 43 2 1 4 1 2 menended from a spiral spring of natural length L the spring gets stretched through a

1 0 5 kw 2 5 kw 3 50 kw A man is riding on a cycle with velocity 7 2 km hr up a hill having a slope 1 in 20 The total mass of the man and cycle is 100 kg The power of the man is 98 W 2 49 W 3 196 W 4 147 W A body of mass m kg initially at rest attains a velocity of v m sec in time t under the action of a constant force F The

1 s 2 s 3 s A force acts on a 3 gm particle in such a way that the position of the particle as a function of time is given by x 3t 4t t where x is meters and t is in seconds The work done during the first 4 second is 1 384 mJ 4 541 mJ od to 2 168 mJ 3 528 mJ lowor vertically a block of mass M at a distance x at a constant downward acceleration g 2 The work

1 total energy kinetic energy 3 potential energy A body starts from rest with uniform acceleration and acquires a velocity V in time T The instantaneous kinetic energ of the body after any time t is proportional to 1 V T t 2 V T t 1 V T 3 V T t If u mand F denote the velocity momentum and kinetic energy of the particle then

A square ABCD of sides 1m rest on side AB A force of 100 N acting at 45 deg with AB acts at point C which is diagonally opposite to A The moment of this force about A is 2 Points zero 71Nm 100Nm 144Nm

1 A collar B of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5 m The spring lying in the plane of the circular track and having spring constant 200 Nm undeformed when the collar is at A If the collar starts from rest at B the normal reaction exerted by the track on the collar when it passes through A is is e 7m B 15m C

7 BC D E F X The force acting on a particle constrained to move along x axis varies as shown Identify the correct option s 1 E is a neutral equilibrium position 2 F is a stable equilibrium position A 3 B D are unstable equilibrium positin 4 Both 1 and 3

The block in Fig 2 of mass m is pressed against the ideal spring of elastic constant k and compresses it by a distance d The block is released and ascends the inclined plane whose angle of inclination is 8 The coefficient of kinetic friction between the block and the plane is u What maximum height h does the block rise in the plane Express h as a function of m k d 0 and g Do the free body diagram k m u h

Force acting on a particle is F ayi Bxy j Find the work done in Joule by this force when particle is moved along the line 2x 3y from origin to the point 3 2 take all quantities in SI units and a 1 1

A 100 00 kg roller coaster car is pressed against a spring of constant 1 425 N m and compresses it 5 00 meters It is then released and rolls up an inclined portion of the track How high up the incline will car roll before coming to a stop

7 12 SolveLancer Test A body of mass m moving at velocity u collides with a body of mass m which is initially at rest The second body is moving with a velocity of u in its initial direction after the collision Determine the kinetic energy lost by the first body following the collision Restitution coefficient SolveLancer Test a 15 mu 16 b 16 c 1 5 mu 32 9 d mu 32 a mu b

A body of mass m was slowly pulled up the hill by a force F which at each point was directed along the tangent of the trajectory All surfaces are smooth Find the work performed by this force m h

A force F k yi xj where kis a positive constant 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 force Fon the particle is 1998 2M

An ideal spring with spring constant kis hung from the ceiling and a block of mass M is attached to its lower end The mass is released with the spring initially unstretched Then the maximum extension in the spring is 2002 2M

A particle of mass 0 2 kg is moving in one dimension under a force that delivers a constant power 0 5 W to the particle If the initial speed in ms 1 of the partial is zero the speed In ms 1 after 5s is

Consider the conservation of energy equation below AK AU AE int W Q TMW TMT TET TER A ball of mass m falls from a height h to the floor a Identify the appropriate version of the equation above for the system of the ball and the Earth O AEint Q TET TER O AU W OAK W OAK AU 0 Use this equation to calculate the speed of the ball just before it strikes the Earth Use the following as necessary m for mass h for height g for acceleration due to gravity V b Identify the appropriate version of the equation above for the system of the ball O AK W O AEint Q TET TER OAK AU 0 O AU W Use this equation to calculate the speed of the ball just before it strikes the Earth Use the following as necessary m for mass h for height g for acceleration due to gravity

Two smooth spheres made of identical material having masses m and 2m undergoes an oblique impact as shown in figure The initial velocities of the masses are also shown The impact force is along the line joining their centres along the x axis The coefficient of restitution is 5 9 The velocities of the masses after the impact and the approximate percentage loss in kinetic energy A 101 8 51 4 15 i 3 3 c 101 81 10 i 41 25 3 3 y axis 2m v 5m s m v 10m s 5 B 1 81 1 4 20 3 D 101 81 1 4 20 3 sin 4 5 x axi

16 A particle of mass m is located in a unidimensional potential field where the potential energy of the particle depends on the coordinate x as U x U 1 cos ax Up and a are constants Find the period of small oscillations that the particle performs about the equilibrium position ba Solve the foregoing problem if the potential energy has the form x a x b x where a and b are positive constants

A block of mass m placed on a smooth horizontal surface is attached to a spring and is held at rest by a force P as shown Suddenly the force P changes its direction opposite to the previous one How many times is the maximum extension of the spring longer compared to its initial compression SME

20 A particle can be moved in the xy plane from O to P along different paths as shown in figure A force that continuously acts on the particle during its motion along any path is F 41 6j N Consider the action of only the given force and match column I and column II y Column I A Work done is 80 J B Mechanical energy is conserved C Linear momentum is not conserved D Angular momentum about O is non zero at some instant M N P 8m 8m L Column II P For the path OP Q For the path OLP R For the path OMP S For the path ONP T For the path OQP