Work, power & energy Questions and Answers

A bullet is fired from horizontal ground at some angle passes through the point 3R R 4 4 the range of the bullet Assume point of the fire to be origin and the bullet moves in x y plane with x axis horizontal and y axis vertically upwards Angle of projection is radian Find a T 180 1 1 where R is

A massless platform is kept on a light elastic spring as shown in the figure When particle of mass 0 1 kg is dropped on the pan from a height of 0 24 m the particle strikes the pan and the spring is compressed by 0 01 m From what height hould the particle be dropped to cause a compression f0 04 m 0 96 m b 2 96 m d 0 48 m 0 1 kg llllll

Find the de Broglie wavelength of electrons with kinetic energies a 10 eV b 1 0 keV c 10 keV

4 A small disc of mass m on an inclined plane of inclination with the horizontal is connected to a nail driven into the plane with the help of a light inextensible cord of length 1 Coefficient of friction between the plane and the disc is tane The disc is given such a horizontal velocity at the lowest position that it moves on a complete circular path around the nail without wrapping the cord on the nail a Where is the disc when tensile force in the cord becomes minimum b How much minimum velocity should be given to the disk at the lowest position to round a complete circle

1 A light elastic cord of force constant k and relaxed length is suspended from the ceiling A bead of mass m threaded on the cord is held motionless close to the ceiling and released If the bead slides down the cord with a constant speed u relative to the ceiling find expression for thermal power dissipated during sliding of the bead

A block attached to a spring kept on a smooth surface is pulled by a constant horizontal force as shown in the figure Initially the spring is in the natural state Then the maximum positive work that the applied force F can do is Given that spring does not break kc 2 0 A F k B 2F k ression x of the spring C 00 0000000 D F2

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

Kinetic energy of a particle moving in a straight line is proportional to the time t The magnitude of force acting on the particle is 1 Directly proportional to velocity of particle is 2 Inversely proportional to t 3 Inversely proportional to speed of the particle 4 Both 2 and 3

A certain amount of water boils in 10 minutes in an electric kettle If same amount of water has to be boiled by another coil having double resistance then time taken by the coil is using same supply 1 20 minute 2 5 minute

D P Q sine and W Q cose A perfect smooth sphere A of mass 2 kg is in contact with a rectangular block B of mass 4 kg and vertical wall as shown in the figure All surfaces are smooth Find normal reaction by vertical wall on sphere A 2 25 N A 37 B INT C 80 N D 45 N

as FA A B C 7 x 1 At point A the particle is at stable equilibrium 2 At point B the particle is at stable equilibrium 3 At point C the particle is at stable equilibrium

06 Laws of Motion 2 3 For a uniform rope of mass Mg a Stationary system T Msgx b Accelerating upwards Tx c Accelerating downwards Tx M M a Tx X Msgx L Mg b Tx Msx M g a c Tx Msx M g g a Msx L g Msx L a FBD of g a mot inproqmco na noist M gx L T M gx stationary Mg FBD of section muando ebru fre accelerating upward accelerating downward

A projectile is fired at 30 with momentum p neglecting friction the change in kinetic energy when it returns back to the ground will be 2 30 1 zero 3 60

A block strikes the free end of a horizontal spring with the other end fixed placed on a smooth surface with a speed v After compressing the spring by x the speed of the block reduces to half Calculate the maximum compression of the spring Solution Let maximum compression be x max 1 2mv 1 2m 1 2 12 27 lustration 27 mv then by COME 1 2kx 1kx 72 max 4 X X 2 max max 2 3 X

A ring of mass m 0 3 kg can slide freely on smooth vertical rod A light and inextensible string is connected to the ring and passes over a smooth and fixed pulley as shown in the figure The distance of the pulley from the rod is 0 8 m and the other end of the string is connected to a block of mass M 0 5 kg The ring is held in level with pulley and then released from rest Determine a the distance by which the ring moves down before coming to rest for the first time b how far below the initial position is the equilibrium point M L 0 8 m ME

Problem 10 A 10 kw drilling machine is used to drill a bore in a small aluminium block of mass 8 0 kg How much is the rise of temperature of the block in 2 5 minuts assuming 50 of the power is used in heating the machines itself or lost to the surroundings Specific heat of aluminium 876 J kg K Ans 107 02

Three blocks with masses m 2m and 3m are connected by strings as shown in the figure After an upward force F is applied on block m the masses move upward at constant speed v What is the net force on the block of mass 2m g is the acceleration due to gravity 11 F 2m 3m tv 2 2 ma 1 2 ma

A force of 10 N is required to move a conducting loop through a non uniform magnetic field at 2 ms Variable rate of production of electrical energy in watt in loop is 1 5 2 20 3 10 4 Zero

Work done by internal forces on a system may be 1 Positive 2 Negative 3 Zero 4 All of these sino by A

A vehicle of mass m is moving on a rough horizontal road with momentum P If the coefficient of friction between the tyres and the road be u then stopping distance is p A B 2 m g p 2 m g C P 2 mg P mg D

The blades of a wind mill sweep out a circle of area A If wind flows with velocity v perpendicular to blades of wind mill and its density is p then the mechanical power received by wind mill is PAV 1 2 3 pAv 2 pAv 2 4 2pAv

A uniform rod of length 1 m having mass 1 kg rests against a smooth wall at an angle of 30 with the ground Fig 1 64 Calculate the force exerted by the ground on the rod 13 2 N fy 30 G F mg 30 D

A body of mass 10 kg is displaced from point A 2 1 3 to point B 3 3 4 under the effect of a force of magnitude 20 N in the direction of 61 81 Calculate W D by the force 2 20 6J 3 44 J 1 22 J 4 Zero

Two blocks A and B each of mass m are connected by means of a pulley spring system on a smooth inclined plane of inclination as shown in the figure All the pulleys and spring are ideal Now B is slightly displaced from its equilibrium position It starts to oscillate Time period of oscillation of B will be Take m 4 kg K 5 N m 3 3 14 6 28 A B m

A fixed wedge ABC is in the shape of an equilateral triangle of side Initially a chain of length 2 and mass m rests on the wedge as shown The chain is slowly being pulled down by the application of a force F as shown Find the work done by gravity till the time the chain leaves the wedge 60 60

3 A block of mass 2 kg initially at rest moves under the action of an applied horizontal force of 6 N on a rough horizontal surface The coefficient of friction between block and surface is 0 1 The work done by the applied force in 10 s is Take g 10 m s

7 A particle of mass m is driven by a machine that delivers a constant power k watts If the particle starts from rest the force on the particle at time t is AIPMT 2015 1 1 mk t2 2 2 mk V2 1 t2 1 3 mk tz

C d 9 8 erg A body of mass 10kg is moving at a constant speed of 20 m s over a frictionless surface The workdon by the weight is C a 200 J b 100 J d 300 J c zero

23 An object of mass 500 g initially at rest acted upon by a variable force whose X component varies with X in the manner shown The velocities of the object a pointX 8 m and X 12 m would be the respective values of nearly F N 20 10 10 20 25 4 58 10 12 x m a 18 m s and 24 4 m s b 23 m s and 24

15 A gardener waters plants by a pipe of cross section 1 mm The water comes out at the rate of 100 cc s The reactionary force exerted on the hand of the gardener is 1 10 N 3 1000 N 2 100 N 4 500 N

kr protons which may be written as F Ce r r a Write down the dimensional formulae and appropriate SI units of C and k b Suppose that k 1 fermi and that the repulsive electric force between the protons is just balangod

An object of mass 500 g initially at rest is acted upon by a variable force whose X component varies with x in the manner shown The velocities of the object at the points x 8 m and x 12 m would have the respective values of nearly NEET 2019 Odisha F N 20 10 10 20 25 45 8 10 12 1 18 m s and 20 6 m s 2 18 m s and 24 4 m s 3 23 m s and 24 4 m s x m

A child s pogo stick figure stores energy in a spring with a force constant of 2 5 x 10 N m At position A x 0 10 m the spring compression is a maximum and the child is momentarily at rest At position B xg 0 the spring is relaxed and the child is moving upward At position C the child is again momentarily at rest at the top of the jump The combined mass of child and pogo stick is 25 kg Calculate the total energy of the child stick earth system if both gravitational and elastic potential energies are zero for x 0 C A B LAA TL Xe 3 150 J 4 75 J

9 A 1000 kg roller coaster car moves from point A to B then C Find the potential energy at each point A 30 m B 10 m C 25 m

A table of height 1 m has a hole in the middle of its surface A thin platinum chain of length 1 m is placed loosely coiled close to the hole as shown in the figure One end of the chain is pulled a little way through the hole and then released Friction is negligible and as a result the chain runs smoothly through the hole with increasing speed 1 m FRA 1m FOR 7 With what speed the first end strikes the floor RET 1 1 56 m sec 3 3 56 m sec the chain reach the floor 2 2 56 m sec auktur foon Sich 4 4 56 m sec

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

50 A force acts on a 3 g particle in such a way that the position of the particle as a function of time is given by x 3t 4t 3 where x is in metres and t is in seconds The work done during the first 4 second is 1 490 mJ 3 576 m l 2 450 mJ 4 528 m J

A small block of mass 2 kg is projected on a horizontal smooth floor with speed 4 m s which merges into a rough vertical circular path in shape of a quarter circle as shown in the figure The coefficient of friction between the block and circular path is 0 2 If the radius of the circular path is 0 2 m then the speed of the block when it reaches end of circular path is the figure shows side view 1 2 m s 2 2 7 m s A

39 A 2 kg ball is thrown up with an initial speed 12 m s and reaches a maximum height of 10 m How much energy is dissipated by air drag acting on the ball during the ascent 1 40 J 2 56 J 3 36 J 4 72 J

The gravitational field is given as 7 41 61 N kg If a particle is moved from 0 5 3 m to 5 2 0 m on the line 6y 4x 10 then work done is m 1 kg 1 30 J 2 10 J 3 20 J 4 Zero 7

7 A cubical block of wood of edge 3 cm floats in water The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot Find the maximum weight that can be put on the block without wetting it Density of wood 800 kg m constant of the spring 50 Nm Take g 10 m s 3 and spring

i In this case force exerted by the spring F and displacement of the block point B are in the same direction so 1ooooooooo W XO 0 W Fdx kxdx 1 10x 0 2 XO 4 0 XO Je 0 In this case work done by spring is negative F Immo ooooo In this case work done is positive ii In this case force exerted by spring on the block and its displacement an opposite so kx dx kx 1x xo Ans

A spring of mass m is pulled such that a given instant velocity of both of its end is v in the opposite direction Find the kinetic energy of the spring 68000000

APQ is a rough surface The portion AP is parabolic given by equation x 16y The point A assumed to be origin The portion PQ is a straight line of length 20 3 m the coefficient of friction between block and 1 A block of mass 3 kg 3 is moved on surface APQ by applying a force on it The direction of force is always tangential to the surface APQ The line PQ is tangent on the curve AP at P If the block moves very slowly on the surface then find the work done by applying force in joule surface APQ is A 12 m

2 A particle of charge q 4 C and mass m 10 mg starts moving from the origin under the action of an electric field E 4i and magnetic field B 0 27 Its velocity at x 3 0 is 47 3j The value of x is 125 115 a m 16 b 135 16 c m d m 16 145 16 m

mason is supplied with bricks by his assistant who is 3 m below him the assistant tossing the brick vertically up The speed of the brick when it reaches the mason is 2 m s What percentage of energy used up by the servant serves no useful purpose a 9 8 b 4 9 d 10 c 5 6

In a two atom system equilibrium distance between centers is r Ro Centre of one atom is at origin and centre of other is at r away Potential energy of system is given by 12 U U where U is a positive constant with units of joules The atoms Ro r 2 vibrates with restoring force for this potential energy function is given by F kx where 9nUo k R n will be

An ammeter and a voltmeter of resistance R are connected in series to an electric cell of negligible internal resistance Their readings are A and V respectively If another resistance R is connected in parallel with the voltmeter then a Both A and V will increase b Both A and V will decrease c A will decrease and V will increase A will increase and V will decrease

Three forces 3 1 31 k 7 2i 9k and 11 21 j 6k are acting on a particle Calculate the work done in displacing the particle from point 4 1 1 to point 11 6 8 A horizontal force F is used to pull a box placed on a floor Variation in the force with position coordinate

A system of wedge and block as shown in fig released with the spring in its natural length Al surfaces are frictionless Maximum elongation in the spring will be 373 1 3 2mg sin 0 K 4mg sin 0 K 8888 112 4 mysi no kx 0 X mg sin 0 K mg sin 0 K