Work, power & energy Questions and Answers

8 A uniform chain of length and mass moverhangs 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 1 mgl 3 mgl 2 mgl 4 5 mgl

5 A mass M slides on a 45 smooth inclined plane of height H as shown The mass M moves downwards strikes the ground and sticks to it Masses of blocks are equal The distance moved by mass M along the inclined plane before it finally stops is S Which of the following is correct Take 2 1 4 1 S 3 S 5H 7 7H M 45 80 g M H H 2 2 S 4 S H 7 3H

The 300 kg bar B originally at rest is being towed over a series of small rollers Compute the force in the cable when t 5 sec if the motor M is drawing the cable for a short time at a rate of v 0 4t m s where t is in second 0 t 6s How far does the bar move in 5s Neglect the mass of the cable pulley P and the rollers Assume no friction acts on block B M 55 PO 1 T 5 00 KN s 0 300 m 2 T 1 200 kN s 1 25 m 3 T 5 00 kN s 4 00 m 4 T 1 20 kN s 16 670 m

The magnitude of the resistive force on a cruising plane is directly proportional to v2 where v is the planes velocity The power expended by the plane is P when the plane is cruising at velocity v The power expended by the plane when the plane is cruising at velocity 2v is X The value of X P is

7 Two parallel plate capacitors A and B of capacitance 1 F and 5 F are charged separately to the same potential of 100 V Now the positive plate of A is connected to the negative plate of B and negative of A to positive of B 1 Final charge on capacitor A is a 76 67 F c 66 67 uF b 84 43 uF d 37 74 F 2 Final energy stored in the capacitors a 1 67x10 2 J c 1 2x10 2 J b 6 71x10 2 J d 1 33x10 2 J

4 D 2 and 3 A weight is hung freely from the end of a spring A boy then slowly pushes the weight upwards until the spring becomes slack The gain in gravitational poetential energy of the weight during this process is equal to A The work done by the boy against the gravitational force acting on the weight B The loss of the stored energy by the spring minus the work done by the tension in the spring C The work done on the weight by the boy plus the stored energy lost by the spring D The work done on the weight by the boy minus the workdone by the tension in the spring plus the stored energy lost by the spring

2 moles of monatomic gas at temperature 27 C is mixed with 3 moles of diatomic gas at temperatur 127 C then temperature of mixture is approximately 1 98 2 57 C 3 37 C 4 87 C

5 A small disc is projected on a horizontal floor with a speed u Coefficient of friction between the disc and the floor varies according to equation u Ho kx where to and k are positive constants and x is distance travelled by the disc Find distance slid by the disc on the floor Acceleration of free fall is g

Two beads of mass m are positioned at the top of a frictionless hoop of mass M and radius R which stands vertically on ground The beads are now given tiny kicks and they slide down the hoop one to the right and one to the left as shown in figure Then choose the correct options m M A The contact force from the ground immediately after the tiny kicks on the hoop is M 2m g time during the motion is B The contact force from the ground on the hoop is M 2mig at the instant when radius vector makes an angle of cos 2 3 with the upward vertical for which the hoop will rise off the ground at some C The smallest value of 3 2 D The hoop will never rise off the ground irrespective of the values of m and M

3 A force F 10 0 50 x acts on a particle in the x direction where F is in Newton and x in metre Find the work done by this force during a displacement from x 0 to x 3 0 m A 21 J C 30 0 J B 32 25 J D 30 25 J

The binding energy per nucleon for C12 is 7 68 MeV and that for C13 is 7 47 MeV What is the energy required to remove a neutron from C13 a 0 21 MeV c 4 95 MeV b 2 52 MeV d 2 75 MeV

ustration 20 A body falling on the ground from a height of 10 m rebounds to a height 2 5 m calculate the i percentage loss in K E ii ratio of the velocities of the body just before and after the collision

A particle is moved from 0 0 to a a under a force F 31 4 from two paths Path 1 is OP and path 2 is OQP Let W1 and W be the work done by this force in these two paths Then O W W O W 2W2 W2 2W1 p a a K 45 X

A particle of mass m is moving on a circular path under the action of a radially inward acting conservative force F the particle is r is the radius of the circular path 2r Ok 2r Ok 2r The total energy of

e potenital energy U in joule of a particle of mass 2 kg moving in X Y plane follows the law 2x 4y where x y are the co ordinates in meter of the particle If the particle is at rest at 4 4 at ne t 0 then Choose the incorrect statement at t 2 2sec the particle crosses the y axis at t 2sec the particle crosses the x axis The particle has kinetic energy of 40 joule when it crosses y axis The kinetic energy of the particle when it crosses axis is 40 joule

The system of the wedge and the block connected by a massless spring as shown in the figure is released with the spring in its natural length Friction is ab maximum elongation in the spring will be 3Mg 5k O 6Mg 5k 4Mg 5k eeeeeeeee M k M 37

A block of mass m sliding down an incline at constant speed is initially at a height h above the ground as shown in the figure above The coefficient of kinetic friction between the mass and the incline is m If the mass continues to slide down the incline at a constant speed how much energy is dissipated by friction by the time the mass reaches the bottom of the incline Omgh O mgh h m 90

Water in a bucket is whirled in a vertical circle with a string attached to it The water does not fall down even when the bucket is inverted at the top of its path We conclude that in this position mv mg r mg is greater than my r mg is not greater than mg is not less than mv r mv r

3 69 A particle is suspended vertically from a point inextensible massless string of length L as shown in figure 3 132 A vertical line AB is at a distance L 8 from O as is given a horizontal velocity u At some point its motion ceases to be circular and eventually the object passes through line AB At the instant of crossing AB its velocity is horizontal Find u 12 at 1 O L L 8 B Figure 3 132

coast the 3 45 The resistance to motion of an automobile depends on road friction which is almost independent of speed and on air ame drag which is proportional to speed squared For a car with a weight of 12000 N the total resistance force F is given by F 300 1 8 v where F is in newtons and v is in meters per second Calculate the power required to accelerate the car at 0 92 m s when the speed is 80 kph ime Ans 51 kW the

3 17 Show that the height h to which a man of mass m can jump is given approximately by 1 2g m h 2 W 4SP 3 where P is the maximum power the man can use and s is the height of centre of mass of man from ground F tra th an

2 A massless string of length 21 connects two hockey pucks that lie on frictionless ice A constant horizontal force F is applied to the midpoint of the string perpendicular to it What is the kinetic energy of the puck just before the pucks collide A B FI C 2FI D F

following graphs represents the above situation E 4 28 ALLEN k A mmmm m x 0 0 O 0 m B 9 The system is released from rest when spring is at its natural length Spring constant is 100 N m and mass of each block is 10 kg The velocity v of block A as a function of position x is given as v ax bx The value of a b is equal to 1001CJA101620000 Leader Phase VII VIII Live VI VII 10 10 2021 Paper 12 A car travels around a horizontal circular track with non uniform speed The acceleration vectors at four different points are shown in Fig four nonzero vectors have equal length At which of these points is the car s speed the largest

312 2 ower supplied to a particle of mass 2 kg varies with time as P 3 ere t is in seconds If velocity of particle at t 0 is v 0 then velocity of article at t 2 will be 01ms 1 02ms 04 ms watt 06ms 1

A disc of mass M rotates freely about a fixed horizontal axis through its centre A thin cotton pad is fixed to its rim which can absorb water The mass of water dripping onto pad is m g s After what time will the angular velocity of disc get reduced to half of its initial value Ignore friction R Wheel Disc O 2M m OM 2m OM 4m Water OM m

Question 2 A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm How much further will it penetrate before coming to the rest assuming that it faces constant resistance in motion 1 5cm 1cm 3 cm 2cm

a Given a vector field F 2xyi x 3y z j y 2z k i Determine whether if F is conservative or not 3 mark Find the potential function of F and evaluate it at the point A 1 3 2 13 mark

72 A small block slides without friction down an inclined plane starting from rest Let S be the distance travelled from time t n 1 to t n is Then a Sn Sn 1 2n 1 2n b 2n 1 2n 1 c 2n 1 2n 1 2n 2n 1 0 starts d

Two men of masses m and m hold on the opposite ends of a rope passing over a frictionless pulley The man m climbs up the rope with an acceleration of 1 2 m s relative to the rope The mann m climbs up the rope with an acceleration of 2 m s relative to the rope Find the tension in the rope if 40 kg and m 60 kg Also find the time after which they will be at same horizontal level if they start from rest and are initially separated by 5 m 5m m2 B

3 A mass of 0 5 kg is suspended from wire the length of wire increase by 3 mm then find out wo done 1 4 5 x 10 3 J 3 9 3 x 10 2 J 2 7 3 x 103 J 4125 x 10 21

Two rigid rods of same material and of length L and are placed in equilibrium on a smooth horizontal plane at temperature 2 as shown in figure Springs are in their natural length If the temperature is increased by AT amount energy stored in springs 9 5 3 ka L AT where k is the spring constant of spring A and a is the coefficient of linear expansion of material Note Neglect the change in spring constant due to increase in temperature L k voooooo A a 2k mmmmm B 2 a k wwwwwww C

A force F K y1 x1 where K is a ve constant acts y x on a particle moving in xy plane starting from origin the particle is taken along the positive x axis to the point a 0 and then parallel to y axis to the point a a If the total work done by force F on the particle is nka find n 3

A car having mass 1300 kg climbs up to a hill 300 m high It then moves on a level oad with speed of 40 ms while running on the top of the hill what is its total mechanical energy Take 8 9 8 m s a 3 80 x 106 b 4 00 x 106 c 4 86 x 106 d 4 2 x 1061

Ubcan clearly are l is neither 2 nor 1 it is 0 77 so gor gods sake dont send wrong solutions 14 54 Consider a flat plate of area S moving horizontally through a medium having stationary particles of mass m each The nubmer of particles volume in medium is n The collision of particles with plate is elastic If angle a is varied the maximum force on the plate in the vertical direction is knmu S Find the value of k take 3 1 732 Correct answer 00 77

40 4 positive and negative A light inextensible string that goes over a smooth fixed pulley as shown in the figure 40 connects two blocks of masses 0 36 kg and 0 72 kg Taking g 10 ms2 find the acceleration of the block 1 3 33 m s 3 7 77 m s2 2 5 33 m s 4 10 m s2 59 5 2 4 4 s d allall kg 1 3 3 7

A ring of mass m radius r can oscillate in a vertical plane about is top most point O as shown Axis is normal to the plane of ring Maximum speed of lowest point P of ring is v 2r A Time period of SHM for small amplitudes is 2 g B Acceleration of centre of mass of ring at lowest position is zero C Hinge force when centre of mass is at lowest point is mv 4r mv D Mechanical energy of oscillation is D P when potential energy ot mean position is taken as zero

Diagram shows a wedge kept on a rough surface A ball of mass m is dropped on the slant face of the wedge If the collision is perfectly elastic choose the correct statement s h M 2m m 0 H A The ball of mass m may jump to the same maximum height from the poin impact for some values of 0 except 0 B Friction acting between wedge and ground is impulsive in nature C Momentum of the system M m can be conserved in horizontal direction

Calculate the horizontal force P on the light 10 wedge necessary to initiate movement of the 54 kg cylinder The coefficient of stati friction for both pairs of contacting surfaces is0 37 Also determine the friction force Fg at point B Caution Check carefully your assumption of where slipping occurs Answers P FB i 105 54 kg B N N

A block of mass m is suspended from a spring of force constant k it is held to keep the spring in its relaxed length as shown in the figure a The applied force is decreased gradually so that the block moves downward at negligible speed How far below the initial position will the block stop b The applied force is removed suddenly How far below the initial position will the block come to an instantaneous rest

1 AB is a quarter of a smooth horizontal circular track of radius R A particle P of mass m moves along the track from A to B under the action of following forces F F always towards y axis F F always towards point B F F always along the tangent to path AB F F always towards x axis Column I A Work done by F B Work done by F C Work done by F D Work done by F Column II P 2 FR Q R FR S FR TFR 2 2FR R DZ R F Stoni A X

A block of mass m is attached to two springs of spring constants k and k as shown in figure The block is displaced by x towards right and released The velocity of the block when it is at x 2 will be A k k x 2m B 3 k k x V4 m C k k x m 0000000 m vooro D k k x 4m

38 A particle of mass m moving with a velocity 31 2 ms collides with a stationary body of mass M and finally moves with a velocity 21 m 1 then M 13 a the impulse is tm 51 3 ms If b the velocity of the Mis 5 13 c Both a and b are wrong d Both a and b are correct 39 A mass of 10 g moving horizontally with a velocity of 100 cms strikes a 1

2 22 A man is throwing bricks of mass 2 kg onto a floor from a height of 2 m Bricks reaches to floor with speed 2 10 m s Man throws 10 bricks in a minute If power of man is W watt 3 then W is equal to W 10

A nucleus of mass M emits y ray photon of frequency v The loss of internal energy by the nucleus is Take c as the speed of 1 hv 3 hv 1 hv 2Mc electromagnetic wave 2 0 4 hv 1 hv 2Mc

A bullet of mass 0 05 kg moving with a speed of 80 m s enters a wooden block and is stopped after a distance of 0 40 m The average resistive force exerted by the block on the bullet is 1 300 N 2 20 N 3 400 N 4 40 N

4 Four massless springs whose force constants are 2k 2k k and 2k respectively are attached to a mass M kept on a frictionless plane as shown in figure If the mass M is displaced in the horizontal direction then the frequency of the system is a c 1 k 2T V4M 1 k 2 V7M 2k 2k oooooooo M k mor m 2k b d 1 2T 4k M 1 7k 2 VM

2 Initially system is in equilibrium If the spring between A B is cut then just after cutting Assume all springs are massless and identical eeeeee A 2m C oooooo B3m B Feeeeee m A Acceleration of block A is 2g upwards B Acceleration of block A is 4g upwards C Acceleration of block B is 4g 3 downwards D Acceleration of block B is 4g downwards

A particle is thrown up with initial velocity v along a smooth fixed wedge as shown in figure The particle reaches upto P and returns The height h of point P is P A 10 h B 2g sin 0 C sin 0 2g D cos

ample 30 Figure shows two discs of same mass m They are rigidly attached to a spring of stillness k The system is in equilibrium From this equilibrium position the upper disc is pressed down slowly by a distance x and released Find the minimum value of x if the lower disc is just lifted off the ground m Solution Let us first find out the minimum elongation x needed to lift the lower disc from the ground The free body diagram of the lower disc at this instant will be kx m N 0 mg Now lower disc The system given in the question is in equilibrium thus for the equilibrium of upper disc initial compression x in spring is mg m k kx mg mg k mg k kx Now from this equilibrium state spring is further compressed by an amount x and released Now let us apply energy conservation from this compressed state and final state Let us take the reference for gravitation potential energy at unstretched position then 1 k x x 1 mg x x mgx kx mg mg k x

Q16 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 3 4t t where x is in meters and t is in seconds The work do during the first 4 second is CBSE AIPMT 1998