Work, power & energy Questions and Answers

A ball of mass 200 g collides with a fixed smooth vertical surface The horizontal component of the ball s velocity just before and just after the collision is 5 m s and 3 m s respectively During the collision the force acting on the ball due to the surface varies as F t At Br where A and B are constants and t is the time elapsed since the ball first made contact with the surface The total time for which the ball in contact with the surface is 0 02 seconds The constant A is equal to x104 N s

A bullet of mass m travelling horizontally with speed u strikes a wooden block of mass M placed on a smooth horizontal plane The penetration is assumed uniform and the bullet comes to rest after penetrating a distance d into the block Then choose the correct statement A Ultimately the total loss of kinetic energy is mMu 2d M m C The distance covered by the bullet w r t the ground before it comes to rest w r t block mMu 2 M m B The value of the resistance force assumed constant offered by the wood is F dm M m D The block moves greater distance than the bullet w r t ground is m u

A force F x y j N where x and y coordinates are in metres acts upon a body and it moves along the path ABCDA as shown The work done by the force is 0 2 D O A 0 0 O 20 J 20 3 J 42 J O Zero 3 2 B 3 0 X

Consider the potential energy given by x4 x3 4 3 where the coefficients of the various powers of x have units such that U has units of joules U x Find the equilibrium points and classify them O x 0 stable Ox 1 stable Ox 2 stable Ox 0 neutral

Q 10 54 Two blocks of mass 1 kg each are moving with equal velocity 2 m s at the instant shown 7 0 and the string is tight Block 1 is moving on a fixed frictionless horizontal surface Immediately after 7 0 the velocity of block 1 is suddenly increased to 6 m s Assume that the string and pulley are ideal Which of these options is are correct g 10 m s The string becomes tight again at r 0 4 s When the string becomes tight again it applies an impulse 2 kg m s directed upwards on block 2 The velocity of block 1 immediately after the string becomes tight is 8 m s The heat generated when the string becomes tight is 4 Joules

A 5kg body is displaced along x axis by a force The position x in meter as a function of time is given by x 32 2t The work done by the force in first two second 2 t 0 to 1 2 sec is O 100J O 125J O 150 J O 50 J

A bob is suspended by a string of length 1 m The bob is given a horizontal velocity Vo 30 m s at lowest position The minimum speed in m s of bob in subsequent motion is T Find the value of n g 10 m s 10

This section contains THREE 03 question stems There are TWO 02 questions corresponding to each question stem The answer to each question is a NUMERICAL VALUE For each question enter the correct numerical value corresponding to the answer in the designated place If the numerical value has more than two decimal places truncate round off the value to TWO decimal places Answer to each question will be evaluated according to the following marking scheme Full Marks 2 If ONLY the correct numerical value is entered at the designated place 0 In all other cases Zero Marks A block and wedge are displaced slowly from A to B as shown in diagram 5 Kg block is at rest wirt wedge Work done in J by normal contact force on 5 kg block is A 6kg 37 10m B 5kg 372

Consider the potential energy given by x4 x U x 4 3 where the coefficients of the various powers of x have units such that U has units of joules O O x If total energy is 16 J and mass of particle is 2 kg which of the following option is incorrect O 1 Particle will present at x 1 at origin v 4 m s Acceleration of particle at x 0 will be 4m s Momentum of particle at x 0 will be 8 m s

The potential energy of a particle oscillating on x axis is given as U 20 x 2 2 Here U is in J and x in metre Total mechanical energy of the particle is 36 J The maximum kinetic energy of the particle is 1 16 J 2 32 J 4 8J

Hollow hemisphere is fixed and has radius R 8r where r is radius of small solid sphere released at top as shown Sphere rolls without slipping When sphere reaches bottom velocity of top most point of sphere is y 12xx

A particle is projected from the foot of one wall towards other parallel wall as shown in figure After various collisions as shown finally after striking at point D the highest point of its trajectory it comes back directly to the point of projection If e is coefficient of restitution for each impact then find the value of e e e B

Suppose you are in a gym and your trainer asks you to lift a heavy rope The rope has a length I and is on smooth horizontal surface in form of a coil You are pulling the top end of the rope at a To constant speed u pull the entire rope just the off ground calculate the average to you need power you apply

A massless spring of spring constant 100 N m in its unstretched position is hanged from the ceiling A mass of 2 kg is attached and let go Find the maximum elongation in the spring A 0 2m B C 0 4m 0 6m D 0 8 m

In the figure the variation of potential energy of a particle is represented wrt its x coordinate The particle moves under the effect of this conservative force along the x axi Choose correct option s 20 U in J 15 x 5 m and x 10 m positions of the particle are stable and unstable equilibrium respectively 0 If particle is released from rest at origin it will move towards negative x axis If particle is released from rest at origin it will move towards positive x axis x 10 m and x 2m positions of the particle are stable and neutral equilibrium respectively 10 X in metre

0 1 s tance 9 A bullet of mass 5 g travelling with a speed of 210 m s strikes a fixed wooden target One half of its kinetics en ergy is converted into heat in the bullet while the other half is converted into heat in the wood The rise of tem perature of the bullet if the specific heat of its material is 0 030 cal g C 1 cal 4 2 x 107 ergs close to a 87 5 C b 83 3 C c 119 2 C d 38 4 C 10 An object undergoing SHM takes 0 5 s to travel from one gaitu to the next such point The diston

The pulley mass system is released from rest Neglecting friction Pulley mass less and assuming the string to be light and inextensible Choose the correct option s 16 m 2m mg t 6 A The kinetic energy of the system after time t is B The total work done by the tension on the given system is zero C The work done by tension on heavier block is negative D The C O M of the given system goes down with acceleration of m s

The given diagram represents the potential energy curve of a particle in a field The magnitude of the force on the particle will be maximum when its position co ordinate x is equal to U X X X2 X3 X4

A massless spring of spring constant k 100 N m hangs in a vertical plane from point O its other end is attached with block of mass m 2 kg and system is in equilibrium Now another small spherical ball of same mass moving with a velo Vo 10 m s collides with the block and gets stuck to it as shown in the figure The new amplitude of oscillation will wwwwww 2kg m 5 10 eeeeeee 1 m m Vo 10 m s m k 100 N m m 2kg

Consider a small spherical ball inside a circular tunnel of radius R and inner diameter size of the tunnel nearly equal to that of the spherical ball rigidly held in a vertical plan shown in the figure Assume no friction between the surface of the tunnel and the spherical ball Which of the following is correct R If u 5gR 2 then the ball loses contact with the tunnel s sides at some instant during the motion If u 11gR 2 then the ball loses contact with the tunnel s sides at some instant during the motion If u 11gR 2 the ball will come to rest at some instant before it reaches the highest point of the circular motion If u 5gR 2 the contact force acting on the ball is zero at the instant when it comes to rest A

Q2 A classic assembly in thermal equilibrium at room temperature consists of 4000 systems distributed over three energy bands with the same number of states and energies 0 0 0125 ev and 0 025 V respectively Find the number of systems in each energy segment and the total energy when the assembly is in its most probable general position

10 kg block of aluminum is heated at atmospheric pressure such that its temperature increases from 22 C to 40 C then find change in internal energy in kJ QAI 2 3 10 5 K 1 SAI 0 9 kJ kg C PAI 2700 kg m

the locomotive during the first t seconds A uniform chain of length is released from rest by pulling the right end slightly down when the chain was in equilibrium Find the speed of the chain when it loses contact with the pulley t 2 2 ing are placed on a smooth inclined plane of inclination sin 1 3 such that so Over the top of the plane If acceleration at vertex b

A box is being pulled across a rough floor at a constant speed What can you say about the work done by friction A friction does no work at all friction does negative work C friction does positive work Can t comment B D

Four forces are applied on an object as shown in the figure The magnitudes of the forces are F 5 N F2 9 N F3 3 N and F4 10 N The angle 0 60 The object moves 2m under the action of these forces During the displacement a What is the net work done on the object b Does the kinetic energy of the object increase or decrease F

An athlete lifts a 160 kg barbell through a vertical displacement of 1 26 m requiring 4 40 s for the lift a Calculate the average mechanical power he must deliver to the barbell during the lift W b For a short period he lifts the barbell at a constant speed of 0 790 m s What instantaneous power does he deliver to the barbell during that W

Four blocks and two springs are arranged as shown in figure The system at rest determine the acceleration of all the loads immediately after the lower thread keeping the system in equilibrium has been cut Assume that the threads are weightless the mass of the pulley is negligible small and there is no friction at the point of suspension

Two identical thin rings each of radius R are coaxially placed at a distance R If the rings have a uniform mass distribution and each has mass m and m respectively then the work done in moving a mass m From centre of one ring to that of the other is R Y

A car of mass m starts from rest and accelerates such that its instantaneous velocity is proportional to t where t is time in seconds What should be the instantaneous power delivered to the car if its instantaneous velocity is 20 m s after 10 seconds 50 kW 3 4 20 kW 40 kW

A uniform chain of length L and mass M is lying 1th on a table and 4 vertically down over the edge of the table If g is acceleration due to gravity the work required to pull the hanging part back on the table 1 2 3 MgL 16 of its length is hanging MgL 8 4 MgL 32 MgL 4

Two objects A and B both with a mass of 2 kg collide The velocities before the collision are ViA 15i 30j m s V B 10i 5j m s After the collision object A has a final velocity What is VJA 5i 20j m s a the final velocity of B s and b the change in the total kinetic energy of the system including sign B4

12 A particle of mass m moves with constant speed v on a circular path of radius r Find magnitude of average force on it in half revolution 13 On an object of mass 1 kg moving along x axis with constant speed 8 m s a constant force

reeeeeee 3 k spring constant m Calculate the maximum elongation of the sp considering that the block is released from rest the natural length position of spring 2mg k mg le 2 4mg k 4 Zero

A 10 H P motor pumps out water from a well of depth 20m and fills a water tank of volume 22380 litres at a height of 10m from the ground the running time of the motor to fill the empty water tank is g 10ms O 5 minutes 10 minutes O15 minutes O20 minutes

A person is pulling a mass m kg from ground on a fixed rough hemispherical surface upto the top of 11 the hemisphere with the help of light inextensible string Assuming block is pulled with negligible velocity find the work done in joule by tension in the string R 1m Rough 0 1

Two bodies A and B connected by a light rigid bar 10 m long move in two frictionless guider as shown in figure B starts from rest when it is vertically below A If the velocity of B is found to be 138 cm s when x 6 m Find B Assume m m 200 kg and mc 100 kg use g 9 8 m s 10 m TX B

Two charged di electric spheres A solid and B hollow of same radius R and masses 2m and m respectively are kept on a horizontal rough surface The two spheres A and B have charges 2Q and Q respectively and uniformly distributed They are released from rest when their centres are separated by very large distance Assuming there is no sliding List I Sold EXXT P Kinetic energy of system just before A and B meet Q Kinetic energy of A just before A and B meet R Kinetic energy of B just before A and B meet Codes P A 2 B 1 C 3 S Rotational kinetic energy of system just before A and B meet 1 R 1 2 List II 838kQ 2345R kQ R 25kQ 67R 42kQ 67R

6 A series of n elastic balls whose masses are m em e m etc are at rest separated by intervals with their centres on a straight line Here e is coefficient of restitution for the collision The first is made to impinge directly on the second with velocity u Then 1 The first n 1 balls will be moving with the same velocity 1 e u 2 The last one ball will move with velocity u 3 The kinetic energy of the system is mu 1 e e 4 None of these

78 A particle A has charge q and particle B has charge 4q with each of them having the same mass m When allowed to fall from rest through same electrical potential difference the ratic of their speeds VA VB will become 8 a 2 1 b 1 2 c 1 4 d 4 1

A man of mass m is standing in an elevator moving downward with an acceleration bottom surface of the elevator on the man will be 1 3 3mg 4 5mg 4 2 4 mg 4 7mg 4 g 4 The force exerted by the

A uniform chain of length L is suspended in equilibrium by an elastic string of natural length h as shown The chain is then suddenly cut at point A which is x distance below the upper end of chain 2h X If x L 3 the velocity of suspended part of chain when it rises by from its equilibrium position is gh

50 Two fixed charges A and B of 5 C each are separated by a distance of 6 m C is the mid point of the line joining A and B A charge Q of 5 C is shot perpendicular to the line joining A and B through C with a kinetic energy of 0 06 J The charge Q comes to rest at a point D The distance CD is a 3 m c 3 3 m b 3 m d 4 m Karnataka CET 55

4 and r 7 A cell can be balanced against 110 cm and 100 cm of potentiometer wire respectively with and without being short circuited through a resistance of 10 2 Its internal resistance is AIPMT Prelims 2008 1 Zero 2 19 3 0 5 9 4 20

State the work Energy theorem A block is moving up an inclined plane which makes an angle of 30 with the horizontal The mass of the block is 5 0 kg and its initial speed is 6 0 ms How far will it slide up the incline till it comes to rest The coefficient of kinetic friction between the block and the plane is 0 2 Draw the free body diagram Take g 10 ms 2 404 DUE M 1 4 1

33 A current of 2 A flows through a 2 2 resistor wher connected across a battery The same battery supplies a current of 0 5 A when connected across a 9 resistor The internal resistance of the batter is AIPMT Prelims 2011 1 1 Q 3 1 3 Q 2 0 59 4 1 4

A man can swim in still water with a speed of 2 ms If he wants to cross a river of water current speed 3 ms along the shortest possible path then in which direction should he swim O O O O At an angle 120 to the water curren At an angle 150 to the water current At an angle 90 to the water current None of these

1 A roller coaster is shown below The speed of the roller coaster at the top of the loop where the black dot is in the diagram is 10 0 m s Assuming that the roller coaster starts from rest at the top of the first hill what is the height h of the first hill Assume that the track is frictionless and there is no friction in this question I 4 marks h O 16 m ground level

0 The reference level is the ground in this question A person lifts a bucket of water of mass of 1 50 kg from a height of 1 00 m below the ground to a height of 1 0m above the ground How much work was done by the force of gravity on the bucket of water during the entire lift a 14 7 J b 14 7J c 29 4J d 29 4J e none of the above

8 Two people have different masses and run up the same set of stairs Which of the following statements is correct a their power ratings are always equal b the person with the larger mass will always have the larger power output c the person with the smaller mass will always have the larger power output d more information is needed to determine which student has the larger power output e the power is 0 watts for both people as the value of Ek is not changing

5 The gravitational potential energy of a bird of mass 2 kg situated on a tree branch that has a relative to the ground height of 150 cm off the ground is a 3 x 10 J b 3 x 10 J c 3 x 10 J d 3 x 10 J e 3 x 10 J