Work, power & energy Questions and Answers

11 Potential energy is defined 1 Only in conservative fields 2 As the negative of work done by conservative forces 3 As the negative of workdone by external forces when AK 0 4 All of these

A particle crosses the topmost point C of a vertical circle with critical speed then the ratio of velocities at points A B and C is Question Type Single Correct Type 3 2 1 190 2 5 3 1 B

9 A body moves a distance of 10 m along a straight line under the action of a force 5 N If the work done is 25 joule the angle which the force makes with the direction of motion of body is 1 0 2 30 3 60 4 90

Example 6 3 A cyclist comes to a skidding stop in 10 m During this process the force on the cycle due to the road is 200 N and is directly opposed to the motion a How much work does the road do on the cycle b How much work does the cycle do on the road

SolveLancer Test Consider the four statements and then select the correct statement from options given below i The energy lost due to damping force is compensated by the work done by restoring force for forced oscillation ii The tangent at any point on the line of flow for flowing fluid gives perpendicular direction of motion of the particle iii The area of force time F t curve for one dimensional motion predicts loss in kinetic energy iv In a standing wave different particles move with different amplitudes SolveLancer Test a i iii b ii iv c iv only d i iv

An atomic power nuclear reactor can deliver 300 MW The energy released due to fission of each nucleus of uranium atom U238 is 170 MeV The number of uranium atoms fissioned per hour will be Question Type Single Correct Type 1 30x1025 24 1022

A block of mass m is allowed to slide down a fixed smooth inclined plane of inclination and slope length L What is the power developed by the force of gravity when the block reaches the bottom 1 2m L gsin V 2 Lg sin 0 3 m Lg V T

A block of mass 20 kg is being brought down by a chain If block acquires a speed of 2 m s in dropping down 2 m Find work done by the chain during the process g 10 m s 1 360 J 2 400 J 3 360 J 4 280 I

246 Two objects have the masses of 15 kg and 10 kg respectively The 15 kg object is placed on the surface of Earth to 4 m height and the 10 kg one is placed to 2 m height on a planet whose acceleration due to gravity is 2 5 times to that of Earth surface What is the ratio of their gravitational potential energies Take gearth 9 8 m s

A woman pushes a box on railway platform which has rough surface She applies a force of 20 N over a distance of 5 m thereafter gets tired and applied force which reduces linearly to 10 N with distance The total distance which box has been moved is 10 m Work done during second displacement is 1 175 J 3 75 J NCERT Pg 119 2 19 5 J 4 14 65 J

A block of mass m 1 kg is moving on horizontal surface with speed of 4 m s 1 enters a rough patch ranging from x 0 1 m to x 1 6 m The retarding force in this range is inversely proportional to x F 0 1 x 1 6 m X What is final kinetic energy of the body 1 9 2 J 3 6 84 J NCERT Pg 120 2 7 3 J 4 5 23 J

Figure shows two holes in a wide tank containing a liquid column The water streams coming out of these holes strike the ground at the same point The height of liquid column in the tank is 1 Question Type Single Correct Type 2 10 cm 8 cm 6 cm 3 9 8 cm 4 cm

VI A particle of mass m moves under the action of a central force whose potential is V r kmr k 0 then a for what values of energy and angular momentum will the orbit be a circle of radius a about the origin b calculate the period of circular motion c if the particle is slightly disturbed from the circular motion what is the period of small

A parallel plate capacitor has plate area A and separation d It is charged to a potential difference Vo The charging battery is disconnected and the plates are pulled apart to three times the initial separation The work required to separate the plates is 3e AV 1 2 3 AV 2d AV 3d AV

A rubber bullet is fired at the stationary 3 6 kg block suspended from a spring Calculate a The block s speed after the bullet bounces off it 4 b The block s kinetic energy after the bullet bounces off 4 c The spring constant 4 d The period of the resulting oscillation 4 28 cm 0 cm 180 mmmmmm m

7 A body initially at rest breaks up into two pieces of masses 2 M and 3 M respectively together having a total kinetic energy E The piece of mass 2 M after breaking up has a kinetic energy 2017 Gujarat 2E E 5 2 3E a C E b d

The mass of the bob of a simple pendulum is m and it is raised to a maximum height h The work done by gravity in moving it from one extreme end to other is Question Type Single Correct Type 1 2 mgh 2 mgh 3 3 mgh

The combined frictional and air resistance on a bicyclist has the force F aV where V is his velocit and a 4 newton sec m At maximum effort the cyclist can generate 400 watts propulsive power Wha is his maximum speed in m s on level ground with no wind

In figure the smooth pulley is massless friction is absent everywhere If the blocks are released from rest with the connecting cord taut what is their total kinetic energy in J when the 2 kg block has fallen 40 cm Wedge is fixed 1kg 30 2kg

3 The 50 lb package starts from rest slides down the smooth ramp and is stopped by the spring as shown in Fig Q3 Note spring force F KAx and g 32 2 ft s 20 points a Draw appropriate Free Body Diagram b If you want the package to be brought to rest 6 inches from the point of contact what is the necessary spring constant k c What maximum deceleration is the package subjected to Fig Q3 ww

A light plank AB can rotated about a horizontal axis provided by a fixed hinged O it rests on a platform at the end B A small block of mass m is placed on the plank near the end B at distance from the hinge A small ball of mass m falls from height ho on the platform at distance from the hinge If the collision is perfectly elastic and block and plank are perfectly rigid find the height h to which the block will jump If the answer is Nh then find N m

A MW me Smooth a 2 3 m b 11 14 m c 7 23 m d 76 34 m X Wall 0 60 u 12 m s m 4 2 kg k spring 2 N m O A ball whose weight on moon is 16N projected on the surface of earth making angle from horizontal at the highest point of its trajectory It strikes a block spring system The compression in the spring is Assume perfectly inelastic collision Given gmoon Take ge Take ge 9 8 m s S

The K E of a person is just half of K E of a boy whose mass is just half of that person If person increases its speed by 1 m s then its K E equals to that of boy then initial speed of person was A 2 1 m s B 2 2 m s C 2 2 2 m s D None

A particle of mass m and charge q is given velocity v as shown in the figure What minimum distance it ca 2KqQ ravel before stopping for the first time A and B fixed charges Given that v 1 4TEO am A Q M q m B Q where K

Two identical masses placed on a smooth horizontal surface are connected by a light string of length 2 A constant force F starts acting on the system in the direction shown After some time the masses collide inelastically The energy lost in this collision is Find the value of n n F

speed 3 A particle moving with kinetic energy 3J makes an elastic head on collision with a stationary particle which has twice its mass During the impact A the minimum kinetic energy of the system is 1J B the maximum elastic potential energy of the system is 2J C momentum and total energy are conserved at every instant D the ratio of kinetic energy to potential energy of the system first decreases and then increases 8 Cos

3 22 A body of mass m was slowly hauled up the hill by a force F which at each point was directed along a tangent to the trajectory as shown in figure 3 123 Find the work performed by this force if the height of the hill is h the length of its base 1 and the coefficient of friction Figure 3 123 h

3 6 Consider a spring that does not obey Hooks s law One end of the spring is held fixed When it is stretched or compressed by an amount x the force it exert is F ax bx cx Where a 50 N m b 150 N m and c 5000 N m How much work must be done to stretch this spring by 1m from its unstretched length

1 5 3 12 A small ball is suspended from a point O by a thread of length 1 A nail is driven into the wall at a distance of 1 2 below O at A The ball is drawn aside so that the thread takes up a horizontal position At what point to the ball trajectory will be the highest point to which it will rise

3 29 An object is attracted toward the origin with a force of magnitude F kx where k 5 N m How much work is done by the force F when the object moves from 1m to 2 m Is the work positive or negative 199 11

body of mass 3 kg acted upon by a constant force is displaced by 5 metre given by relation 5 2 where t is in secore 3 rce is constant linearly increases with time Increases with time as t3 2 Increases with time as t 2

SolveLancer Test The motion of 10 kg mass is represented by a graph as shown Calculate the change of KE of body S displacement a acceleration S 10 m a 100 J b 1000 J c 500 J d 501 5 15 a m s SolveLancer Test

A person climbs a ladder starting from bottom and stops at last step Which of the following options is true with reference to work energy theorem Change in kinetic energy of person from initial to final situation A KE Work done by normal reaction of ladder on the foot of man W N Work done by gravity W mg A KE 0 WN W 0 mg A KE 0 WN W 0 mg A KE 0 WN W 0 mg A KE OW I W

A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by x 3t 4t t3 where x is in metres and t is in seconds The work done during the firs 4 second is 1 5 28 J 2 450 mJ 1

8 A particle moving in the xy plane undergoes a displacement given by Ar 2 01 m as a constant force F 5 0 2 0 N acts on the particle Calculate the work done on the particle A 10 J B 12 J C 7J D 21

A chain of mass M and length is held vertically such that its bottom end just touches the surface of a horizontal table The chain is released from rest Assume that the portion of chain on the table does not form a heap The momentum of the portion of the chain above the table after the top end of the chain falls down by a distance 8

A 10 kg box was placed on a ramp that is 25 inclined with respect to the ground It was pushed with a 100N N force where it moved 5 m downward How much work is done on the block by a gravitational force b applied force c friction force and d normal force The coefficient of the kinetic friction is 0 30

apv d ap 15 A chain of length L and mass M is held on a frictionless table with 1 n th part hanging over the edge Work done in pulling the chain is directly proportional to a b n c n d n 16 For the same mass which of the following will have c 2

The gravitational potential due to earth at infinite distance from it is zero Let th gravitational potential at a point P be 5 J kg Suppose we arbitrarily assume th gravitational potential at infinity to be 10 J kg then the gravitational potential at point will be A B C D 5 J kg 5 J kg 15 J kg 15 J kg x My An Correct Am

7 System shown in the figure is released from rest when spring is unstretched Pulley and spring is massless and friction is absent everywhere The speed of 5 kg block when 2 kg block leaves the contact with ground is Take force constant of spring k 40 N m and g 10m s a 2m s b 2 2m s c 2 m s 5kg to 00000 RALL 2kg d 4 2m s

20 A wire lying along y axis from y 0 to y 1 m carries a current of 2 mA in the negative 0 3 T m yi y direction The wire lies in a non uniform magnetic field given by B 0 4 Tm y The magnetic force on the entire wire is a 3 10 N c 3x10 4k N b 6 10 KN d 3 10 4KN

T A Carnot engine whose sink is at 300 K has an efficiency of 40 By how much amount should the temperature of source be increased so as to increase its efficiency by 50 of original efficiency 1 150 K 2 250 K 3 300 K 4 450 K

3 A body of mass m accelerates uniformly from rest to v in time t As a function of t the instantaneous power delivered to the body is a mv t b 4 mv t 4 44 A solid sphere of uniform c d 4 myt

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

3 20 points The car A has a weight of 4500 lb and is traveling to the right at 6 ft s Meanwhile a 3000 lb car B is traveling at 3 ft s to the left The cars crash head on and become entangled a Determine their common velocity just after the collision Assume that the brakes are not applied during collision

Two heating elements each of 220 V 3 5 kW rating are first joined in parallel and then in series to heat same amount of water through same range of temperature The ratio of tim taken in two cases would be mains voltage remains same 1 2 2 1 1 4 2 3

m 4 A box with mass m 1 25 kg is attached to a spring that is compressed a distance of 0 550 m with a spring constant of 225 N m as shown in the diagram below The surface is initially frictionless and the spring releases the box as soon as it reaches its natural length Use conservation of energy to answer the following questions k 225 N m x 0 550m 9 55 m s m vy 0m s 4 150m

A wind with speed 40 m s blows parallel to the roof of a house The area of the roof is 250m Assuming that the pressure inside the house is atmosphere pressure the force exerted by the wind on the roof and the direction of the force will be Pair 1 2 kg m Question Type Single Correct Type 1 4 8 x 105N upwards 2 2 4 x 105N upwards 3 2 4 x 105N downwards

Power is rate of doing work or the rate at which energy is supplied to the system A constant force F is applied to a body of mass m Power delivered by the force at time t from the start is proportional to a t b t

particle travelling horizontally with speed u collides and sticks with a particle having double its mass hanging vertically at rest at the end of light inextensible string of length if s tates through an angle 60 before its velocity becomes zero then value of u will be Ogl O 2 2gl