Work, power & energy Questions and Answers

An object has displacement from position vector 1 21 m to 2 21 31 m under the effect of a force F 3xi yj N The work done by this force will be O 14 J 07J O 5 J O 10 J

In scattering experiment find the distance of closest approach if a 6 MeV particle is used 1 3 2 10 16 m 2 3 79 10 14 m 3 4 6 10 15 m 4 3 2 10 15 m

Ihree identical blockS A D placed on horizontal frictionless surface The blocks B and C are at rest But A is approaching towards B with a speed 10 m s The coefficient of restitution for all collision is 0 5 The speed of the block C just after collision is A B A 5 6 m s B 6 m s C 8 m s D 10 m s C

A block of mass m is released from the top of a smooth inclined plane of angle of inclination 45 If the vertical height of inclined plane is 20 m then speed which it will strike bottom of plane is 1 ms 1 10 ms 1 2 ms 1 20 ms 1

In the figure shown a block A moving with velocity 10 m s on a horizontal surface collides with another block B at rest initially The coefficient of restitution 1 is Neglect friction everywhere The 2 distance between the blocks at 5 s after the collision takes place is 5x in m Then is A 10m s

QTwo blocks of mass 2 Kg are connected by a massless ideal spring of spring constant K 10 N m The upper block is suspended from roof by a light string A The system shown is in equilibrium The string A is now cut the acceleration of upper block just after the string A is cut will be g 10 m s A 2kg Jun 2kg

A ball of mass m with a charge q can rotate in a vertical plane at the end of a string of length in a uniform electrostatic field whose lines of force are directed upwards What horizontal velocity must be imparted to the ball in the upper position so that the tension in the string in the lower position of the ball is 15 times than the weight of the ball

Two identical blocks are resting on supports as shown Two identical bullets travelling with the same speed hit the blocks get embedded in them in very short time The blocks leave the contact immediately after bullet strikes them In case i bullet s velocity is toward centre of mass and in case ii bullet s velocity is off centre The kinetic energies after collision are K K and maximum height reached by the centre of mass are h h respectively Then NRK D TC W Case i H Case ii You sh mb h

Two blocks of masses m 1 kg and m2 2 kg are connected by a non deformed light spring They are lying on a rough horizontal surface The coefficient of friction between the blocks and the surface is 0 4 What minimum constant force F has to be applied in horizontal direction to the block of mass mi in order to shift the other block g 10 m s F m 00000 m A 8 N B 15 N C 10 N D 25 N

An object of mass 2 kg is placed at rest on a 14 frictionless horizontal surface at origin A horizontal force given by F x 9 i N acts on it along x axis Kinetic energy of the object will be maximum at cux x 3 m 3 x 1 8 m 2 x 3 m 4 x 1 8 m

2 A current is flowing through the branch of a cube of side 1 m then choose incorrect statement 12A 72A 1 The magnetic force acting on a moving charge at the centre of the cube is zero 2 The net magnetic field at the centre of cube is zero 3 The magnetic force on a charge particle at rest inside the cube is zero 4 The magnetic force acting between the parallel side of cubo in

of inertia 0 01 kgm about its massless cord wrapped around its rim kg mass M is attached to the end o cord The pulley can rotate about its without any friction Find the acceleratic the mass M Assume g 10 m s M Question Type Single Correct Type

An experiment is performed to determine the unknown mass of a sphere A spring loaded launcher is used to launch the sphere The launcher is set to exert a force with an average magnitude of F on the sphere over a distance D The sphere is launched vertically upward and takes a time t to reach a height H as shown in the figure Which of the following gives the minimum data needed to determine the mass of the sphere A Fonly D F and D only F H and t H t and D F D and H

PHYSICS A bucket tied at the end of a 1 6 m long string is whirled in a vertical circle with constant speed What should be the minimum speed so that the water from the bucket does not spill when the bucket is at the highest position Take g 10 m sec When a particle is rotated in 20 20

15 16 Paragraph for Questions no 15 16 Figure shows a schematic view of an electrostatic analyzer It can sort out charged particles by speed and charge to mass ratio Spacecraft uses such analyzers to characterize charged particles in interplanetary space Two curved metal plates establish an electric field given by E E b r where E and b are positive constants The field points towards the centre of curvature and r is distance from centre There is no influence of gravity Proton charge e mass m enters along y axis and exits along x axis while moving along a circular path Electric field Analyzer Mark the CORRECT option s A Speed with which proton is to be projected is given by v B If v X b C Electric force on proton is given by E m Proton beam E B centripetal acceleration of electron is a is given by a m D Electric force on proton is given by 2eE 2eEb Mark the CORRECT option s A Work done by electric field on proton is zero 2eE b m Exit eE b m proton may strike outer surface of analyzer C If v proton may strike inner surface of analyzer D If an electron is released with zero initial velocity from inner surface of analyzer it will strike outer

2 AAJ KA TOPPER A uniform rod of length L and mass M has been placed on a rough horizontal surface as shown in the figure The rod is pulled by applying a horizontal force The coefficient of friction between the 0 x L x L where 4 is a positive constant The heat surface and the rod is given by 0 generated due to friction as the rod moves by a distance Lis H4MgL 0 0 L 0 H4MgL x H4M L

Velocity v time t graph of a particle moving in a straight line is shown in the figure Mass of the particle 2 kg Work done by all the forces actin on the particle in time interval between t 0 to t 10 s is v m s O 10 125 J 125 J O 75 J 10 t s

55 A car is moving along a straight horizontal road with a speed If the coefficient of friction between the tyres and the road is v In The shortest distance in which the car be stopped noris A C F Ho g B D Ho g 2 Ho 2 g B H U 2002

A dumbbell constructed by affixing small identical balls each of mass m at the ends of a light rod of length 1 stands vertically on a frictionless floor touching a frictionless wall as shown in the figure If the lower ball is gently pushed away from the wall the dumbbell begins to slide Denoting acceleration due to gravity by g Mark the CORRECT statements A The maximum speed of the lower ball is attained when upper ball looses contact B The maximum speed of the lower ball is attained when tension in the light rod is zero C The maximum speed of the lower ball is tg 8gl V 27 D The speed of the upper ball when lower ball acquires maximum speed is 10gl

A uniform metal rod is suspended from one end When it is displaced through 60 from downward vertical the change in potential energy is The further change in potential energy when it is displaced further 30 OU O2U O 4U 3U 2

In a ballistics demonstration a police officer fires a bullet of mass 40 0 g with speed 200 m s on a soft plywood of thickness 4 00 cm The bullet emerges with only 25 of its initial kinetic energy The emergent speed of the bullet will be O 25 m s O 75 m s O 40 m s O 100 m s

When a body moves with a constant speed alon a circle 1 no acceleration is present in the body 2 no force acts on the body 3 its velocity remains constant 4 no work gets done on it

2 Bullets of mass 40 g each are fired from a machine gun with a velocity of 10 m s If the person firing the bullets experience an average force of 200N then the number of bullets fired per minute will be 1 300 2 600 3 150 4 75 CM0012

The relationship between the force F and position x of a body is as shown in figure The work done in displacing the body from x 1 m to x 5 m will be fffx X fix 1mx5m fenfia fari F N KHAC 1 2 3 4 5 6 Ar 5 0 5 10 A 30 J B 15 J C 25 J D 20 J Your Answer x m

the in figure A spring of Consider part A 40 spring constant 400 Nm is attached at one end to a mass is released from rest while situated at a height wedge fixed rigidly with the horizontal the spring is nearly equal to Take g 10 ms 5 cm the curved track The minimum deform n g AIIMS 2015 J m 5 m b 9 8 cm 400 m c 0 98 m yh d 0 009 km

11 A particle is placed at the point A of a frictionless track ABC as shown in figure 8 W7 It is pushed slightly towards right Find its speed when it reaches the point B Take g 10 m s 2 1m B 0 5 m 20

Use the values from PRACTICE IT to help you work this exercise Suppose the same elevator car with the same load descends at 3 00 m s What minimum power is required Here the motor removes energy from the elevator by not allowing it to fall freely KW hp TAKS SEROPTES 00001 01 2 3 NOTES Three identical balls are thrown from the top of a building all with the san initial speed The first ball is thrown horizontally the second at some angl above the horizontal and the third at some angle below the horizontal as the figure below Neglecting air resistance rank the speeds of the balls an they reach the ground from fastest to slowest

43 Power supplied to a particle of mass 2 kg varies with time as P 3 watt Here t in 2 seconds If velocity of particle at t 0 is v 0 the velocity of particle at time t 2 s will be V 1 m s b 4 m s a C d 2 m s 2 2 m s

Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t as a function of time t is given by 1 3 2 2 V 2 t mv 2 2 t 2 m V 2 t 4 T 2 2 25 S 1

Two masses each of m are attached at mid point B end point C of massless rod AC which is hinged at A It is released from horizontal position as shown Find the force at hinge A when rod becomes vertical L 2 B L 2 C

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 1 200 W 3 125 W 2 175 W 4 98 W

A uniform chain of mass m and length L is kept on a horizontal table with half of its length hanging from the edge of the table Work done in pulling the 1 chain on to the table so that only th of its length now hangs from the edge is

A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table The total mass of the chain is 4 kg What is the work done in pulling the entire chain on the table 2004 a 12 J 3 6J c 7 2J 1200 J b d

A small disc is attached at one end of a light inextensible string that passes through a hole in a frictionless horizontal tabletop Initially the disc moves on a circle of radius R with kinetic energy K The other end of the string is slowly pulled so that the disc finally moves on a circle of radius R y What is the work w done by the pulling agency A W 0 B W y K C W y 1 K D W y 1 K

3 Zero A bar magnet of magnetic dipole moment 57 A m is placed in region of magnetic field B 21 31 4k tesla the magnitude of torque acting on magnet is 1 Zero 2 10 Nm 3 15 Nm

A block of mass 100 gm slides on a rough horizontal surface If the speed of the block decreases from 10 m s to 5 m s the thermal energy developed in the process is 2 37 5 J 3 0 375 J 4 0 75 J 1 3 75 J 1 Thermal energy developed Loss in kinetic energy

52 4 J of work is required to stretch a spring through 3 10 cm beyond its unstretched length The extra work required to stretch it through additional 10 cm shall be 7 S gravz VZ 1 4 J 7 XX 10 3 12 J 2 8 J 4 16 J

which is free to mo through the plank 4 36 Sphere A of mass m moving with a constant velocity u hits another stationary sphere B of the same mass If e is the velocity relative co efficient of restitution then ratio of velocities of the two A fu C 2f 1 u spheres VAV after collision will be v VB

4 26 A smooth semicircular tube AB of radius r is fixed in a vertical plane and contains a heavy flexible chain of length r and weight Wir as shown Assuming a slight disturbance to start the chain in motion the velocity v with which it will emerge from the open end B of the tube is A 4gr TC 2 C 2gr T TC Figure 4 106 B D 2gr TC 2 gr 2 TC TC 2

Figure below shows two paths that may be taken by gas to go from a state A to a state C In process AB 400 J of heat is added to the system and in process BC 100 J of heat is added to the system The heat absorbed by the system in the process AC will be AIPMT 2015 PA 6 10 Pa 2 10 Pa 1 300 J 2 380 J 3 500 J B A 2 10 m 4 x 10 m V

The bob A of a pendulum is released from 30 to the vertical hits another identical bob B of same mass at rest at bottom The collision is elastic in nature The string length of pendulum A is 1 m The height through which bob A rises after collision with B is 1 Point O 1 0 25 m 2 0 5 m 3 0 33 m

Light wave is travelling along y direction If the corresponding E vector at any time is along the x axis the direction of B vector at that time is along YA 1 y axis 2 17 oxig Z 2 x axis 1 777 oxio X

in airplane of mass 1 20 x 10 kg is moving at 58 0 m s The pilot then Increases the engine s thrust to 7 00 x 10 N The resistive force exerted by air on the airplane has a magnitude of 6 00 x 10 N a Is the work done by the engine on the airplane equal to the change of the airplane s kinetic energy after it travels through some distance through the air Yes No Is the mechanical energy conserved Explain your answer This answer has not been graded yet b Find the speed of the airplane after it has traveled 5 00 x 10 m Assume that the airplane is in level flight throughout the motion 195 73

rzan swings on a 34 0 m long vine initially inclined at an angle of 42 0 with the vertical a What is his speed at the bottom of the swing if he starts from rest 8 73 Your response differs from the correct answer by more than 10 Double check your calculations m b What is his speed at the bottom of the swing if he pushes off with a speed of 6 00 m s 17 05 Your response differs from the correct answer by more than 10 Double check your calculations m

Two blocks of equal masses m are connected by a relaxed spring with a force constant k The bloc rest on a smooth horizontal table At t 0 the block on the left is given a sharp impulse J towards right and the blocks begin to slide along the table Find the velocity of the left block as a function time J

allel then iod T ithout vill energy is 1 10 J 2 20 J 4 2 J 3 200 J 21 A trolley of mass 1 kg is connected to two identical spring of spring constant 100 N m each If trolley is displaced from mean position by 1 cm then maximum velocity of trolley is mmmm 1 0 01 m s 2 01 mala Imm 2 1 4 m s 1 11 m s

31 32 ast Course A body of mass 1 kg thrown upwards with a velocity of 10 m s comes to rest momentarily after moving up by 4m The work done by air drag in this process is Take g 10 m s 1 20 J 2 10 J 4 0 J 3 30 J The force acting on a body moving along x axis varies with position of particle as shown in figure The body in stable equilibrium at F X X CAREER INSTITUTE Path to Success KOTA RAJASTHAN X

A bucket of water with total mass 23 kg is attached to a rope which in turn is wound around a 15 cm radius cylinder at the top of a well A crank with a turning radius of 25 cm is attached to the end of the cylinder What minimum force directed perpendicular to the crank handle is required to just raise the bucket Assume the rope s mass is negligible that cylinder turns on frictionless bearings and that g 9 8 m s 45 N 135 N 68 N

D A ball of mass 2 kg and another of mass 4 kg ar dropped together from a 60 feet tall building Afte a fall of 30 feet each towards earth their respective kinetic energies will be in the ratio of 1 14 2 1 2 3 1 2 4 2 1

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source The displacement s time t graph that describes the motion of the particle is graphs are drawn schematically and are not to scale