Work, power & energy Questions and Answers

38 A crane lifts a mass of 200 kg to a height of 10 m in 10 second The power of the crane is g 10 m s 1 1 KW 3 3 kW 39 Power supplied to a varies with time as P 2 2 kW 4 4 kW particle of mass 1 kg 3t watt t is in second 2 and initially particle was at rest Velocity of the particle at t 3 sec is 1 2 ms 1 2 4 ms 1 3 3 3 ms 1 4 6 ms 1 Medica

The escape speed of a projectile on the earth surface is 11 2 km s A body is projected out with three times of escape speed The speed of body far away from the earth is Ignore the presence of sun and other planets

D A body of mass m is moving with a speed of 8 ms 1 It strikes with another identical body at rest in such a way that after collision direction of each ball makes an angle of 30 with original direction of motion The speed of each ball after collision is 1 3 16 3 4 3 ms 1 ms 2 4 30 N 501 00 8 ms 1 ms 1 Work energy theorem is applied when 1 Force is variable 2 Roth 1 and 2 2 Force is constant 4 Noithor 1 por 2

W A heavy weight is suspended from a spring A person rais the weight till the spring becomes slack The work done him is W The energy stored in the stretched spring was What will be the gain in gravitational potential energy

In a shooting competition a contestant fires a bullet of mass 100 g with speed of 400 m s on a soft plywood of thickness 5 cm The bullet emerges with 4 of its initial kinetic energy Then emergent speed of the bullet is

An engine pumps water through a hose pipe Water passes through the pipe and leaves it with a velocity of 2 m s The mass per unit length of water in the pipe is 100 kg m What is the power of the engine 1 800 W 2 400 W 3 200 W 4 100 W

A particle of mass m approaches a region of force starting from r 0 The potential energy function in terms of distance r from the origin is given by U r where a b c K 3 a r for 0 r a K r for r a 3 2 a K 0 positive constant Derive the force F r and determine whether it is repulsive or attractive With what velocity should the particle start at r to cross over to other side of the origin If the velocity of the particle at r is 2 K am towards the origin describe the motion

Ex 7 A cannon of mass M resting on a rough horizontal plane of coefficient of friction u is fired with such a charge that the relative velocity of the ball and cannon at the moment when it leaves the cannon is u Show that the cannon will recoil a distance m u 12 g m M 2 along the plane m being the Ajmer 2002 mass of the ball

A ball falls under gravity from a height of 10 m with an initial downwards velocity u It collides with the ground losses 50 of its energy in collision and then rises back to the same height The initial velocity u is 1 7ms 1 2 25 ms 1 3 14 ms 4 28 ms nigh tek piger 1 pagen 2gh gh u glx u SON

In the figure shown the potential energy U of a particle is plotted against its position x from origin Then which of the following statement is correct A particle at A is in stable equilibrium B x is in stable equilibrium C x is in stable equilibrium D none of these

The 4 9 m long ropes of a swing make an initial angle of 12 2 degrees with respect to the vertical at the highest point in the motion of a 40 kg mass child Alice A second child Bobby pushes Alice each time she reaches him at her highest point doing 32 6 J of work What angle in degrees will Alice s swing ropes make after 5 swings

A uniform solid sphere with radius r and mass m compresses a spring with spring constant k by a distance x The spring must be compressed by minimum distance so that the sphere rolls around the interior of a circular loop of radius R depicted in the figure above while always remaining in contact with the track 27mg R r A x 5k B The speed of the sphere at the top of the circular loop must be g R r 10mg R r k C If the surface was made perfectly smooth x required to loop the loop is D in option C above the speed at the top of the circular loop must be R r

A block of mass m is placed on an another rough block of mass M and both are moving horizontally together without slipping with acceleration a then work done by friction on the upper block in moving a distances will be O O O Mass m M as M m

b c 40 J d 20 J Q2 A body moves a distance of 10 m along a straight line under the action of a 5 N force If the work done is 25 J then angle between the force and direction of motion of the body is a 60 b 75 c 30 CBSE AIPMT 1997

A body constrained to move in y direction is subjected to a force given by F 21 153 6k N The work done by this force in moving the body through a distance of 10 m along positive y axis is 150 J 20 J 190 J 160 J

B are ement B gy Q is 5 The binding energy per nucleon of deuterium and helium atom is 1 1 MeV and 7 0 MeV If two deuterium nuclei fuse to form a helium atom the energy released is 1 19 2 MeV 2 23 6 MeV 3 26 9 MeV 4 13 9 MeV

A stone projected vertically up with a velocity u reaches a maximum height h When it is at a height of 3h 4 from the ground the ratio of KE and PE at that point is consider PE 0 at the point of projectory Question Type Single Correct Type 1 1 1 2 1 2 3 1 3

Q3 A box of mass 1 kg is pulled on a horizontal plane of length 1 m by a force of 8 N then it is raised vertically to a height of 2 m at constant speed the net work done is a 28 J b 8 J c 18 J d None of the above

A uniform wire of length 1 800 m and cross sectional area S 1 0 m is made of a material of density p 8 0 x 10 kg m and Young s modul Y 2 0 x 1011 N m The wire is placed straight on a frictionless bo zontal floor and an end is pulled by a constant horizontal force F N uniformly distributed over the face of the end Find displacement this end in a time interval At 0 1 s after the force is applied

Q4 A horizontal force of 5 N is required to maintain a velocity of 2 m s for a block of 10 kg mass sliding over a rough surface The work done by this force in one minute is a 600 J b 60 J c 6 J

Work Energy and Power 2 Q11 Two bodies with kinetic energies in the ratio of 4 1 are moving with equal linear momentum The ratio of their masses is CBSE AIPMT 1999 a 4 1 b 1 1 c 1 2 d 1 4

A force of 10 N making an angle 30 with positive x axis acts on a 2 kg block moving in xy plane Work done by the object as it moves from origin to the point having position vector 21 4 is 2 67 J 2 67 J 20 J 20 J

Q7 An object is displaced from position 2 3 m to 4 6 m under a force F 3x 2yj N Find the work done by this force if it is given that the force is conservative in nature a 81 J b 85 J c 63 J

A bug flying horizontally at 2 3 m s collides and sticks to the end of a uniform stick hanging vertically from its other end After the impact the stick swings out to a maximum angle of 8 0 from the vertical before rotating back If the mass of the stick is 14 times that of the bug calculate the length of the stick in m m

A ball of mass 2 kg is moving with speed 4 m s on horizonta smooth surface collides with a nearly weightless spring of force constant 128 N m as shown in the figure The maximum compression in the spring will be mmmmmm C 0 25 m 0 4 m 2 m s 0 15 m 0 5m

18 Paragraph for Two tennis balls of mass 60 gmare attached with a massless rubber thread and held in the vertical position as shown in the fig In this position length of the rubber thread is 40 cm and it is un stretched The upper ball is slowly raised vertically upward until the lower ball just becomes unsupported by the ground At this time the length of the thread is 1m The rubber thread exerts a force which is proportional to its extension 17 What is the force constant of the rubber cord A 2 N m B 1 N m C 0 5 N m D 0 25 N m How much work is done by external agent while the upper ball was raised A 0 54 J B 0 36 J C 0 18 J D 0 45 J 18

10 Calculate final velocity of the particle of mass 2 kg if initial velocity of it is 6 m s A force if it is acted on it and whose variation with time has been shown below 6 F N 1 10 m s 3 12 m s A ball weighing 10 4 t sec 2 6 m s 4 Zero

015 all t A man racing with his son has half the kinetic energy of the son who has half the mass of the father The man speeds up by 1 m s and has the same kinetic energy as the son What was the original speed of the man a 4 8 m s c 2 4 m s b 3 6 m s d 1 2 m s AMU Med

A 750 g collar can slide without friction along the semi circular rod BCD in Fig 2 The rod BCD is in the yz plane The spring is of stiffness 350 N m and its undeformed length is 220 mm The collar is released with an initial velocity at B Determine the initial velocity if the collar should just reach D Hint Use work energy method Take g 9 81 m s in the negative y direction 300 mm 150 mm 75 min Fig 2

A particle of mass 20 g is released with an initial velocity 5 m s along the curve from the point A as shown in the figure The point A is at height h from point B The particle slides along the frictionless surface When the particle reaches point B its angular momentum about O will be Take g 10 m s Main 12 Jan 2019 II a c A 2 kg m s 6kg m s O a 10 m h 10 m B b 8 kg m s 3 kg m s d

arrangements as shown in the figure A toy car is released at rest and slides down the track air resistance can be ignored The length of the track used is the same in each case and the height through which it falls from the bench to the floor is the same P A B D Q R S Codes 4 List l Speed of the given toy car at the bottom of track i would be compared with the speed at the bottom of track ii 3 Time taken for the car to slide down on track i would be compared with the time taken on track The mass of the car in track i is twice that of that in track ii Now comparison of time taken to slide down P 1 2 3 Average power developed by weight of the car in track i as compared track ii during the motion Q 4 1 1 2 1 1 S3222 Track i 1 2 3 4 List il Greater Smaller Same Track ii Nothing can be concluded gaine SCOL V SUOL 12 gaine dv vdv SVCH 2 VCH

1 A wheel with the diameter 2 cm is rotating in such a way that the time dependence of its rotation angle is o 1 rad At Bt where A 1 rad s B 0 5 rad s What is the acceleration of the points on the wheel rim 2 seconds after the rotation onset

A car of mass m is driven with a constant acceleration a along a straight level road against a constant external resistive force R When the velocity of the car is V the rate at which the engine of the car is doing work will be RV maV R ma V ma R V

A force F 2xy 2yx 1 N acts on a particle where x y denotes the co ordinate of position of the particle The work done by this force in taking the particle from point A a a to point E 2a 2a 1 Zero 3 15a4 2 4 16a4 12a4

displaced from 41 33 k the particle is 2013 d 13 J m 32 A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms It collides with a horizontal spring of force constant 200 Nm The maximum compression produced in the spring will be 2012 Pre d 0 2 m a 0 5 m b 0 6 m c 0 7 m sight line ries

height H its Potential energy will be maximum at 1 2 3 4 starting position as it starts falling lowest position as it is about to hit the ground between the start and end position of its projection Data is insufficient

A solid cylinder of mass mand radius R rolls without slipping down an inclined of height h The angular velocity of the cylinder when it reaches the bottom is 1 2gh RV 3 1 J4gh RV 3 1 3gh RV 2

5 Each of the two uniform hinged bars has a mass m and length 1 and is supported and loaded as shown For a given force P determine the angle 0 for equilibrium figure C6 V Figure C6 P

Q 11 Two identical bullets one s kinetic energy being double that of the other enter a thick wall The faster bullet will penetrate a twice as far as the slower bullet b four times as far as the slower bullet 2 times as far as the slower bullet d the same distance as the slower bullet

A body when acted upon by a force of 10 kgf gets displaced by 0 5 m Calculate the work done by the force when the displacement is i in the direction of force ii at an angle of 60 with the force and iii normal to the force g 10Nkg

A small block of mass m 200gm is projected from point O on a smooth curved surface Assume particle is always in contact with the surface A and B are local peaks of curved surface Find the minimum kinetic energy in joule given to the small block to reach at B Given H 4 meter g 10 m s Assume that there is no kink present anywhere on the surface H 4H 2H B 2H H H

Question No 14 A body of mass 5 kg moves according to the relation x f 2 The power used by the body at t 2 sis O 3640 W 2660 W 1620 W 4440 W

Statement A Work done by frictional force is always negative Statement B A body at rest can have mechanical energy O Both statements are correct O Both statements are incorrect O Statement A is correct and B is incorrect Statement A is incorrect and B is correct

Two springs of spring constants 500 N m and 500 N m are stretched with force 100 N and 200 N respectively They have potential energy in the ratio of 01 2 O 1 1 01 4

1 100 2 16 For the series LCR circuit shown in the figure what is the resonance frequency and the amplitude d current at the resonating frequency 3 30 1 2500 rad s and 5 2 A 5 A 3 2500 rad s1 and 220 V 8 mH mooooooo 4402 20 F 2 2500 rad s 1 and 5A 4 25 rad s 1 and 5 2A

A block of mass m kept on a wedge of mass M interconnected by an ideal spring of stiffness k Wedge is placed on a smooth horizontal surface The block is released from rest with spring in natural length Select incorrect statement s Net force on the system is zero Acceleration of centre of mass is zero Velocity of centre of mass is non zero Displacement of centre of mass is non zero mmmmmm M

A block P of mass m is moving with velocity v and collides elastically with identical block Q at shown in the figure If spring constant of the spring is K then maximum compression in the spring in subsequent motion is 1 Vo 2m P 3m 2 Vo2K 4 2m 3 Vo 3K V2m 3K Q mm smooth K R 2m

A smooth cylindrical glass lies on the ground A small particle of mass m lies on the bottom surface touching circumference as shown in the figure The minimum value of Vo along the circumference such that particle just reaches at the top of glass is V Kgh Find the value of K

1 Two springs of spring constants 500 N m and 500 N m 1 are stretched with force 100 N and 200 N respectively They have potential energy in the ratio of 01 2 O 1 1 O 1 4 01 3

Q A simple pendulum with a bob of mass m oscillates from A to C and back to A such that PB is H If the acceleration due to gravity is g then the velocity of the bob as it passes through B is a mgH b 2gH c 2gH d zero A P I I B C