Work, power & energy Questions and Answers

arged plate he intensity tal bar 1 cm planes The 2 56 A capacitor of capacity C is charged to a potential difference V and another capacitor of capacity 2C is charged to a potential difference 4V The charging batteries are disconnected and the two capacitors are connected with bit de reverse polarity to each other in parallel The heat produced during the redistribution of charge between the capacitors will be such that connected Cis A 125CV 3 B 50CV2 3 25 TAS enorigo

In the below arrangement all the string and pulleys are massless and the inclined plane is frictionless At t 0 spring is unstretched and a constant force F mg starts to act Fi the maximum extension in the spring Assume incline to be sufficiently long 4 8mg k 4 mg 5 k 8 mg 15 k 8mg 3k mmm 53 BEST

16 A net force along the x axis that has x component Fx 16 0 N 0 320 N m x is applied to a 5 kg object that is initially at the origin and moving in the negative x direction with a speed of 7 90 m s What is a the work that has been done by this force on the object by the time it reaches the point x 4 80 m and b the speed of the object when it reaches this point

Q20 A Railway engine weighing 40 metric ton is travelling along a level track at a speed of 54 km hour What additional power is required to maintain the same speed up an incline of 1 in 49 Take g 9 8m s 2 and coefficient of friction 0 1

A particle is moving on x axis has potential energy U 2 20x 5x Joules along x axis The particle is released at x 3 The maximum value of x will be x is in meters and U is in joules A 5 m B 3 m C 7 m D 8 m

A ball is thrown from the top of 36 m high towe with velocity 5 m s at an angle 37 above th horizontal as shown Its horizontal range on th ground is closest to g 10 m s 5 m s 1 12 m 3 24 m 36 m 37 2 18 m 4 30 m

All springs string and pulley shown in figure are light Initially when both the springs were in their natural state the system was released from rest The maximum displacement of block m is Calculate x X X he 5mg k Spring Spring2 K U reageer 10000er K O m 11

35 An almost inertia less plank AB can rotate about a stationary horizontal axle O Its end B rests on a platform where a small block of mass m is placed on it at a distance I from the axle as shown in the figure A bead of mass mo dropped from a height ho hits the platform near the end A at a distance lo from the axle If all the collisions are perfectly elastic and every object is perfectly rigid find height h to which the block will jump O mo ho Alo 0

9 4 6 g If W is the amount of work done in forming a 39 soap bubble of volume V then amount of work in forming a bubble of volume 2V from the same solution 1 W 2 2W 3 W 22 3 4 W X 24 3 A tiny sphere of mass m and density x is dropped 40 4 6 g afe enga fand wat Jag fax 1 W 2 2W 3 W x 223 4 W x 243 X 741 PERI

A spherical conductor of radius 2 m is charged to a potential of 120 V It is now placed insid another hollow spherical conductor of radius 6 m Calculate the potential of bigger sphere if th smaller sphere is made to touch the bigger sphere a 120 V c 80 V b 60 V d 40 V

2 Two springs are stretched by applying forces in two situations 1 A VN B F If the potential energy stored in them are UA and U then the ratio UA UB is 1 K k 0000000 F F K voord00 2 K K

13 A particle of mass m is executing oscillations about the origin on the X axis with amplitude A Its potential energy is given as U x bx where is a positive constant The x coordinate of the particle where the potential energy is one third of the kinetic energy is A 1 2 A 3 4 A 2 2 4 A

Potential energy U as a function of r is shown below If a particle P of mass m and energy E starting from r a moves towards the origin then U 1 0 b Um a m E There is only one turning point for the particle Speed of the particle starts to increase at r a and reaches its maximum atr c Speed at b is minimum Speed of the particle at r a and r b are equal

22 The variation of potential energy of harm is as shown in figure The spring constant is K 10 N m Find the value of K U Joule A 0 0 0 04 0 01 y in mm

3 Three particles of masses 1 kg 2 kg and 3 kg are situated at the corners of an equilateral triangle move at speed 6 ms 3 ms and 2 ms respectively Each particle maintains a direction towards the particle at the next corner symmetrically Find velocity of CM of the system at this 2kg instant 1 3 ms 2 5 ms 3 6 ms 6ms 3 ms 4 2mr 3 kg

A 3 kg block is sliding across a horizontal surface The initial speed of the block is 4 m s but because of friction the block s speed will decrease at a constant rate i e constant acceleration until the block finally comes to a stop after sliding 8 m What is the average power in W supplied by friction as the block slows to a stop

A Carnot s engine operates with an efficiency of 40 with its sink at 27 C By what amount should the temperature of the source be increased with an aim to obtain the efficiency 50 1 50 K 2 150 K 3 80 K 4 100 K

3 A person pulls on the spring stretching it 3 0 cm which requires a maximum force of F 75 N Fig 4b a Find the spring constant k for this spring b How much work does the person do c If instead the person compresses the spring 3 0 cm Fig 4c how much work does the person do a www b F Fs Fig 4

ALLEN Adjacent figure shows the force displacement 9 fafferde fam graph of a moving body the work done in fax 0x35m forenfura displacing body from x 0 to x 35m is equal to Force N 22 5 05 10 15 20 25 30 35 40 Displacement m 2 25 J 4 200 J 1 50 J 3 287 5 J Force N 29 M 1 50 3 287 5 05 10 15 20 25 30 35 40 Displacement m 2 25 4 200

3 287 5J 4 200 J A force of 5 N making an angle 8 with the 10 horizontal acting on an object displaces it by 0 4m along the horizontal direction If the object gains kinetic energy of 11 the horizontal component of the force is 1 1 5 N 2 2 5 N 3 3 5 N 4 4 5 N When a 1 0 kg mass hangs attached to a spring of 11 3 287 5 f 4 200 0 fard 0 4 m fenfura azan afe and effe 1 15 N 3 3 5 N 2 25 N 4 4 5 N 1 0 kg 50 cm fem cell

A truck weighing 8000 kg is moving along 30 a track with negligible friction at velocity 1 8 m s the engine turn off when it begins to rain hard The raindrops fall vertically in the truck The speed of the truck when it has collected 1000 kg of rain water is 1 1 6 ms 2 10 ms 3 3 ms 4 9 ms 8000 kg 1 8 m s faa ti i f 1000 k 1 1 6 ms 3 3 ms 2 10m 4 9 ms

A man is running on horizontal road kinetic energy of a boy of half of his mass When man speeds up by 1 m s then his KE becomes equal to KE of the boy the original speed of the man is 1 2 m s 2 2 1 m s 4 2 1 m s 3 2 m s

Energy 5 A chain is on a frictionless table with one fifth of its length hanging over the edge If the chain has length L and mass M the work required to be done to pull the hanging part back onto the table is 1 3 MgL 5 MgL 2 4 MgL 50 MgL 10

The rate of doing work by force acting on a particle moving along x axis depends on position xo particle and is equal to 2x The velocity of particl is given by expression 1 3 3x m 2mx 9 1 3 1 2 2 4 3x 2m 1 3 2 71 2 mx 3

A bullet of mass 20 g leaves a riffle at an initial speed 100 m s and strikes a target at the same level with speed 50 m s The amount of work done by the resistance of air will be 1 100 J 2 25 J 3 75 J

22 A particle located in one dimensional potential field a b has potential energy function U x x where a and b are positive constants The position of equilibrium corresponds to x 1 6 3 3a 2b 2a 2 4 2b 3a 3b 2a

10 A spring of force constant K is first stretched by distance a from its natural length and then further by distance b The work done in stretching the part b is 1 3 Ka a b 2 Kb a b 2 2 1 2 Ka a b 4 Kb 2a b 2

52 A small sphere of radius falls from rest in a viscous liquid As a result heat is produced due to viscous force The rate of production of heat when the sphere attains its terminal velocity is proportional to a 3 c r5 b 4 d NEET 18

A girl of mass 65 2 kg is travelling at a speed of 18 2 m s at the top of a 21 5 m high roller coaster loop a Determine the girls kinetic energy at t he top of the loop b Assuming negligible losses of energ y due to friction and air resistance dete rmine the girls total mechanical energy at the bottom of loop h 0 m

Consider a drop of rain water having mass 1g falling from a height of 1 km It hits the ground with a speed of 50 m s Take g constant with a value 10 m s2 The work done by the i gravitational force and the ii resistive force of air is NEET 2017 1 i 1 25 J ii 8 25 J 2 i 100 J ii 8 75 J 3 i 10 J ii 8 75 J 10 16 8 25 1 4 6

9 A He ion is at rest and is in ground state A neutron with initial kinetic energy K collides head on with the He ion For which value of K collision between these two particle may be inelastic 1 40 8 eV 3 20 3 eV 2 48 3 eV 4 52 eV tions

3 2g 5 3g 4 30 8 A particle is displaced from 1 2 m to 0 0 m along the path y 2x Work done by a force F x y N acting on the particle during this displacement is 1 1 5 J 3 3 J 2 3 5 J 4 2 5 J Medi

1 2 3 5 3 3J 4 2 5 J Maximum acceleration of block A after its collision with block B as shown in figure has magnitude assume collision to be elastic both blocks are of mass m 1 3 m A ve 2 m B

2 10 The potential energy function in one dimension is given as shown in figure If total energy of the particle is 5J Then in the region from x to x2 the value of its kinetic energy will be U x 8 J 3 J 1 8 J 3 5 J X ons X 2 11 J AY X

A sphere of mass m is tied to end of a string of length and rotated through the other end along a horizontal circular path with speed v The work done by centripetal force in full horizontal circle is 1 0 2 mv 2 l 3 mg 2 l 4 1 1

A mass m slips along the wall of a semispherical surface of radius R The velocity at the bottom of the surface is MP PMT 1993 m 1 Rg V 2 2 Rg 3 2 TRg 4 TRg R

A body starts moving from rest in straight line under a constant power source Its displacement in time t is proportional to 1 t 2 2 t 3 t 2 4 2

Potential energy U related to coordinates is given by U 3 x y Work was done when the particle is going from 0 0 2 3 is 1 15 J 2 15 J 3 12 J 4 10 J

The velocity given to the block of mass m 7 is gl to rotate it in a circle of radius I Calculate the height h where the block leaves the circle 1 2 AO WA N W 31 41 3 51 10 4 None of these

lying at rest on a horizontal surface The wedge has a cavity which is the portion of a sphere of radius R A small sphere of mass m is released from the top edge of the cavity to slide down All surfaces are smooth Choose correct option s A R 60 B 4gR V3 B The maximum height above B to which the sphere will rise after treaking off the wedge is 10R 11 C The distance moved by the wedge when the sphere reaches B is R 3 A The maximum speed acquired by the sphere is R D The maximum speed acquired by the wedge is V3

estions 1 A body of mass 1 kg falls freely from a height of 100 m on a re platform of mass 3 kg which is mounted on a spring having spring constant k 1 25 x 106 N m The body sticks to the platform and the spring s maximum compression is found to be x Given that g 10 ms 2 the value of x will be close to 2 a 8 cm c 40 cm JEE Main 2019 11 Jan Shift I b 4 cm d 80 cm

In the Bohr s model of hydrogen like atom the force between the nucleus and the electrons is modified as e 47 0 F Option 3 Ta ao Where is a constant For the atom the radius of the nth orbit in the terms of the Bohr radius 0h m 2 ao Option 1 Tn aon B Option 2 rn ao n B n n Option 4 Tn ao nt 3 Correct Answer In ao n B

A circular current loop of magnetic moment M Is in an arbitrary orientation in an external magnetic field B The work done to rotate the loop by 30 about an axis perpendicular to Its plane is MB 3 MB 2 MB 2

3 1 05 4 0 15 An engine of a motor pulls up a 20 kg mass slowly through a height of 10 min 10 s The power consumption of the engine if it works at an efficiency of 60 is g 10 m s 1 200 W 2 666 6 W 3 600 W 4 333 3 W er

A block of mass m is dropped onto a spring of constant k from a height h The second end of the spring is attached to a second block of mass m as shown Find the minimum value of h so that the block M bounces off the ground if the block of mass m sticks to the spring immediately after it comes into contact with it M 2mM g 2Km M 2mM g 2Km M mM g 2Km None of these m K

A B 00000000 3 K C i The spring between ceiling A is cut ii The string inextensible between A and B is cut iii The spring between B C is cut Also find the tension in the string when the system is at rest and n the above 3 cases

3 ML T A2 T 4 M L T2A T 19 A particle moves along the x axis from x 0 to x 5 m under the influence of a force given by F 5 2x 3x N The work done in this process is process 20 1 100 J 3 135 J On the horizontal surface of a truck a block of 2 125 J 4 90 J Me

0 Two ideal helical springs have spring constants K 20 N m and K 40 N m respectively If they have been pulled by same force and potential energy stored in first spring is 60 J then potential energy stored in second spring will be O 60 J O 30 J 015 J 4 points 0 10 J

13 A particle of mass m is moving with a velocity v and another particle of mass m is moving with a velocity V Both of them have the same momentum but their different kinetic energies are E and E respectively If m m then 2 A E E B E m E m C E E 7 D E E 00 A

A body of mass 0 5 kg travels in a straight line with velocity v ax 2 where a 5 m s The work done by the net force during its displacement from x 0 to x 2 m is A 1 5 J B 50 J AM 900 C 10 J D 100 Je owT S