Work, power & energy Questions and Answers

Water falls from a height of 60 m at the rate of 15 kg s operate a turbine The losses due to frictional forces a 10 of energy How much power is generated by t turbine g 10 m s 1 12 3 kW 3 8 1 kW 2 7 0 kW 4 10 2 kW

Q 95 Consider a drop of rain water having mass 1 g 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 s The work done by the i gravitational force and the ii resistive force of air is a i 1 25 J b i 100 J c i 10 J d 101 ii 8 25 J ii 8 75 J ii 8 75 J Gil 8 251

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 1 60 J 2 30 J 3 15 J 4 10 J

A neutron makes a head on elastic collision with a stationary deuteron The fractional energy loss of the neutron in the collision is 1 16 81 8 9 8 27 2 3 3 4 ect Answer 2 Answer 4 us incorrect dd to Bookmark List 36 Four Statomipro 0 0 COTOUC 20 7GVITOGE 20 0 A neutron makes a head on elastic collision with a stationary deuteron The Right Answer 2 Your Answer 4 Difficulty Level medium Topic physics collisions and centre of mass

A 75 0 kg box is pulled from rest along a friction less horizontal floor by a rope that is angled upward at 24 00 above the horizontal The tension in the rope is 98 4 N What is the speed in m s of the block after the block has moved 3 00 m along the floor

A bomb of mass 9kg initially at rest explodes into two piece of masses 3 kg and 6 kg The kinetic energy of the 3 kg mass is 216 J The kinetic energy of the 6kg mass will be A 213 J C 432 J B 108 J D 54 J

A bomb of mass 5m initially at rest explodes and break into three pieces of masses in the ratio 1 1 3 The two pieces of equal mass fly off perpendicular to each other with a speed V Then the velocity of the heavier piece is 1 1 3 2 V 2 3 V 2 3 4 Vo

The graphs below shows the magnitude of the force on a particle as the particle moves along the positive x axis from the origin to x x The force is parallel to the x axis and is conservative The maximum magnitude F has the same value for all graphs Rank the situations according to the change in the potential energy associated with the force least or most negative to greatest or most positive F F X X 1 1 1 2 3 F F 2 X X F 2 1 3 2 3 X

Work done by external agent on a test charge q in moving it in an electrostatic field 3 D depends on initial and final speeds depends on its initial and final positions is independent of its initial and final positions both a b 2 both a c 4 b only C 1 3 a only

And answer the questions i to iv based on the above diagram 4 i S I unit of work done for the given system is 1 Newton 2 Joule Sec 3 Joule 4 Newton sec ii Work done by the given system is its initial position at a constant acceleration of 2 m s2 1 5 J 2 5 N 3 2 N 4 2 J iii According to the work energy theorem which of the following statement is correct Here K change in kinetic energy and W work 1 K 1 W 2 K W 3 K W 4 None of these iv What will be the velocity of an object for the given system if 100 N of force is applied to it as we can see in the given figure 10 Kg A 1 25 m s 2 20 m s 3 15 m s if it s displaced by 10 cm from 2m F B

no a A coil having a resistance of 702 and an inductance of 31 8mH is connected to 230V 50Hz supply Calculate i the circuit current ii Phase angle iii Power factor iv Power consumed v Voltage drop across resistor and inductor

1 In the figure shown below all pulleys and ropes are massless and frictionless Initially the 5kg and 3kg blocks are at rest When released it is noticed that the 5kg block goes up by a height 4m above its initial position At this instant find the speed of 3kg block Enter the answer in two decimal places 5kg 3kg

3 A massless spring of force constant k 25 N m is tied to a massless string that passes over a smooth pulley and is connected to the roof as shown From the pulley hangs a block of mass M 16kg Initially the spring was unstretched and the block was at rest Then block is released find the maximum speed of the block g 10m s 4 eatter M

A DC shunt motor being fed from a 200v supply runs at 750 rpm with field current 2A Neglecting armature copper loss and all parameter kept constant Find the speed with field current 1 5A a 750 rpm 1000 rpm b 350 rpm d 1500 rpm

A small particle slides along a track with elevated ends and a flat central part as shown in figure The flat part has a length 3m The curved portions of the track are frictionless but for the flat part the coefficient of kinetic friction is 0 2 The particle is released at point A which is at a height h 1 5 m above the flat part of the track The position where the particle finally come to rest is A left to mid point of the flat part C Mid point of the flat part h B right to the mid point of the flat part D None of these 3 0m

Ves the masses slowly along the paths PQR and along ABC The rough surfaces shown are AB and PQR and coefficient of friction for these paths is Select the correct alternative from follow 30 2h m II Work done by external agent in case I is greater than work in II O Work done by external agent in case 1 is less than work in II

The block has mass M and rests on a surface for which the coefficient of friction If a force F kt is applied to the cable see figure the power P developed by the force F at t t is approximately kilowatt Write P 10 in OMR sheet Given M 20 kg 0 4 k 40 N s t 3 sec F

see 2011 x axis It is at rest at t 0 If the force on the particle varies with time then its kinetic energy at 4 5 s is F N 4 2 2 25 J 3 s 3 5 J 4 5 s t s 2 1 25 J 4 Zero au of mors m starts from rest with a constant 1 2 72 74 3 12 2 4 1 SECTION B Previous Years Questions 1 A body initially at rest and sliding frictionless track from a height h as shor figure just completes a vertical circle of AB D The height h is equal to NE A

ERA A particle of mass 0 5 kg is subjected to a force which varies with distance as shown in graph F N 16 21 Sec 10 myjt 2 16 m s 4 4 m s Nime X m 4 8 12 If the speed of the particle at x 0 is 4 m s then its speed at X 8 mis 1 8 m s 3 32 m s A ball of mass m moving a head on collision with an ide kinetic energy of the ball at of the original Find the coe 3 5 1 5 2 10 In head on elastic collision masses 1 The velocities are inter 2 The speeds are interc

Current through a resistance Rvaries with time ras Kn 41 Osrst If total charge flown through resistance in time interval t 0 to t to is Qo then heat n GR Find the value of n issipated in resistance R in this time interval is Answer

A paricle of mass 2kg is free to move al ong x axis under the influence of a con servative force Ux x4 5x If total mec hanical energy is equal to zero Calculat e a Maximum speed of the particle b Plot the potential energy function gra ph

In the figure shown if extension of spring is xo at time t the displacement of first block is initially the blocks are at rest and spring is relaxed block 1 k m ooooooooo smooth block 1 61 DAR 1 Ag u ich chi faz ua 4 ich Part block 2 block 2 k moordver m F 0 1 1 5PM A Ft 2m smooth c faxia Ft m XO 2 11 m F xo Correct Answer xo Ft co m

For the series LCR circuit shown in the figure what is the resonance frequency and the amplitude of the current at the resonating frequency 220V 8mH mmmmm ww 4492 20 F 1 2500 rad s and 5 2A S 2 2500 rad s and 5A 5 2 4 25 rad s and 5 2A 3 2500 rad s and S A

The 6 0 kg object below is released from rest at a height of h 5 0 m on a curved frictionless ramp At the bottom of the ramp the object then slides a distance d on a rough horizontal surface before hitting a spring of force constant k 500 N m The object then compresses the spring a distance x before comin momentarily to rest The coefficient of kinetic friction between the block and the horizontal surface is uk 0 2 6 The 6 0 kg object below is released from rest at a height of h 5 0 m on a curved frictionless ramp At the bottom of the ramp the object then slides a distance d on a rough horizontal surface before hitting a spring of force constant k 500 N m The object then compresses the spring a distance x before coming momentarily to rest The coefficient of kinetic friction between the block and the horizontal surface is 0 2 Dram a What is the speed of the object at the bottom of the ramp b What is the speed of the object at the instant it collides with the spring c Find the compression distance x fa 9 90 m s h 7 66 m s c 082 ml

Question 11 A body of mass 10 kg is initially at a height of 20 m above the ground It falls to a heightof 5 m above the ground Its potential energy in the new position is a 490 J b 50 J c 100 J 2001

The work done on a body when taken from point A to B along three different paths is as shown figure Same conservative force is applied along the three path but one of the path has a non conservat force also The workdone by non conservative force will be The number show work done in part 12J 10J O 40J A 5J 25J 18J 8 J B D 21

If the dimensions of a physical quantity are given by MALT then the physical quantity will be a velocity if a 1 b 0 c 1 b acceleration if a 1 b 1 c 2 c force if a 0 b 1 c 2 d pressure if a 1 b 1 c 2

1 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 mm 1 0 01 m s 3 0 14 m s O O mor 2 1 4 m s 4 14 m s

Consider the following sketch of potential energy for a particle as a function of position There are no dissipative forces or internal sources of energy The maximum total mechanical energy in Joule that the particle can have if it is to be trapped within the region of x shown is 6 PE J 10 x m

An observer and a vehide both start moving together from rest towards right with acceleration 1 m s and 2 m s respectively There is a 1 kg block on t floor of the vehide and coefficient of friction between their surface is 0 1 What is the magnitude of the work done in J by frictional force on the 1 kg block observed by the running observer during first second of the motion 1kg 2 m s 1 m s

The areas of a ship s waterplanes commencing from the load waterplane and spaced 1m apart are as follows 800 760 700 600 450 and 10 square meters respectively Midway between the lowest two waterplanes the area is 180 square meters Find a the load displacement in salt water and b the height of the centre of buoyancy above the keel 2966t 3 01m

If force acting on the block of mass M is F F ex where Fo a are constants and x is x co ordinate of block Find the work done by force F from x 0 to x d will be A Fo ead 1 a B Fo dead C Fo end 1 a D Zero

A non conducting rod of length 2m is hinged at one end and a charge of C is 10 distributed uniformly over it At t 0 it is released from the position shown There exist a uniform magnetic field of 15 T inside the plane of motion of rod If mass of rod is 100 g then find the value of hinge force in N when rod T is rotated by due to gravity 2 released at t 0

When a train is acclerated motion some pebbles are dropped from the train So what will be frame of reference inertial or non inertial with respect to me when I rest And same question for velocity when velocity substitute accleration 4 35 PM

64 A particle is attached to the lower end of a uniform rod which is hinged at its other end as shown in the figure The minimum speed given to the particle so that the rod performs circular motion in a vertical plane will be length of the rod is l consider masses of both rod and particle to be same a 5gl b 4gl m I m c 4 5gl d 2 25 gl

b A sphere of mass 1 kg moving at 3 m s overtakes another sphere of mass 5 kg moving in the same line at 60 cm s Find the loss of kinetic energy during impact and show that the direction of motion of the first sphere is reversed Take coefficient of restitution as 0 75 5 marks

3 x 1 8 m 4 x 1 8 m A small ball is pushed from a height h along a 15 smooth hemispherical bowl With what speed should the ball be pushed so that it just reaches the top of opposite end of bowl The height of the top of the bowl is R 1 2gh 2 2gR 3 4 2gR R h 2gR R h V V R 3 x 1 8 m gan faena ardhitellen 2 x 3 m 4 x 1 8 m en any auch an dies ada o gut f r dan uma R 1 2gh 2 2gR 3 2gR R h 4 2gR R h R 1 0999DMD31032

16 In the circuit shown in the figure if the potential at point A is taken to be zero the potential at point B is a 1 V c 2 V 1A R A R www 2 V Pelill D HIB 292 1V AC2A www b 1 V d 2 V 42A 17 A galvanometer of resistance G is shunted by a resistance Sohm To keen the main qu 22 7071

A block of mass mis suspended by a light thread from an elevator The elevator is accelerating upward with uniform acceleration a The work done by tension on the block during 1 seconds is m

In two dimensional motion instantaneous speed v is a positive constant Then which of the following is necessarily true The average velocity is not zero at any time Average acceleration must always vanish Displacement in equal time intervals are equal Equal path lengths are traversed in equal time intervals

7 A simple pendulum bob in position when the is vertical is projected with such a velocity t velocity in the horizontal position becomes t projected velocity The net force on the bob horizontal position is 1 mg 2 13 2 16 3 7 mg

A particle of mass M and charge Q moving with velocity v describes a circular path of radius R when subjected to a uniform transverse magnetic field of induction B The work done by the field when the particle completes one full circle is 1 BQv2 TR adt 121 2P 2 4 Mv R none of these 2 R

The force acting on a particle cons move along y axis varies as shown below F CDE Fdx casi Poso AB Consider the following statements a D is neutral equilibrium position neutral b E is stable equilibrium position unstable Choose the correct statement s 1 Only a 2 Only b 3 Both a and b Neither a por b Aa fooo

In figure I the winch is mounted on axle and the 6 sided nut is welded to the winch By turning the nut with a wrench as shown in figure II a person can rotate the winch in order to lift the block of m Here one end of the thread is connected to block and other end is connected to periphery of winch Which of the following statements are correct regarding lifting of block by one meter in 10 seconds nut block winch wrench Force Figure I Figure II A By using a longer wrench decreases the average force applied by the person on wrench B using of a longer wrench reduces the work to be done by the person C using of a longer wrench reduces the power to be delivered by the person D using of a longer wrench reduces the number of rotations to be rotated

Displacement of a particle of mass 1 kg varies with time as 2 2t 10 where s is in m and tin s The total work don on the particle in a time interval from t 0 to t 2 s will be 16 J 32 J 18 J 36 I

A motor takes water from 10 m underground and delivers it into a tank at a height of 10 m The tank receives water at rate of 0 5 kg s at speed 10m s Find the power of the motor if its efficiency is 60

A particle moves in x y plane under the action of a path dependent force F yi xj N Find the work done by the force on the particle when A The particle moves along a straight line From origin to a a B The particle moves from 0 0 to a 0 and then from a 0 to a a in straight line paths

A car of mass 1250 kg is moving at 30m s Its engine delivers 30 kW while esistive force due to surface is 750 N What max acceleration can be given in the car RPET 2000 1250kg Power delivered to raise the speed Pret Pnet P friction Fmax 30 30000 750 x 30 30KW 30m s Fm 3K 30000 225 00

24 The potential energy of a particle moving along the x axis is given by U x 8x 2x4 where U is in joule and x is in meters If the total mechanical energy is 9 0 J the limits of motion are 2 2 2 m 2 2 m 1 0 96 m 0 96 m 3 1 6 m 1 6 m 4 0 96 m 2 2 m 5 0 96 m 1 6 m

A coil of resistance 202 is immersed in 1kg of water and is connected to the terminals of the battery of internal resistance 40 and e m f6 volt for 3 minutes The increase in temperature of water is A 0 93 C C 1 92 C B 0 085 C D 4 31 C