Work, power & energy Questions and Answers

Statement A Energy is cause for doing work and work is th effect Statement B Energy is scalar quantity but power is a vector quantity A and B are correct A and B are incorrect A is correct and B is incorrect A is incorrect and B is correct

4 kg mass F moving at 5 m s to the x direction collides with a 3 kg mass G at rest After the collision mass F moves at 3 m s rig and the 3 kg mass moves at 1 m s right also What energy was lost after the collision A 40 5 J B 50 5 J C 60 5 J D 70 5 J 30 5 1

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

51 A cricketer hits a ball and it possess kinetic energy E ball making an angle 30 with horizontal then its K E at the highest point is a C 3E 2 3E 4 b E d 3E 4

36 A body of mass mis tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity The elongation in the spring is 5 cm The original length o the spring is EAMCET Med 2003 a 16 cm d 13 cm b 15 cm c 14 cm

The hysteresis loss for a specimen of iron weighing 12 kg is 250 J m cycle 1 The density of iron is 7500 kg m 3 The energy loss at a frequency of 50 cycle s in 20 minute is 6 4 104 J 4 4 104 J 2 4 104 J 8 4 104 J

A sphere of mass m makes SHM in a hemispherical bowl ABC and it moves from 4 to C and back to A via ABC so that PB h If m acceleration due to gravity is g the speed of the ball when it just crosses the point B is a 2gh b mgh c 2gh d h

65 Calculate power generated by tension in the string in first 2 seconds of motion Jaz 1 250 W 2 P F V 10 2 500 W 3 750 W 109 10 9 0 4 1000 W 150 10 15000 10 9 T 10 16 70x39 10 a tog 159 2 2

For the system shown in figure both particles has equal mass 5 kg and charge 100uC The spring is in its natural length and has a spring constant 10 N m find the maximum elongation in the spring when thread is burnt Take g 10m s thread 15 PE mmmmmm spring

2 A hammer with a head of mass M is to be used to drive nails horizontally into a wall A force of Frequired to penetrate the wall Each blow should force the nail a distance x into the wall What should be the velocity of the hammer s head to strike the nail 2M 2Fx M Fr Fx 1 M Fx 2 EX V 2M 3 V 4 1

A particle of mass m initially at rest is acted upon by a variable force f varying with time t It begins to move with a velocity u after the force stops acting curve is a semi circle Force 1 u 2 u 3 u 4 u 2 f 2m T 8m f T 4m f T 0 fo 0 t T

A pump is used to deliver water at a certain rate from a given pipe To obtain n times water from the same pipe in the same time by what factor the force of the motor should be increased 1 n times 3 n times 2 n times 1 4 times

Two rings of same mass and radius R are placed with their planes perpendicular to each other and centres at a common point The radius of gyration of the system about an axis passing through the centre and perpendicular to plane of one ring is 1 2R 3 R R 2 2 4 3R

A particle of mass m moves on a straight line with its velocity varying with the distance travelled If the relation between velocity and distance is v Kx K is constant then find the work done by the forces during a displacement x 0 to x d 1 mkd2 2 2 mk d 2

6 14 A smooth tunnel is dug along the radius of earth that ends at centre A ball is released from the surface of earth along tunnel Coefficient of restitution for collision between soil at centre and ball is 0 5 Calculate the distance travelled by ball just before second collision at centre Given mass of the earth is M and radius of the earth is R Ans d 2R

In a hydroelectric plant the available head is 80 m for a discharge 12m sec and overall efficiency of the Power Station of 80 The specific weight of water is 9 81 k m2 Then the power developed is in MW

An object does 50 J of work Which of following statements is a correct description of what happens to the energy of the object afterwards Select one O a Its energy does not change O b Its energy decreases 50 J O c None of the options are correct d Its energy increases by 50 J

a At a certain instant a particle like object is acted on by a force F 3 30 N 7 2 00 N 6 40 N while the object s velocity is 2 20 m s i 5 50 m s k What is the instantaneous rate at which the force does work on the object b At some other time the velocity consists of only a y component If the force is unchanged and the instantaneous power is 17 0 W what is the velocity of the object just then Give your answer without a unit vector a Number Units

A 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 7 If string rotates through an angle 60 before its velocity becomes zero then value of u will be 3gl 2 2gl 2gl 3 fgl

In the figure shown below masses of blocks A and B are 3kg and 6kg respectively The force constants of springs S and S are 160N m and 40N m respectively Length of the light string connecting the blocks is 8m The system is released from rest with the spring at their natural lengths The maximum elongation of spring S will be A S B S

A source of sound emits 400 W power which is uniformly distributed over a sphere of 10 m radius What is the loudness of sound on the surface of a sphere 1 200 dB 2 200 dB

A particle A suffers an oblique elastic collision with a particle B that is at rest initially If their masse the same then after the collision A they will move in opposite directions B A continues to move in the original direction while B remains at rest C they will move in mutually perpendicular directions D A comes to rest and B starts moving in the direction of the original motion of A 10

Two blocks A and B of mass 2kg and 1kg respectively are kept on a frictionless horizontal surface They are connecte by a massless spring of spring constant 100 N m An initial velocity 1 m s and 6 m s is imparted to blocks 2kg and 1kg respectively in same direction when spring is in its natural length The ratio of maximum speed to minimum speed for the block of mass 2kg is 2 kg 1 kg 1 0 O mrrrrr 13 3 8 3 1 None of these

27 The force required to stretch a spring varies with the distance as shown in the figure If the experiment is performed with the above spring of half the length the line OA will F V Ha a shift towards F axis it in X b shift towards X axis d become double in length

The potential energy of a particle of mass m 4kg in a conservative force field can be expressed as U 3x 4y where x y denote the position coordinates of the body The acceleration in m s2 of the body is 1 35

A particle of mass 1 5 kg moves along x axis in a conservative force field Its 2x 9x 12x where all quantities are written in SI units The plot of this potential energy is given below potential energy is given by U x U H 5 4 Which among the following is are correct A x 1 is stable equilibrium B x 2 is stable equilibrium C x 1 is unstable equilibrium D x 2 is unstable equilibrium

pushed by a 30 N force Find work done by contact force between 8 kg 2 kg block o the 2 kg block 30 N during first 4 seconds a 144 J b 144 J c 72 J 8 kg 2 kg d 72 J

Sing A large block of wood of mass M 5 99 kg is hanging from two long massless cords A bullet of mass m 10 g is fired into the block and gets embedded in it The block bullet then swing upwards their centre of mass rising a vertical distance h 9 8 cm before the block bullet pendulum comes momentarily to rest at the end of its arc The speed of the bullet just before collision is take g 9 8 ms 2 831 4 m s 811 4 m s ay B m M

A large block of wood of mass M 5 99 kg is hanging from two long massless cords A bullet of mass m 10 g is fired into the block and gets embedded in it The block bullet then swing upwards their centre of mass rising a vertical distance h 9 8 cm before the block bullet pendulum comes momentarily to rest at the end of its arc The speed of the bullet just before collision is take g 9 8 ms 2 O 831 4 m s 811 4 m s 841 4 m s E to M

3 Internal forces can change a the linear momentum but not the kinetic energy b the kinetic energy but not the linear momentum c linear momentum as well as kinetic energy d neither the linear momentum nor the kinetic energy

The positively charged particles X and Y are initially far away from each other and at rest X begins to move towards Y with some initial velocity The total momentum and energy of the system are p and E 1 If Y is fixed both p and E are conserved 2 If Y is fixed E is conserved but not p 3 If both are free to move p is conserved but not E 4 If both are free E is conserved but not p

A hand generator is attached to a motor and the hand crank is turned Which answer best describes the conversions of energy in this process a Electric energy is converted to mechanical kinetic energy then the kinetic energy is converted to electric energy b Mechanical Kinetic energy is converted to electrical energy then the electrical energy is converted to mechanical kinetic energy c Electric energy is converted to mechanical kinetic energy then the kinetic energy is converted to potential energy d Mechanical Kinetic energy is converted to electrical energy then the electrical energy is converted to light energy

2 A small sphere of radius r falls from rest in a viscous fluid 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 1 r 3 r5 2 14 4 r 2

Q1 A small train game moves in a straight line If the force applied is 20 N as shown in the fig and the work done which lead to move the train 5 m is 86 6 J compute the value of 0 which is between the force and the moving direction Then re compute the work done if 0 is reduced 20 of its value W 86 6 J 1 0 D 5m F 20N

8 With what minimum speed v must a small ball should be pushed inside a smooth vertical tube from a height h so that it may reach the top of the tube Radius of the tube is R a 2g h 2R c g 5R 2h R b R d 2g 2R h s

Which of the following is always true of an object whenever work is done on the object A The object moves B The object accelerates OC The forces acting upon the object are balanced O D The forces acting upon the object are unbalanced

small object of uniform density rolls up a curved surface with an initial velocity v It reach 3v to a maximum height of with respect to the initial position The object is 4g ring B solid sphere C hollow sphere D disc

A block of mass m is released at rest from a point P of a rough circular path of radius r as show in the figure There is a spring of stiffness k at the other end of the path acceleration due gravity g unite to weite tactenos guhegandW P miur me beniuper sorol al II 21 0 01 200 oluot to m 2 15 12 ani bohovito sextoold ad of boilqque al varsas aud b more than 2mgr km 5 2 001 d less than 2mgr k The maximum spring deflection is a independent of r c equal to 2mgr k till

3 A stationary body explodes into two fragments each of rest mass 1 0 kg that move apart at speeds of 0 6c relative to the original body Find the res mass of the original body 1 Point 2 5 kg 2 0 kg O 1 6 kg

S Testy body of mass m starting from rest from origin moves along x axis with constant power P Calculate relation between velocity distance 1 x x 1 2 2 x x v 3 x x v 4 x x v dv Ly

A block of mass 2kg is placed on a s mooth horizontal surface Two forces F1 20N and F2 5N start acting on th e block in opposite directions as sho wn If block gets displayed by 5m in t he direction of net force then work d one by F2 is A block of mass 2 kg is placed on a smooth horizontal surface Two forces F 20 N and F25 force on the block in opposite directions as shown If block gets displaced by 5 m in the direction of net work done by F is 1 75 1 2 F 75 1

15 A force F 6i 8j N acts on a particle and displaces it over 4 m along the X axis and then displaces it over 6 m along the Y axis The total work done during the two displacements is 21

C 17 A force acts on a body and displaces it in its direction The graph shows the relation between the force and displacement the work done by the force is 60 N a 420 J c 840 J F 02 m S b 360 J d 720 J 14 m

d 12 J 14 A rain drop of mass 1 10 gram falls vertically a constant speed under the influence of the forces o gravity and viscous drag In falling through 100 m the work done by gravity is a 0 98 J b 0 098 J d 98 J c 9 8 J

23 A system consists of two cubes of masses my and m2 respectively connected by a spring of force constant k The force F that should be applied to the upper cube to keep it at rest for which the lower one just lifts after the force is removed is IF m a mig c m m g eeeee m b mm m m d m2 g g 27 A 28

24 A block of mass m 2 kg is moving with velocity vo towards a massless unstretched spring of force constant k 10 N m Coefficient of friction between 1 Find maximum the block and the ground is 5 a 12 m s c 10 m s value of vo so that after pressing the spring the block does not return back but stops there permanently b 4 2 m s d 6 4 m s

A block given a velocity u on horizontal ground not frictionless is observed a distance s away a time 7 later Find coefficient of kinetic friction between the floor and the block Acceleration of free fall is g Answer u 2gs 2 0 s UT 2

30 In the figure the variation of components of acceleration of a particle of mass 1 kg is shown with respect to time The initial velocity of the particle is u 31 4j m s The total work done by the resultant force on the particle in time interval from t 0 to t 4 s is ax in m s a 15 J c O 37 t in s ay in m s 1 37 earm to hoold 1120016 b 10 J d 20 J t in s Swisd

1 2 2 3 3 4 4 525 23 A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity v An elastic impact lasts for a time At 21 1 the average elastic force acting on the balls is m u v A 2m u v Ar 2 the average elastic force acting on the balls is 3 the kinetic energy of the ball increases by mu u v 4 the kinetic energy of the ball remains the same after the collision article is mor girouler poth and its comploration vector in making onala of 20

are 36 Three components of a force acting on a particle varying according to the graphs as shown To reach at point B 8 20 0 m from point A 0 5 12 m the particle moves on paths parallel to x axis then y axis and then z axis then work done by this force is Fx in N Fy in N 10370 a 192 J c 250 J x in m F in N 16 20 12 15 y in m z in m b 58 J d 125 J