Work, power & energy Questions and Answers

A boy jumps from rest straight upward from a flat stationary concrete surface The boy of mass M leaves the concrete surface with speed u and his centre of mass rises a distance d to the highest point of the motion How much work did the normal force of contact N between the boy s feet and the concrete do the boy A Nd B Mv2 2 C No Nd 4

30 4 sin 0 cm s 15 Q 165 A body of mass 2 kg falls from a height 20 m If it reaches the ground with speed 10 m s then work done by air resistance is 1 300 J 3 200 J 2 100 J 4 400 J 3 30 cm 4 sin 0 cm s Q 165 2 kg a 1 af fer 1 300 J 3 200 J 20m af 10 m s fr 2 100 J 4 400 J

A bead of mass m is attached to lower end of a light inextensible thread that passes through a small frictionless hole in a horizontal tabletop The upper end of the thread is held motionless The bead is pulled aside and projected horizontally to move on a circular path of radius R with a speed vo at a particular depth below the tabletop Find work done in slowly pulling the thread upwards to reduce the depth of circular path of the bead to half of its previous value Do

103 Four identical particles each of mass placed at the corners of a square of side 2 m If this system of particles is rotated about the diagonal AC then moment of inertia of the system will be A D 1 4 kg m 3 4 2 kg m B C 2 8 kg m 4 16 kg m

4 51 A particle of mass m having collides with a stationary particle of mass M deviated by an angle 2 whereas the particle M recoiled at an angle 0 30 to the direction of the initial motion of the particle m How much in percent and in what way has the kinetic energy of this system changed after the collision if M m 5 Ans L 40 1

Q12 A 15 g ball is shot from a spring gu whose spring has a force consta 600 Nm The spring is compressed 5 cm The greatest possible horizontal rang of the ball for this compression Take g 10 ms a 6 m b 8 m c 10 m d 12 m Q13 A car of mass 1000 ka moving with

A mass m is suspended by a spring of force constant k from the ceiling of a lift of mass M The lift moves up with acceleration a due to a constant force F acting on it Potential energy stored in the spring is A O 1mF 2 k m F2 kF P 1 m F a m Cellllllll M

Q4 The potential energy of an object of mass m moving in xy plane in a conservative field is given by U ax by where x and y are position coordinates of the object Magnitude of its acceleration is a a b m a b b m a b c m d Zero

A block of mass 4kg moves on horizontal smooth surface with velocity 31 4 m s as shown in the figure The block collides with spring of force constant 100 N m attached with wall The average value of the force of impact on the block due to the spring is 4kg A 1600 N B 1200 N C 800 N D 400 N mmmm

32 A body of mass 3 kg is under a constant force which causes a displacements in metres in it given by the 1 2 relation s t where t is in seconds Work done 3 by the force in 2 seconds is a 19 1 10 5 J b 5 3 8 J c J d J 2006 19 8 3

4 A pendulum of length L 15 cm is held with its string horizontal and then released The string runs into a peg a distance d below the pivot as shown in figure What is the smallest value of d in cm for which the string remains taught at all times L

3 63 A smooth rubber cord of length whose coefficients of elasticity is k is suspended by one end from the end O as shown in figure 3 131 The other end is fitted with a catch B A small sleeve of mass m starts from the point O Neglecting the masses of the thread and the catch find the maximum elongation of the cord O CA B Figure 3 131 25 od blo LE

move along y axis varies as shown below F y A B C D E Consider the following statements a D is neutral equilibrium position b E is stable equilibrium position Choose the correct statement s 1 Only a 2 Only b 3 Both a and b 4 Neither a nor b A

Q 162 An ideal spring of unstretched length and Q 162 3rfar unstretched atas k amet fe force constant k is stretched by a small length x It is further stretched by another small length y The work done in second stretching omen is 2 k x y 3 ky 2x y en are my 3 ky 2x y 2 k x y

Following figure shows two blocks of masses m and m placed on a surface They are connected by an ideal spring of stiffness k The spring is at its natural length Now a constant pulling force F as shown starts acting on m Find the maximum elongation in the spring FTT m k 00000000 m F o longth of the spring developing

The cars are equipped with a coupling arrangement similar to the one on railroad cars Car 1 overtakes car 2 and they have a totally inelastic collision and become coupled together You know hass of each car m 12 0 kg and m 41 0 kg In addition you are provided with the following graph which shows the momentum of car 1 before during and after the collision p kg m s 100 40 t s

3 A block of mass 5 0 kg is pushed against a horizontal spring with spring constant 250 N m compressing it by 0 20 m The block is released from rest and leaves the spring It then encounters another spring with spring constant 210 N m and compresses it by 0 17 m before coming to rest In between springs the block travels a distance of 0 40 m a What is the coefficient of kinetic friction between the block and the surface Friction exists everywhere between the block and surface including when a spring is compressed b The block then leaves the second spring and heads back toward the first Will it reach the first spring again If so what will be its speed when it just reaches it The block is just touching the spring but not yet compressing it leeeeee weeen un Ju

There are two concentric conducting spherical shells The capacity of system is C when inner sphere is charged and outer is earthed and C when inner sphere is earthed and outer sphere is charged Then C ratio is radius of inner sphere 20 cm radius C of outer sphere 60 cm A 3 C 9 B 6 D 3

D A spring of spring constant k is compressed by an amount of x and a mass m is just placed in contact with it and released Calculate minimum value of x for which the mass m completes the vertical circle in the circular track k vvvvvv 1 2gR E Natural length position 2 R smooth 5gR m V 2 Vk

A block is placed on horizontal smooth surface If a force of constant magnitude F 16 N is acting towards a fixed point C as shown in the figure Then find work done in J by the force F to displace the block from A to B 02x8 072 A 7m B 9m C 12m go 0 43

Shown in the figure below is a block and track system All locations indicated by solid black lines are frictionless The region indicated by the tan hash is a patch of friction with coefficient k 0 255 A small block of mass m 0 67 kg is initially compressed against a spring The spring constant is k 64 0 N m and the initial compression is x 0 24 m After the mass leaves the spring it glides down the hill of height y 0 28 meters and eventually slides to a stop after entering the frictional patch wwwww m X Y V V d Calculate all the following The velocity of the mass after it leaves the spring but before it encounters the hill v The velocity of the mass at the bottom of the hill V3 m s stopped friction m s

ant sed B it 3 46 A particle of mass 0 01 kg travels along a space curve with velocity given by 4i 16k m s After some time its velocity becomes 81 20j m s due to the action of a conservative force The work done on the particle during this interval of time is A 0 32J C 9 6J B 6 9 J D 0 96 J

3 60 Power supplied to a particle of mass 2 kg varies with time 31 2 watt Here t is in second If velocity of particle at t 0 is v 0 The velocity of particle at time t 2s will be A 1 m s B 4 m s C 2 m s D 2 2 m s as P

Marks 4 0 0 A vertical spring mass system with lower enc of spring is fixed made to undergo small oscillations If the spring is stretched by 25cm energy stored in the spring is 5J Find the mas in Kg of the block if it makes 5 oscillations each second

22 System shown in the figure is released from rest when spring is unstretched Pulley and spring are massless and friction is absent everywhere G T wars m N 22 doing Kating 2 ing ka mg 3mg 2 3m A Speed of Block A when block B leaves the contact with ground is g k g 3m B Speed of Block A when block B leaves the contact with ground is 2 k N mas 2 PHYSICS

A light spring of force constant k is placed on a smooth horizontal surface and fixed at one end and other end is connected by a block B of mass m An other block A of mass m moves with a velocity v and collides perfect inelastically with B as shown in figure Find the maximum compression of the spring k B mor A

21 A particle is released from a height H At certain height its kinetic energy is two times its potential energy Height and speed of particle at that instant are was a c H 2gH 3 3 2H 2gH 1 3 3 1941 2 OH gH 3 d 2gH 3

26 The force acting on a body moving along x axis varies with the position of the particle as shown in the figure The body is in stable equilibrium at F 2 a x x c Both x and Yo X2 X Xb x x2 d Naith

19 Power supplied to a particle of mass 2 kg varies with 3t time as P watt Here tis in second If velocity 2 of particle at t 0 is v 0 The velocity of particle at time t 2 s will be S gt a 1 m s c 2 m s b 4 m s d 2 2 m s

10 A block of mass 250 g is kept on a vertical spring of spring constant 100 N m fixed from below The spring is now compressed to have a length 10 cm shorter than its natural length and the system is released from this position How high does the block rise Take g 10 m s 2 a 20 cm b 30 cm c 40 cm d 50 cm

3 A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface figure The rough surface has a friction coefficient of 0 20 with the block If the block is released from rest on the track from a point 1 0 m above the horizontal surface the distance it will move on the rough surface is 1 0 m a 5 0 m c 15 0 m B Rough b 10 0 m d 20 0 m

9 A block of mass 50 kg is projected horizontally on a rough horizontal floor The coefficient of the friction between 61 block and the floor is 0 1 The block strikes a light spring of stiffness k 100 N m with a velocity 2 m s the maximum compression of the spring is b 2 m a 1 m c 3 m d 4 m 0 1 2 m s 50 kg k 0000000

1 A block of mass m is 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 t seconds is u 0 m g a at 2 m c gat 2 a m T a b g a at d 0

2 The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure The mass of the body is 25kg and initial velocity is 2 m s When the distance covered by the body is 4m its kinetic energy would be F N a 50 J c 90 J 20 10 1 ES 20 b 40 J d 10 J

In a race a 70 kg sprinter covers first 20 m in 5 0 s starting from rest and accelerating uniformly What is the average power the sprinter generate during the 5 0 s interval A B C D 1120 W 112 W 224 W 448 W

Column A 1 Force 75 N distance 5 m 2 Force 33 N distance 12 m 3 Work 1 500 Joules Force 30 N 4 Work 1 280 Joules distance 8 m 5 Work 240 Joules distance 20 m 6 Mass 5 kg height 4 m 7 Mass 15 kg height 3 m 8 Potential Energy 147 Joules mass 3 kg 9 Potential Energy 441 Joules mass 5 kg 10 Potential Energy 235 2 Joules height 6 m 11 Work 2200 J time 20 s 2 Potential energy 735 height 3 m 3 Kinetic Energy 2 250 Joules velocity 15m s 4 Power 300 Watts time 10 seconds 5 Kinetic Energy 1 600 Joules velocity 20 m s A 5 meters B 9 meters C D E Column B F 50 meters 4 kilograms 8 kilograms 12 Newtons G 160 Newtons H 196 Joules 1375 Joules J 396 Joules K 441 Joules L 110 watts M 25 kilogram N 20 kilogram O 3 000 Joul

A particle is projected from infinity with a velocity of The perpendicular distance between the target and initial velocity is b The mass of the particle m experiences repulsive inverse square force k r Then closes approach d is O

A body of mass 20 kg is initially at a height of 3 m above the ground It is lifted to a height of 2 m from that position Its increase in potential energy is a 100 J b 392 J c 60 J d 100 J

A frictional less track ends in a circular loop of radius R A block is released from point A on the track then block slides on the track Then find out a Speed of block at point B b Normal reaction force at point B R A m R

A sphere of mass m and radius r is released from a wedge of mass 2m as show ABC is hemispherical position of radius R Impulse imparted to the system consisting wedge and sphere by the vertical wall w w till the time sphere reaches at the bottom most position of spherical portion for the first time is 10g R r Find a Friction between wedge and horizontal surface is absent and between sphere a and wedge friction is sufficient to avoid slipping between them RA COM Made RKH sir 2013 14 CO IM W A m B 2 m

2 A thermally insulated rigid container contain an ide gas heated by a filament of resistance 100 22 throug a current of 1 A for 5 min then change in internal energy is a 0 kJ c 20 kJ b 10 kJ d 30 kJ DQ

v t graph of an object of mass 1 kg is shown Selec the wrong statement 20 v m s 10 10 20 30 t s a Work done on the object in 30 s is zero b The average acceleration of the object is zero c The average velocity of the object is zero

Three balls A B and C each of mass m and same size are placed along same line on smooth horizontal surface A is given a velocity u towards B as shown If coefficient of restitution for collision 1 between A and B is and between B and C is Choose the correct option s Assume all the 1 2 3 collisions to be headon Made RKH Sir 2013 14 AB 3 A The total energy loss due to all possible collisions will be 16 5 B The total energy loss due to all possible collisions will be mu 16 C Final velocity of A and B will be same D Final velocity of C is twice than A mu

1 A chain consist of 10 links each of mass 50 g is lifted vertically with a constant acceleration of 4 m s2 The force of interaction between the top link and link immediately below it will be g 10 m s2 1 7 N 2 6 3 N 3 5 6 N 4 5 0 N

eral ball of mass 1 kg is heated using a 40 W heater in a room at 30 C The temperature of the ball becomes steady at 70 C Assuming Newton s law of cooling the rate of loss of heat to the surrounding when the ball is at 40 C is Options 1 2 3 20 W 5 W 25 W 10 W

Options 1 A small disc of mass I gm slides down a smooth hill of height 10 m from rest and gets on to a plank of mass 100 gm as shown in the figure Due to friction between the disc and the plank the disc slows down and moves as one piece with the plank The work done by the frictional force is approximately Use g 10 ms 2 0 01 J 10 J 0 1 J 100pm

7 A simple pendulum consisting of a mass Mattached to a string of length L is released from rest at an angle a A pin is located at a distance below the pivot point When the pendulum swings down the string hits the pin as shown in the figure The maximum angle 0 which the string makes with the vertical after hitting the pin is A 1 cos 3 cos 1 L cos a 1 L 1 L cos a L 1 0 cos 1 2 cos 4 cos L cos a 1 L 1 L cos a 1 L 1

Two blocks each of mass m moving with speed v collide with the spring of force constant k as shown in figure The maximum compression of the spring is mom A C E mv k 2 mv 21 B 2mv k D zero

A uniform stick with mass m and length I is initially at rest along the y axis on a frictionless table as shown in figure An identical stick oriented in x direction is travelling with speed v in x direction sticks to one of the ends of first stick forming a right angled rigid object The energy lost to heat in collision is xmv2 40 Find x

A dumbbell consists of a light rod of length r and two small masses m attached to it The dumbbell stands vertically in the corner formed by two frictionless planes After the bottom end is slightly moved to the right the dumbbell begins to slide Find the speed u of the bottom end at the moment the top end loses contact with the vertical plane