Work, power & energy Questions and Answers

5 Water is moving with a speed of 5 0 m s through a pipe will cross sectional area of 4 0 cm2 The water gradually descends 10 m as the pipe increase in area to 8 0 cm If the pressure at the upper level is 1 5 x 105 Pa the pressure at lower level will be 1 2 8 x 105 Pa 2 2 6 x 105 Pa 3 2 4 x 105 Pa 4 2 1 x 105 Pa

74 Let r be the distance of a particle from a fixed point to which it is attracted by an inverse square law force given by F kir k constant Let m be the mass of the particle and L be its angular momentum with respect to the fixe point Which of the following formulae is correct abou the total energy of the system a 1 m 2 1 b m 2 dr 4 dt m 2 dr dt dr dt k L r k r k r 2 2mr Constant Constant L 2mr Constant

A mass m is attached to the end of a rod of length e The mass goes around a verticle circular path with the other end hinged at the centre What should be the minimum velocity of mass at the bottom o the circle so that the mass completes the circle See lage 5 1 4gl 2 3gl 3 5gl 4 gl

37 If two resistors of 25 22 and 15 Q2 resistor the effective resistance of the combination is a 0 1 Q b 10 Q c 20 92 d 40 Q Th 20 are joined together in series and then placed in parallel with a

1 A book is moved from rest through a distance of 4 m along a straight line path The mass of the block is 5 kg and the force acting on it is 20 N If the kinetic energy quired by the block be 40 J at what angle to the path is the force acting 30 d none of these

5A car of mass 500 kg moving with a speed 36 km h in a straight road unidirectionally doubles its speed in 1 min The power delivered by the engine is 1 1250 W 3 625 W D P F V 2 1250 HP 4 625 HP

The rate of mass of the gas emitted from rear of a rocket is initially 20 kg s If the speed of the gas relative to the rocket is 800 m s and mass of rocket is 1000 kg then the initial acceleration of the rocket is Take g 10 m s NCERT Pg 1101 1 4 m s 2 16 m s 3 6 m s 12 m s2

21 Force 31 2 k N produces a displacement of 21 4 ck m the work done is 16 j then c a 1 b 2 c 1 d 2 22 Two forces 2i 2j 5k and 3i 5j 4k act together on a body and produces displacement of 18i 17j 7k the work done is a 64j b 8j c 16j d 32j

cle about that point What will be the tension of the thread at the moment it will be passing the horizontal position 38 A horizontal plane supports a stationary vertical cylinder of radius R and a disc A attached to the cylinder by a horizontal thread AB of length 1 Fig 1 32 top view An initial velocity vo is imparted to the disc as shown in the figure How long will it move along the plane until it strikes against the cylinder The friction is assumed to be absent 39 A smooth rubber cord of length I whose coefficient of elasticity is k is suspended by one end from the point O Fig 1 33 The other end is fitted with a catch B A small sleeve A of mass m starts falling from the point O Neglecting the masses of the thread and the catch find the maximum elongation of the cord B lo Fig 1 32 A A B Fig 1 33

Sand is poured on a conveyor belt at the rate of 2 kg s If belt is moving horizontally with velocity 4 m s then additional force required by engine to keep the belt moving with same constant velocity is NCERT Pg 95 1 4 N 3 16 N 2 8 N 4 32 N

8 A body of mass 5kg at rest is acted upon by two mutually perpendicular forces 6N and 8N simultanecusly Its kinetic energy after 10s is 1 100 J 2 200 J 41000 J 3 500 J 10 Stu a CU

When a constant power is delivered to an object initially at rest then the graph between velocity and position of the object is motion of object is along x axis 1 3 2 4 X

Three identical balls A B and C each of mass m 3 kg are connected by strings AB and BC as shown in the figure The whole system is placed on a smooth horizontal surface A 1m B 1m C Now the ball B is given an initial velocity vo 3 m s perpendicular to the strings and along horizontal surface Find the tension in Newton in the string just before the balls A and C collida

37 Potential energy of a particle in conservative field is x X given by U x 4 2 2 3 0 1 1 J then maximum P E and minimum P E are 1 1 1 2 1 0 9 4 NOT

5 Potential energy curve of a body of mass m 2 kg is shown in the figure it is released from rest at point A Maximum distance covered by it on the positive x axis till it momentarily comes to rest from the origin is 1 1 m 2 2 m 3 4 3 m U J 321 A 16 www 2x m

Two masses 2m and m are connected by an inextensible light string The string is passing over a light frictionless pulley The mass 2m is resting on a surface and mass m is hanging in air as shown in the figure A particle of mass m strikes the mass m from below and with a velocity vo and sticks to it In another case a particle of mass m strikes the mass m with a velocity vo from top and sticks to it Calculate the ratio of velocities of mass m just after collision in first and second case EO Vo m 10

A particle is attached with massless string It displaced from A to B by a force of conste magnitude but its direction is always alor instantaneous displacement The work done the force Fis 1 A 1 FI 2 1 F 2 FI B Med

43 A uniform chain of mass 4 kg and length 2 m overhangs a smooth table with its one third part lying on the table Find the speed of chain as it completely slips of the table Take g 10 m s 10 1 m s 3 2 3 m s 3 2 2 m s 4 4 3 m s

M strikes the block of mass M with In the shown figure a particle of mass 10 velocity vo and gets attached to it For what velocity vo in ms the block B just able to leave the ground AT Given M 100 gm K 880 N m no mg 00000000 K

F K xi yi is working on a particle which moves from 0 0 to a 0 along x axis and a 0 to a a along y axis Find the work done by the force

Figure 8 E17 R M D Figure 8 E17 shows a smooth track which consists of a straight inclined part of length 1 joining smoothly with the circular part A particle of mass m is projected up the incline from its bottom a Find the minimum projection speed u for which the particle reaches the top of the track b Assuming that the projection speed is 2v and that the block does not lose contact with the track before reaching its top find the force acting on it

A smooth chain AB of mass m rest against a vertical wall in the form of a quarter of a circle of radius R Take potential energy zero at horizontal part of the surface Its potential energy i is R 1 MgR 2 R A 2 MgR TC B

Ca de Ban A cylindrical water tank 4 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level see figure How much work is done in pumping a full tank of water up to ground level The water weighs 9800 newtons per cubic meter newton meters Ay 2 y Ground level 5 y

A ball is dropped from 100 m and it rebounds to a height of 70 m The percentage loss of energy is NCERT Pg 125 1 30 2 60 2 70 4 10

Illustration 12 A block is placed on the top of a plane inclined at 37 with horizontal The length of the plane is 5m The block slides down the plane and reaches the bottom 5m 37 h a Find the speed of the block at the bottom if the inclined plane is smooth b Find the speed of the block at the bottom if the coefficient of friction is 0 25

A vehicle of mass M is accelerated on a horizontal frictionless road under a force changing its velocity from u to v in distance S A constant power P is given by the engine of the vehicle then v 1 3 3 4 2PS M PS M u 1 3 1 3 2 4 PS M u 3PS M u 1 2 1 3

A motorcycle of mass m resting on a frictionless road moves under the influence of a constant force F The work done by this force in moving the motorcycle is given by F212 2m where t is the time in seconds Ratio of instantaneous power to a average power of the motorcycle in t T second is 1 1 1 3 3 2 2 2 1 4 1 2

A body with a mass of 3kg falls from a certan height with an initial velocity of 2 m s directed vertically downward If the work done in J to overcome the forces of resistance during 10sis WF and if it is known that the body acquired a velocity of 50 m s at the end of the 10s interval then find the value of W 507 Assume that the force of resistance is constant

Interaction between atoms of a diatomic molecule is a B described by the relation P E x where x12x6 P E is potential energy If the two atoms enjoy stable equilibrium the distance between them would be 1 B 3 215 1 6 20 1 6 2 4 2 B B 1 6 1 6

2 Now the force acts in a direction 30 00 above the horizontal as shown below If the block is again moved 2 50 m how much work is done by the force Show your work below and include units F 4 50 N 30

An engine of mass m is moving up a slope of inclination 0 at a speed V The coefficient of friction between engine and the rail is u If the engine has an efficiency n then the energy spent by engine in time t is 1 nmg sin 0 cos 0 vt 2 mg cos 0 vt n 3 mg sin 0 cos 0 vt n 4 mg sin 0 vt

The unit of thermal W m K 1 c Jm K conductivity is b Jm K 1 d W m K 1

Illustration 8 A pump is required to lift 1000 kg of water per minute from a well 20m deep and eject it at a rate of 20 m s a How much work is done in lifting water b How much work is done in giving it a KE c What HP horse power engine is required for the purpose of lifting water

A rod of mass m and length is kept on a smooth wedge of mass M as shown in the figure If the system is released when the rod is at the top of the wedge find the speed of the wedge when the rod hits the ground level Neglect friction between all surfaces in contact m M H

A block of mass m is being pulled up the rough incline inclined at an angle 37 with horizontal by an agent delivering constant power P The coefficient of friction between the block and the incline is u Find the maximum speed in m s of the block during the course of ascent Take P 60W m 1kg 0 5 m 0 37 P

Calculate the work done in pulling an object with a constant force F as shown in figure so that the block moves with a constant velocity through a distance d given that the ground is rough with coefficient of friction F M 10 1 THEORY P65

A stone is falling freely in free space Its velocity is x when it has lost y units of potential energy in the gravitational field of earth The mass of the stone is 1 xy 3 x y 2 4 2y x 2y X 9 8

5 What are conservative and non conservative forces explain with examples 6 What is meant by power and energy Give their units Art 4 6 Arts 4 7 and 4 8 moving uniformly

A force given by F fxi fyj f k acts on a particle which moves from a b c to d e f The work done by force F is here A A2 are A magnitude of area bounded area A fy 1 A A A3 2 A A A3 3 A A A3 4 A A A3 area A e b area A Z

13 A person weighs 600 N He is wearing shoes with a total area of 0 02 m What pressure do they exert on the floor

When a current of 2 A flows in a battery from negative to positive terminal the potential difference across it is 12 V If a current of 3 A flowing in the opposite direction produces a potential difference of 15 V the emf of the battery is a 12 6 V b 13 2 V c 13 5 V d 14 0 V

The potential energy of a system increases if work is done 1 Upon the system by a nonconservative force 2 By the system against a conservative force 3 By the system against a nonconservative force 4 Upon the system by a conservative force

A rope of length is pulled by a constant force F over a friction less horizontal surface Linear mass denstiy of the rope at a distance x from the end where F is applied is 1 x l Find the tension in the rope at a disance x 20 1 FL X FL 2 F L x L Fx

A cradle is h meters above the ground at the lowest position and H meters when it is at the highest point If v is the maximum speed of the swing of total mass m the relation between h and H is 1 mv h H 2 v 2g h H 3 v g 2h H 4 v 2g H h

Two riffles fire the same number of bullets in a given interval of time The second fires bullets of mass twice that fired by the first and with a velocity that is half that of the first The ratio of their powers is 11 4 2 4 13 1 24 2 1

A body is released from position A as shown in figure The speed of body at position B is NCERT Pg 121 50 m 1 10 m s 3 20 m s 10 m B 2 10 2 m s 4 20 2 m s

The internal energy of a substance a Increases with increase in temperature b Decreases with increase in temperature c Can be calculated by the relation E mc d Remain unaffected with change in temperature

ple kg and amplitude A 2 m the variation of potential energy U as a function of displacement x from mean position is as shown The time period of oscillation in second is U A 1 T 3 BIN 2 30 J 10 J 0 S A 2 2 4 4 X

A particle is thrown with kinetic energy k straight up a rough inclined plane of inclination a and coefficient of friction u The work done against friction before the particle comes to rest is 1 2 3 ku sina cosa usina ku cos cosa sina ku sina sin cosa ku cos a

9 The angular momentum of a particle performing uniform circular motion is L If the kinetic energy of partical is doubled and frequency is halved then angular momentum becomes 1 3 1 2 L 2 2L 4 4