Work, power & energy Questions and Answers

For Questions 13 14 A In a diatomic molecule potential energy of two atoms is approximately given by U r 612P where r is the interatomic spacing and A and B are positive constants Assuming the interatomic force to be conservative the corresponding force law is also called Lennard Jones Law It can be made out from the interatomic force law that atoms exert attractive forces on each other as the separation between them reduces The force law also tells that the force is repulsive at very short separations 14 13 Equilibrium distance between the two atoms in a diatomic molecule can be expressed as 1 6 B A D 28 B B 4A A 2B A B A B A B If the interatomic separation is equal to its equilibrium value what minimum energy must be given to the molecule in order to dissociate it C 1 6 B2 2A B 1 6 4B

has half the mass When E becomes peed of the m s m s from origin ith position mx 3 37 If F 2x 3x 2 then select the correct statement 1 1 x is the position of stable equilibrium 2 2 x 2 is the position of stable equilibrium 1 is the position of unstable equilibrium 2 3 X 4 x 2 is the position of neutral equilibrium 38 When a conservative force does positive work on a body then the

A light rod of length L is hinged to a plank of mass m The plank is lying on the edge of a horizontal table such that the rod can swing freely in the vertical plane without any hindrance from the table A particle of mass m is attached to the end of the rod and system is released from 0 0 position a Assume that friction between the plank and the table is large enough to prevent it from slipping The minimum normal force applied by the plank on the table is xx mg Value of x is

President Duterte is driving his BMW motorcycle mass 980 kg and wants to accelerate from 18 m s to 32 m s is 7 seconds President Duterte is amazed of the power of his motorcycle What is the horsepower of it 47 hp 50 hp 77 hp

The bob of a pendulum is 0 2 kg It is hung by mean of 1 2 m string from the ceiling If it is pulled horizontally and make a distance of 0 3 m from the ceiling what will be its velocity at the lowest point when released 4 2 m s 5 2 m s 1 0 m s 11 2 m s

15 The volume V of a monatomic gas varies with its temperature T as shown in the graph The ratio of work done by the gas to the heat absorbed by it when it undergoes a change from state A to state B is 3 8 1 A 2 B T alm

A block is suspended by an ideal spring of the force constant K If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is 8 then A 8 2F K C 8 F K B 8 2F K 1 KS D Increases in potential energy of the spring is K8

9 A coil in the shape of an equilateral triangle of side is suspended between the pole pieces of a permanent magnet such that B is in plane of the coil If due to a current in the triangle a torque t acts on it the side of the triangle is AIPMT Prelims 2005 1 2 3 Bi T 1 2 1 2 T 2 3 Bi 17 2 1 T

3 Problem 8 The force F 6 28 N i 4 15 N j acts on a particle as it moves along a straight line from Cartesian coordinate 0 75 m 3 49 m to 7 55 m 8 41 m What is the work done in joules by the force

A 101 2 kg person sits on a 4 0 kg bicycle The total weight is borne equally by the two wheels of the bicycle The tires are 0 013 m wide and are inflated to a pressure of 8 6 x 105 Pa What length in m of each tire is in contact with the ground

When a proton is released from rest in a room it starts with an initial acceleration ao towards west When it is projected towards north with a speed v it moves with an initial acceleration 3a toward west The electric and magnetic fields in the room are a b c mag e mao e mao C east east west 3mao evo 3mao down evo 2mao evo up up

View In English A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0 5 m s What is the height of the plane of circle from vertex of the funnel 1 2 3 4 Correct Answer 4 Status unattempted 0 25cm 2cm 4cm 2 5cm

A ball is released on a smooth plane A of constant length as shown After that it moves smoothly to another smooth incline of inclination 60 Find the angle of plane A with vertical in degrees so that the ball reaches the incline in the shortest time A g 4

3 A particle of mass m hits another particle in rest of mass m obliquely If both the particles after elastica collision moves perpendicular to each other then m m 1 1 is 2 2

A 0 034 kg mass ping pong ball is dropped from a height 1 76 m in a place where gravity is 9 8 m s Air friction is negligible but it loses an energy of 0 14 J when it bounces What height does it return to on its first bounce m

Problem 2 A bag with a mass of 5 kg is being held 3 m above the table and a ball with a mass of 2 5 kg held with a height of 2 m Which has a greater gravitational potential energy the bag or the ball acceleration due to gravity 9 8 m s2

The work done by a variable force is measured by taking an infinitesimal length element di dxi dyj dzk such tha W fF di A particle of mass 2 kg is being acted upon by a variable force F K x2y i x y2j The particle is taken from 0 0 to a a along different paths Based upon the above facts answer the following questions E 3 c du a Zero c 3n6 111 The work done to take the particle from 0 0 to a 0 to a a is a kas ka6 b 2 ka6 d LA

A ring of mass m slide from rest on the smooth rod as shown in the figure due to the block of mass m Pully and string are massless Then find the speed of ring when the string become straight Given 9 60 A 4 gh A A B B C C DI C B 2gh 0 B smooth m C 2 2gh D 8 gh

16 Internal forces acting in a system of particle can change 1 Both kinetic energy and linear momentum of the system 2 The linear momentum but not the kinetic energy of system 3 The kinetic energy but not linear momentum of the system 4 Neither linear momentum nor kinetic energy of

7 A 100 eV electron is fired directly towards a large metal plate having surface charge density 2 x 106 C m2 The distance from where the electron be projected so that it just fails to strike the plate is mm

2 Motor M exerts a constant force of 300 N on the cable Determine the distance S the crate will travel when its speed is 12m s The crate starts from rest and the co efficient of kinetic friction 0 3 Use Work and Energy method to determine S Also find how much time t will it take to achieve 12 m s speed You can use any method to find t M 20 300 T 300N

From a solid sphere of mass M and radius R a spherical portion of radius R 2 is removed as shown in the figure Taking gravitational potential V Oatr the potential at G gravitational constatn

A Smooth a 2 3 m b 11 14 m c 7 23 m d 176 34 m 227 X Wall 0 60 u 12 m s m 4 2 kg k spring 2 N m A ball whose weight on moon is 16N projected on the surface of earth making angle 8 from horizontal at the highest point of its trajectory It strikes a block spring system The compression in the spring is Assume perfectly inelastic collision Given gmoon Take ge 9 8 m s SolveLancer Test

An observer and a vehicle both start moving together from rest towards the right with acceleration 5 m s and 2 m s 2 respectively There is a 2 kg block on the floor of the vehicle and coefficient of friction is 0 3 between their surface Then the work done by the frictional force on the 2 kg block observed by the running observer during the first 2 seconds of the motion A 24 J B 24 J 16 J 2kg 5m s

A block of mass m is released from height h from a fixed smooth inclined plane At the foot plank of mass m is kept on smooth surface Friction coefficient between plank and block is and block just fails to leave the plank of length C Pick the correct options for the work done by friction on the block and the plank mgh A 4 mgh 2 3mgh 4 mgh B C D m m

20 A tidal power plant of the simple single basin type has a basin area of 30 x 10 m The tide has a range of 12m The turbine however stops operating when the head on it falls below 3m Calculate the energy generated in one filling process in kilowatt hours if the turbine generator efficiency is 0 73

Water falls from a height of 60 m at the rate o 15 kg s to operate a turbine The losses due to frictional forces are 10 of energy How muc power is generated by the turbine g 10 m s2 1 12 3 kW 2 7 0 kW 38 1 kW 4 10 2 kW

Two particles A and B have same charge q and different masses m and 2m respectively They are released from rest with initial separation d between them Assuming only mutual electrostatic forces act on them the speed o B when the separation between them becomes 2d is 9 8 md 9 24 md 2q 37 md 9

A frictionless track consists of a horizontal part of unknown length which connects to a vertical semicircle of radius r as shown An object which is given an initial velocity is to move along the track in such a way that after leaving the semicircle at the top it is to fall back to its initial position What should the minimum length of the horizontal part be

The kinetic energy K of a particle moving along a circle of radius R depends on the distanc covered s as K as where a is a constant The force acting on the particle is 1 2 s R 2as R A C 2as B 2as 1 D 2a ing from 100N

For shown situation if collision between block A B is perfectly elastic then find the maximum energy stored in spring in joules B C 3kg 000000 6kg A 3kg 2m s 1 6J 2 8 J 6 4J Smooth 4 10 J e Leader e Achiever MAZC D E F G H I J K L M MLE F G H I J K MO E H 19052021

Two tennis balls of mass 60gm are attached with a massless rubber thread and held in the vertical position as shown in the figure In this position length of the rubber thread is 40cm and it is unstretched The upper ball is showly raised vertically upward until the lower ball just becomes unsupported by the ground At this time the length of the thread is 1m The rubber thread exerts and force which is proportional to its extension What is the force constant of the rubber thread A 2N m B IN m C 0 5 N m How much work is done by external agent while the upper ball was raised A 0 54 J B 0 36 J C 0 18J D 0 25 N m D 0 45 J If we release the upper ball at this position at what speed will it hit the lower one A 4m s B 18 m s C 30 m s D 26 m s

58 A sphere of mass 2 kg is dropped from a height of 0 4 m onto a spring having force constant 1960 N m then maximum compression of spring will be g 9 8 m s 1 0 1 m 3 0 2 m 2 0 15 m 4 0 25 m

4 A tank with a base of 4 feet by 3 feet and a height of 4 feet is full of water see figure How much work is done in pumping water out over the top edge in order to empty half of the tank 4 ft

7 A block of mass m is attached to an undeformed spring of stiffness constant k as shown in figure and released Assume spring string and pulley be ideal The maximum displacement of block is P 1 3 2mg k mg 2k k vooroor 2 mg k 3mg 2k nu

An object is acted on by the force shown in the figure 0 8 Z 0 6 Force F N 0 4 0 2 0 0 25 0 50 Position x m 0 75 1 00 a What is the final position of the object if its initial position is x 0 40 mm and the work done on it is equal to 0 21 J b What is the final position of the object if its initial position is x 0 40 m and the work

Ans a 1 0 m s b 50 m s c 24 5 J 21 A smooth sphere mass 10 kg rolls on a smooth curved surface from the point A with a speed of 10 m s The sphere reaches the point D passing through point B Find a the total energy of the A 20m C 10m E B 13m sphere at the point A b the kinetic energy and the

A block of mass 0 1 kg attached to a spring of spring constant 400 N m is pulled horizontally from x 0 to x 10 mm Find the work done by spring force 1 2 x 10 2 J 2 2 x 10 6 J 3 3 x 106 J 4 4 x 10 J

In colder regions like the poles two identical open containers one fille with hot water and the other filled with cold water if left exposed t atmosphere it is observed that usually the hot water freezes earlie than the cold water I The hot water has more heat to lose II The hot water initially loses heat at a faster rate III More evaporation causes more heat loss in hot water Which of the above reasons can be responsible for this effect a Reason II b Reason III c Reasons II and III d All the above reasons

A particle is rotated in a vertical circle by connecting it to a string of length and keeping the other end of the string fixed The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is A ge C 3gl B 2gl D 5gl

3 A particle with total energy E is moving in a potential energy region U x Motion of the particle is restricted to the region when a U x E b U x 0 d U x E c U x E Karnataka NED

A ball with a speed of 9 m s collides with another identical ball at rest Afte the collision the direction of each ball makes an angle of 30 with the original direction The ratio of velocities of the balls after collision is x y where x is Answer

Two heater wires of same length are first connected in series and then in parallel The ratio of the amounts of heat produced in two cases will be 2 1 4 4 1 2 AJOR SRG ACU ALL ENTHUSE LEADED COU 1 4 1 3 2 1 SEPTEM

Forces acting on a particle have magnitudes of 14 7 and 7 N acts in the direction of vectors 61 2 3k 3 2 6 k and 2 3 1 6 krespectively The forces remain constant while the particle is displaced from point A 2 1 3 to B 5 1 1 Find the total work done in Joule on the particle The coordinates are specified in meters

6 A particle of mass 2 kg is moving along x axis at time t Its position is given as x t2 The work done by the force acting on it in time interval t 0 s to 5 s is 1 900 J 3 120 J 2 150 J 4 100 J

A body of mass 5kg is taken up an inclined plane of length 10m and height 5m and then released to slide down to the bottom If the coefficient of friction between the surface and the body is 0 1 the net work done against frictional force and gravitational force in the round trip are 1 25J 0 3 0 50 3J 2 50 50 3J 0 4 50 3J 50J

here is a negative marking of 1 Mark No marks will be awarded if you leave question unattempted T A block of mass m is attached with a spring of spring constant K It is lowered slowly from the natural length of the spring and left at equilibrium Find work done by the external agent A W mgh C W m g 2K B W D W 2 m g 2K 2m g K

A particle of mass m moves with a velocity v a x where a is constant Find the total work done by all the forces during a displacement from x 0 tox d 1 m 2 ma d 1 M

Position time graph of a particle moving in a straight line is as shown in figure Select the correct alternative s X C 0 A Work done by all the forces in region OA and BC is positive Work done by all the forces in region AB is zero Work done by all the forces in region BC is negative B Work done by all the forces in region OC is zero t

A chain of mass M and Length L is held on a frictionless table in such a way that part is n hanging below the edge of table Calculate the work done to pull the hanging part of the chain Mgl 2n Mgl 2n 4 MgL 2n Mgl 2n