Work, power & energy Questions and Answers

12 EXPLAIN CONCEPT how to solve when HIGHER POWER S OF X are INVOLVED how to find STABLE OR NEUTRAL ju tify in this answer 34 A particle is acted upon by a force given by F ax 3x where a and are positive constants At the point x 0 the particle is A in stable equilibrium B in unstable equilibrium C in neutral equilibrium D not in equilibrium

Q No 1 Marks 4 00 1 00 View In English A position dependent force F acting on a particle and its force position curve is shown in the figure Work done on the particle when its displacement 0 to 5 m is F N 10 35 J 25 J 15 J 10 2 5 x m V

3 A current of 11 Amps 240 Volts flows through an electric range If it is used an average of 1 hour day a Calculate the watts used by the range b Calculate the kwhr used per month c What is the cost to run the range for one month at 8 cents kwhr d What is the cost to run the range for one year at 8 cents kwhr

Two blocks of masses 1 kg and 2 kg are connected with an ideal spring of constant K N m and placed at rest on smooth horizontal surface If they are given velocities v m s and 2 v m s as shown in the diagram then the maximum compression in SI units in the spring is 2v 1 kgm 2 kg 2v K xw K L IK 2 6K K

reaches 1 2 which begins at height h A small block slides along a path that is without friction until the block reaches the section L 3m 3m on a flat incline of angle 37 as shown In that section the coefficient of kinetic friction is 0 50 The block passes through point A with a speed of 136 m s Find the speed in m s of the block as it passes through point B where the friction ends Take g 10 m s B Rough Part L 3m 37 h 3m Smooth Part 136 m s

4 Graph represents potential energy U versus position X of a particle moving under a conservative fore Which of the following is correct U N 1 Equilibrium position will be X X and equilibrium is stable 2 Force on the particle for X X3 will be in the negative X direction 3 Force on the particle at X X is equal to zero 4 Both 1 2 are correct

Consider the set up shown below in the figure The block A is attached to a rigid wall through a spring of spring constant k 10 N m The system is released from rest with the spring unstretched Assume friction to be absent everywhere Take g 10 m s List I gives the mass of block B and list II the magnitude of some quantities in S I unit List 1 List 11 1 kg 11 2 kg 1 4 kg IV 8 kg P 1 Q 2 R 4 S 8 T 10 U 16 The maximum extension produced in the spring is Options A 1 Q 1 P III S IV R B 1 Q 11 R III S IV U C 1 P IS IO IV T A

3 75 A 20 kg block is originally at rest on a horizontal surface for which the coefficient of friction is 0 6 If a horizontal force F is applied such that it varies with time as shown in figure 3 133 1 Determine the speed of the block in 10 s F Nt A 200 Figure 3 133 10 t s ii Determine the work done by this force in this duration iii Determine the work done by frictional force in this duration Ans 24 m s 14480 4 J 8720 4 J

C 3 54 In figure 3 127 a and 3 127 b AC DG and GF are fixed inclined planes BC EF x and AB DF y A small block of mass M is released from rest form the point A It slides down AC and reaches C with a speed Ve the same block is released from rest from point D It slides down DGF and reaches the point F with speed V The coefficients of kinetic friction between the block and both the surfaces AC and GDF are u Calculate Vand V A y B a D y E Figure 3 127 Ans Vc 2g y Hx Vr 2g y x b F

3 40 An engineer is designing a spring to be placed at the bottom of an elevator shaft if the elevator cable should break at a height h above the top of the spring calculate the required value of the spring constant k so that passengers undergo an acceleration of no more than 10 g when brought to rest Let M be the total mass of the elevator and passengers Ans 99 Mg 2h

A 400 W computer including the monitor is turned on for 8 0 hours per day If electricity costs 104 per kWH how much does it cost to run the computer annually for a typical 365 day year O 120 O 150 O 170 O 1200

The work done by a force on a body is said to be zero when 1 No force is applied 2 The body is displaced in a direction opposite to the direction of the force 3 The body is displaced in the direction of applied force 4 The body does not move from its position on the application of force

Work is said to be done by a force 1 if the body has displacement 2 if the magnitude of the force is not equal to zero 3 if the force or component of the force is along the direction of the displacement 4 None of the above

A pendulum bob of mass M is raised to a height h and then released At the bottom of its swing it picks up a mass m To what height will the combined mass rise m h 1 m M M h 2 m M mMh 3 m M mMh 4 12

The curve between potential energy of a diatomic molecule is shown in the figure If FA FB F FD and FE are forces of interaction between atoms of molecules corresponding to points shown on curve then A B C D O FB 0 O FA 0 O FE FC 0 Fars

2 Two balls of equal masses undergo a head on colli sion with speeds 6 m s moving in opposite direc tion If the coefficient of restitution is 0 5 find the speed of each ball after impact in m s 1 3 2 6 3 2 4 4

A smooth tunnel is dug along the radius of the Earth that ends at the centre A ball is released from the surface of Earth along the tunnel If the coefficient of restitution for the collision between the ball and the surface of the tunnel is 0 2 then the distance travelled nR by the ball before the second collision at the centre is Find the value of n S

A block of mass m is lowered slowly from the natural length position of a massless spring by an external agent to equilibrium position The extension produced in the spring was asked to two students Student A 1 kx kx mgx Solution Student B mg mg k A Student A is incorrect Student B is correct C Both are correct X kx 2mg k X mg In equilibrium position mg kx x k F K m 20 B Student A is correct Student B is incorrect so student A is incorrect Ans A

An all electric car is designed to run from a bank of 12 0 V batteries with total energy storage of 2 00 x 107 J If the electric motor draws 8 00 kW the car moves at a steady speed of 20 0 m s how far in km can the car travel before it is out of juice Approximate the answer to nearest integer

A 4 kg block is stacked on top of a long 12 kg block which is accelerating along a smooth horizontal table at a 5 2 m s under application of an external constant force Let minimum coefficient friction between the two blocks which will prevent the 4 kg block from sliding is and coefficient of friction between blocks is only half of this minimum value i e 2 Find the amount of heat in Joules generated due to sliding between the two blocks during the time in which 12 kg block moves 10 m starting from rest smooth 4 kg 12 kg a 5 2 m s

There is a soap bubble of radius 2 4 10 m in air cylinder which is originally at the presure of P 10 Nm The air in the cylinder is now compresed isothermally until the radius of the bubble is halved Now the pressure of air in the cylinder is given by 8 P ax 10 Pa The surface tension of the soap film is 0 08 Nm Find the value of a n from 105 M 10 4

Question 13 A spherical bubble inside water has radius R Take the pressure inside the bubble and the water pressure to be po The bubble now gets compressed radially in an adiabatic manner so that its radius becomes R a For a R the magnitude of the work done in the process is given by 4 TpRa x where X is a constant and y C Cv 41 The value of Vic

A source which can be represented by a voltage source of 8 V rms in series with an internal resistance of 2 k2 is connected to a 50 22 load resistance through an ideal transformer Calculate the value of turns ratio for which maximum power is supplied to the load and the corresponding load power Using MATLAB plot the the power in milliwatts supplied to the load as a function of the transformer ratio covering ratios from 1 0 to 10 0

nswer A kg and radius R 30 cm is hinged at the point A of a stationary surface with the line joining point A to the centre C of the ring is initially vertical The ring is also in contact with the Plank of mass m 5 kg at point B which is placed on a smooth horizontal surface Initially points A and B are almost touching and the line AC is vertical and the system is released from rest Then the velocity of the Plank when the line AC makes an angle 30 with the horizontal as shown will be there is no friction between the ring and the plank and g 10 m s B 1 m s 2 m s C 3 m s A C 30 30 m R B m Rate this question

QIn Figure a thin horizontal bar AB of negligible weight and length L is hinged to a vertical wall at A and supported at B by a thin wire BC that makes an angle u with the horizontal A block of weight W can be moved anywhere along the bar its position is defined by the distance x from the wall to its center of mass As a function of x find a the tension in the wire and the b horizontal and c vertical components of the force on the bar from the hinge at A C

solid sphere is in pure rolling motion In rolling motion a body possesses translational kinetic energy K as well as rotational kinetic energy K simultaneously The ratio of K and K for the sphere is A 10 7 B 5 2 C 7 10 D 2 5

29 A block is released from rest from point A on a smooth track whose cross section in the vertical plane is quarter of a circle of radius R The value of 0 for which the contact force between Typeseblack and surface is equal to the weight of the block is

Two particles P and Q start from rest and move for equal time on a straight line Particle P has an acceleration of Xm s2 for the first half of the total time and 2xm s for the second half Particle Q has an acceleration of 2Xm s for the first half of the total time and Xm s for the second half Which particle has covered larger distance

ing the velocity of sound is 320 m s C Two swimmers start a race One who reaches the point C first on the other bank wins the race A makes his strokes in a direction of 37 to the river flow with velocity 5km hr relative to water B makes his strokes in a direction 1270 to the river flow with same relative velocity River is flowing with speed of 2km hr and is 100m wide Who will win the race Compute the time taken by A and B to reach the point C if the speeds of A and B on the ground are 8 km hr and 6 km hr respectively A 37 300m 100m 2km hr B 125m 127

A 1 2 kg collar C may slide without friction along a fixed smooth horizontal rod It is attached to three springs each of constant K 400 N m and 150 mm undeformed length Knowing that the collar is released from rest in the position shown Determine the maximum velocity it will reach in its motion Here A O B are fixed points 1 2 kg wwwwww wwwwwwww 150 mm 150 mm 150 mm

10 The velocity time graph of a body travelling along a straight line is given below The distance travelled and displacement of the body are respectively A 6m 0 C 6m 3m B 6m 3m D 0 0 V m 1 N 20 10

Between two isotherms we have a cycle as shown The work done by the gas during the cycle is n in J Find the value of n Take T 127 C T 16 C n 1 mole P V T

flowing There are two observers A and B observing electric field E and magnetic Sec Sr Super60 All Space for rough work Page 4 Sri Chaitanya IIT Academy 13 06 2021 Sr Super60 All Jee Adv 2018 P1 GTA 09 Q P field B at a point P near the conducting wire Observer A is stationary whereas observer B is moving with drift speed of electron in the wire in the direction of electric current in it Which options are INCORRECT I P A B A Electric field observed by A and B are same B Electric field observed by A is zero whereas by B is non zero C Magnetic field observed by A and B are same

momentum are conserved A rod of length L whose lower end is fixed along the horizontal plane starts to topple from the vertical position The velocity of the upper end of the rod when it hits the ground is a 3gL b 2gL c gL d 5gL

3 A spring of force constant 600 Nm is mounted on a horizontal table A mass of 1 5 kg is attached to the free end of the spring pulled sideways to a distance of 2 cm and released P E of the system when it momentarily comes to rest and total energy are respectively 1 0 12 J O 3 0 0 2 0 0 12 J 4 0 12 J 0 12 J

4 A steel wire of cross sectional area 4 cm has elastic limit of 2 2 x 108 N m2 The maximum upward acceleration that can be given to a 1000 kg elevator supported by this steel wire if the stress is to exceed one fourth of the elastic limit is Take g 10 m s a 10 m s b 9 m s c 15 m s d 12 m s

A 3kg mass starts from rest and slides a distance d down a frictionless 30 incline see the figure While sliding it comes into contact with an unstressed spring The mass slides an additional 0 2m as it is brought momentarily to rest by compression of the spring k 400N m The initial separation d in m between the mass and the spring is

The potential energy U of a system is given by U A Bx2 where x is the position of its particle and A B are constants The magnitude of the force acting on the particle is 1 Constant wwwwwww M 2 Proportional to x 3 Proportional to x 4 Proportional to N

3 A ball of 4 kg mass moving with velocity 40 m s in east direction collides with another ball of 6 kg mass moving with velocity 20 m s in east direction After collision two balls stick together then loss of kinetic energy is NCERT Pg 129 1 360 J 2 240 J 3 480 J 4 600 J

39 A point particle of mass 0 5 kg is moving along the x axis under a force described by the potential energy V shown below It is projected towards the right from the origin with a speed v What is the minimum value of v for which the particle will escape infinitely far away from the origin a 2 2 ms 1 b 2 ms 1 c 4 ms 1 V in J 3 1 x in m

A particle A of mass kg is moving in the 7 positive direction of x axis At initial position x 0 its velocity is 1 ms then its velocity at x 10 is in m s use the graph given 2 Power W 10 m Fin 875

A string of length 3 is connected to a fixed cylinder whose top view is shown in figure The string is initially slack The other end of the string connected to a marble is moving at a constant velocity of 10 m s as shown The string will get stretched at some instant and impulsive tension occurs in the string If hinge is exerting a force of 40000 N for 0 25 ms on the cylinder to bear up the impact of impulsive tension then mark the correct statements Take string to be light breaking tension of the string is 2 105 N 31 10m s 0 m 2kg The angle made by the velocity of marble with the length of string when it is just stretched is 60 The marble will move in a circular path of varying radius with constant speed of 5 3 m s after the string is

A 2 kg bullet is fired at a speed of 500 m s into a 10 kg mass resting on the edge of a table of height 0 8m speed of the bullet is 200 m s how far apart are the two objects when they land on the floor O 21 7m O 37 4m O 56 6m O 75m 48 3m

A simple pendulum consisting of a mass M attached in 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 string makes with the vertical after hitting the pin is 1 cos 2 cos 3 cos 4 cos L cos a t 1 L 1 1 AT L 1 L cos a L L cos a L t L cos a Perenang C L

A tank shaped like a cone has height 12 meters and base radius 5 meters long It is placed so that the circular part is upward It is full of water and we have to pump it all out by a pipe that is always leveled the surface of the water Assume that a cubic meter of water weighs 10000N i e the density of water is N 10000 How much work does it require to pump all water out of the tank Enter the exact value of m your answer W Joules

The fuel consumption rate Litres of fuel consumed per second of a large ship is given by 3v where v is its speed in m s For a particular journey from city A to city B the captain wishes to consume as less fuel as possible Find the speed with which the ship must travel in m s 96 V

In the figure shown S and S are two identical coherent sources of sound separated by d A receiver moves along line XY which is parallel to S S to detect intensity of sound at various points on the line Distance of line XY from S S is D d Distance of first intensity maxima on line XY measured from O is y Find percentage change in value of y if the temperature of air increases by 1 If your answer is X fill value of 6X

A student skates up a ramp that makes an angle 30 with the horizontal He she starts as shown in the figure at the bottom of the ramp with speed vo and wants to turn around over a semicircular path xyz of radius R during which he she reaches a maximum height h at point y from the ground as shown in the figure Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his her weight only Then g is the acceleration due to gravity Z RY h

v position If the length of pendulum is 2m what is the speed of a pendulum is released from a horizontal 31 fa fa ten with which the bob arrives at the lower most point Assume that 10 of its energy is dissipated against air resistance Take g 10 ms 2 M ch an atas 2 fica a and for nach and qua for sucht nghx 90 1mv 1 4 ms Tro 2 6 ms 3 8 ms 1 4 10 ms A small roller coaster start 2m luft no 10 g 10 ms 1 4 ms 2 6 ms 3 8 ms 4 10 ms arya farty a fak 2 mgh 1 kx 40X2 1012 3 10X3 14 3

3 1 3 4 3 1 2000 Nm are stretched with same force They will have springs of spring constants 1000 Nm and 35 1000 Nm 2000 Nm fein faudies are a fex ant 13 feef potential energy in the ratio of 1 2 1 2 2 1 3 1 2 2 1980 4 1 2 A car of mass 1000 kg moving with a spon THE sm 1 2 1 2 2 1 3 1 2 4 1 2 1000 X 5 X6 25X10 x4 13 50