Work, power & energy Questions and Answers

the disc s to rest tween e two tant 5 47 A small ball is suspended from a point O by a light thread of length 7 Then the ball is drawn aside so that the thread deviates through an angle 0 from the vertical and set in motion in a horizontal direction at right angles to the vertical plane in which the thread is located What is the initial velocity that has to be imparted to the ball so that it could deviate through the maximum angle 2 in the process of motion Ans 2gl sec 0 www

A particle moves with a velocity V 51 31 6k m s under the influence of a constant force F 101 10 20 k N The instantaneous power applied to the particle is in J s Backspace

A constant power delivering machine has towed a box which was initially at rest along a horizontal straight line The distance moved by the box in time t is proportional to 1 t 3 2 t 2 3 t 4 t 2 C

14 A block of mass 2 kg moves such that the V of velocity variation with position position is as represented in the graph The power delivered to the particle at x 2m will be v m s millest dy 2 dx a ydi 16 3 N 1 Aakash Ed 0 0 8 W 3 4 W 2 R R 1 4 2 3R 36 3 4 2 32 W 4 16 W 3R F V P ma v x m a large number of

ime plot for a certain body is shown in the following graph In an interval from 5 s to 10 s the body is displaced by 25 m The work done by the force will be SolveLancer Test P 30 W 18 W a D 5 s 160j a b 120 J c 240 J d 320 J b 1 10 s

33 Two bodies A and B each of mass 100 gm are allowed to move along a frictionless typical path as shown below In order to have the same kinetic energy for both the bodies at M the initial velocity that should be given to B if A starts from rest is 2 2m s 1 10 m s 3 11 m s 4 10 2 m s

The two slits at a distance of 1 mm are illuminated by the light of wavelength 6 5 10 m The interference fringes are observed on a screen placed at a distance of 1 m The distance between third dark fringe and fifth bright fringe will be 1 0 65 mm 3 3 25 mm 2 1 63 mm 4 4 88 mm

Q4 A 0 5 kg block slides from A on horizontal track with an initial speed of 3 ms towards a weightless horizontal spring of length 1 m and force constant 2Nm The part AB of the track is frictionless and the part BC has the coefficient of static and kinetic friction as 0 22 and 0 20 respectively If the distance AB and BD are 2 m and 2 14 m respectively the total distance through which the block moves before it comes to rest completely is A A B C D 2 5 m 4 42 m 4 24 m 2 44 m 0 5 kg 3ms B D k 2Nm 0000 C

A car of mass m starts from rest and accelerate so that instantaneous power delivered to the car has a constant magnitude Po The instantaneous velocity of this car is proportional to 1 1 2 11 2 3 1 2 4 t

A rod is fixed between a vertical wall and a horizontal surface A smooth ring of mass 1 kg is released from rest which can move along the rod as shown At the release point spring is vertical and relaxed The natural g 10 m s 0000000 30 length of the spring is 3 1 m Rod makes an angle of 30 with the horizontal Ring again comes to rest when spring makes an angle of 30 with the vertical A Force constant of the spring is 3 1 N m m 2 B Maximum displacement of ring is 3 1 C Maximum extension in the spring is 3 1 m D Normal reaction on ring due to rod when it again comes to rest is 3 1 N

In the given figure the variation of potential energy of a particle of mass m is represented wr t its x coordinate The particle can move under the effect of this conservative force along the alternatives At point B the acceleration of particle is along the positive x axis At point C the acceleration of particle is along the positive x axis At point A and C particle is in unstable and stable equilibrium respectively At point B and D particle is in stable and unstable equilibrium respectively U in J A D x in m

Under the action of a force a 2kg body moves such that its position x as a function of time is given by X O 16 J O 16 J O 160 J 23 where x is in metre and t in seconds The work done by force in first two secon

Figure shows a smooth curved track terminating in a smooth horizontal part A spring of spring constant 25 N m is attached of 5 m on the curved track Find the maximum compression in m of the spring g 10 m s 5m one end to a wedge fixed rigidly with the horizontal part A 1kg mass is released from rest at a height

30 Figure shows the velocity versus time 30 50 fanf graph for a block of mass 50 g sliding on a rough floor The average rate at which energy dissipates in s due to the force of friction is AKCE 160 J in 8 sec 160 640g 205 in 1 sec 1 5 0 J s 2 10 0 J s 320 0 J s 4 40 0 J s 13 15 SAT ENG HIN v 4 m s 80 88 60 40 20 0 s time S 5 0 J s 10 0 J s 20 0 J s 4 40 0 J s 8 10 1 2 3

When a mass M is attached to the spring of force constant k then the spring stretches by length 1 If the mass oscillates with amplitude 1 what will be the maximum potential energy stored in the springs 1 H 2 2 kl 3 Mgl 4 2 Mgl

An AIR station is broadcasting the waves of wavelength 300 metres If the radiating power of the transmitter is 10 kW then the number of photons radiated per second is 1 1 5 1029 3 1 5 1033 2 1 5 1031 4 1 5 1035

A ball of mass m is projected from a point P on the ground as shown in the figure It hits a fixed vertical wall at a distance from P then after only collisia with wall PO u the ball will return to the point P if half of the horizontal range and collision is elastic the ball will return to the point P if half of the horizontal range and collision is partially elastic the ball can not return to the initial point if half of the horizontal range and collision is partially elastic the ball may return to the initial point if the collision partially elastic and half of the range

A block of mass m is attached to one end of a massless spring of spring constant k The other end of the spring is fixed to a wall The block can move on a horizontal rough surface The coefficient of friction between the block and the surface is The block is released when the spring has a compression of 2 mg then choose the incorrect option s k A The maximum speed of the block is g uma m k www m B The maximum speed of the block is 2 g C The block will have velocity towards left during its motion D The extension in the spring at the instant the velocity of block become zero for the first time after m

Read More Two points N and S are located in the northern and southern hemisphere respectively on the same longitude Projectiles P and Q are fired from N and S respectively towards each other Which of the following options is correct for the projectiles as they approach the equator Both P and Q will move towards the east Both P and Q will move towards the west P will move towards the east and Q towards the west

29 A bus of mass 1000 kg has an engine which produces a constant power of 50 kW If the resistance to motion assumed constant is 1000 N The maximum speed at which the bus can travel on level road and the accel eration when it is travelling at 25 m s will respectively be A 50 m s 1 0 m s B 1 0 m s 50 m s C 5 0 m s 10 m s D 10 m s 5 m s2

A body starts from ous an initial velocity of Ims and moves along n anis under the action of a motor which Power P delivered by Varies with position 21 as shown Mbody 10 K AP watt 4W 2W 10M 2 Mettre Velocity of body at 2 10m is

Question For a simple harmonic oscillator of mass m 10 kg and amplitude A 2 m the variation of potential energy U as a function of displacement x from mean po sition is as shown The time period of oscillat

Catalyst 85 Two particles of equal mass m are connected by a spring of spring constant K kept on a smooth floor Each of the bodies are given equal speed vir the opposite direction Calculate the maximum compression of the spring 1 2 3 2 V 2m k LEL E bas tothod ritroms nainge en hold issiinsbi ONT La novip 21 8

large cruise ship of mass 6 60 x 107 kg has a speed of 10 4 m s at some instant a What is the ship s kinetic energy at this time 3570000000 b How much work is required to stop it Give the work done on the ship Include the sign of the value in your ans 3570000000 J c What is the magnitude of the constant force required to stop it as it undergoes a displacement of 2 40 km 1370000 Your response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in

no For a simple harmonic oscillator of mass 10 kg and amplitude A 2m the variation of potential energy U as a function of displacement x from mean position is as shown The time period of oscillation in seconds is 1 A KIN 3 12 2m 30 J TO J 2 2 X

A particle in a certain conservative force field ha 2x y z a potential energy given by U exerted on it is 1 2 4xy i x i x v k 2 2 3 2x 2 2 42 k 4 4xy 4x y Z 3 2 3 4xy i x 4x y k 2 3 Z 4xy 2x 4x y The force

kg and amplitude A 2m the variation of potential energy U as function of displacement x from mean position is as shown The time period of oscillation in seconds is 1 T 3 RIN 2 2m UA 30 J TO J 0 2m 2 2 4 4 X

A block of mass m is pulled by a force of constant power P placed on a rough horizontal plane The friction coefficient between the block and the surface is Then P The maximum velocity of the block during the motion is mg B The maximum velocity of the block during the motion is P 2 mg C The block s speed is never decreasing and finally becomes constant D The speed of the block first increases to a maximum value and then decreases

A large block of mass M on a smooth inclined plane is connected via a string to a small block m which is attached to a relaxed spring of force constant k with its other end attached to the ground see diagram Which of the following forces do NEGATIVE work as the large block slides down the incline A The tension force on m C The spring force on m M celllle B The gravitational force on m D The tension force on M

In the figure below a ball of mass 5 kg starts at point A with a speed of 15 m s on a flat frictionless surface After point B it trav els on an incline BC with coefficient of kinetic friction 0 15 At point B the ball smoothly changes the direction The length of the incline is 2 2 m and it makes an angle of 15 with the horizontal What is the work done by friction What is the velocity of the ball at point C Given Sin 15 0 25 Cos 15 0 95 A B 8

A wheel is rolling on a horizontal plane At a certain instant it has velocity v and acceleration a of c m as shown in the figure Acceleration of B A is vertically upwards B may be vertically downwards C cannot be horizontal Some point on the rim may be horizontal leftwards B

An object on a spring vibrates in a simple harmonic motion at a frequency of 4 hertz and an amplitude of 8 cm If the mass of the object is 200 g the spring constant is 40 N m X160 N m 126 N m 109 N m

The figure shows a block of mass m placed on a smooth wedge of mass M Calculate the value of M and tension in the string so that the block of mass m will move vertically downward with acceleration 10 m s Take g 10 m s A the value of M is B the value of M C the value of tension in the string is Mcote 1 cot 0 Mtane 1 tane D the value of tension is ug cota Mg tane M M m Smooth 87

In the figure shown M 7 kg is placed on horizontal surface and m 2 kg is attached with a spring of k 700 N m which is initially in natural length and string is just taut Now the m is released from rest During subsequent motion Eeeeee The block of mass M will not leave the contact with horizontal surface The block of mass M will leave the contact Minimum normal force on M by horizontal is 3g Velocity of block of mass m when heavier block just leaves the 1 contact is m s

3 In the figure shown find work done by tension in string on 3 kg block in first two secon beginning of motion The system is set free at t 0 g 10 m s Assume pulley and string i A 96 Joule 2kg 3kg co Joule D 96 Joule

An ideal monoatomic gas is enclosed in a vertical cylinde r An ideal monoatomic gas is enclosed in a vertical cylinder of area of cross section A and length I under massless frictionless piston connected to spring of spring constant K Atmospheric pressure is such that in absence of gas under the piston in equilibrium piston it just touches the bottom of the cylinder and spring is in stretched configuration Initially volume occupied by gas is 3rd of the volume of cylinder and the spring is relaxed Q amount of heat is supplied to gas slowly to move piston to the upper edge If Q 2x K 9 find 7 through the motion of the piston spring is in stretched configuration eeeeeee

101 In the figure shown a small object is released from the position A on a smooth track When the object reaches at B then normal reaction on it by the track is 3h 1 mg 3 2mg and Cylindrical surface 2 4 2mg 3 mag h

the work done by gravity when mass m is displaced slowly by a force F 0 60 from position A to position B 1 mgl 2 3 mal VG m B 0 F A 2 F mgl 2 3

A square wire of side 3 cm is placed perpendicular to principal axis at a distance 25 cm from a concave mirror of focal length 10 cm What is area enclosed by image of the wire 4 cm 9 cm 12 cm 16 cm

A lump of lead with mass 0 5 kg is dropped from height of 20 m onto a hard surface it doesn t rebound but remains there at rest for a long period of time Find change in heat change in work change in internal energy for the lead during this process

Variation of force with time for a body moving along straight line is shown in figure The impulse in N s imparted in the time interval t 0 to t 8 s is 2 F N 2 1 zero 2 4 6 2 8 t s 8 3 8 4 6

The disc of mass M with uniform surface mass density is shown in the figure The centre of mass of the quarter disc the shaded area is at the position x a x a 3 3 Round off to the where x is Nearest Integer a is an area as shown in the figure Y a X

4 The figure shows a pipe of uniform cross section inclined in a vertical plane A U tube manometer is connected between the points A and B If the liquid of density po flows with velocity vo in the pipe Then the reading h of the manometer is a h 0 c h Po Vo p 2g b h vo 2g d h POH P Po

A car travelling at 60 km h overtakes another car travelling at 42 km h Assuming each car to be 5 0 m long find the time taken during the overtake and the total road distance used for the overtake

A box with a mass of 5 0 kg that is moving at 4 0 m s on horizontal frictionless surfaces runs into a light spring with a force constant of 80 0 N cm a Using the work energy theorem find the maximum compression elongation of the sp b What amount of force does the spring exert on the box at the position of maximum compression

31 4 Given moss m of leryth e imparted J bob of ii find Just the a string momenten i Draw diagram of p of bob Bob 6 E of offer letting ground

A 1 00kg block is attached to a spring with a spring constant of k 30N m that is hanging from the ceiling The bottom of the block is then attached to a second spring with a spring constant of k 20N m that is attached to the floor When the two springs are unstretched there is a gap of 50cm between the end of the spring hanging from the ceiling and the end of the spring that is attached to the floor The potential energy function for this block is U mgx 1 2 k1 x 1 2 kz x 0 50m where x is the position of the block above the bottom of the spring that is attached to the ceiling when it is unstretched 1 What is the value of x that is the equilibrium position for this block

A small objects slides height 50 cm shown in figure 3 126 and then loops the vertical loop of radius 20 cm from which a symmetrical section of angle 2a has been removed Find the angle a such that after losing constant at A and flying through the air the object will reach at point B Ans 60 1 H B Figure 3 126 A R

20 P Q R S ACB is a smooth quarter circular path of radius R Four forces are acting at a particle placed at A F1 is always horizontal F2 is always vertical F3 is always tangential to path F4 is always directed from particle s position to point B Magnitude of all forces are equal to F Column l work done by F is work done by F2 is work done by F3 is work done by F4 is A B P21 Q 031 R432 S 5129 1 2 3 4 Column II F R F R 2 TFR 2 F R 2 A

Note Always write your final answers in two decimal places 1 Sky and Blue are lifting some weights inside the gym on a Saturday afternoon They were able to lift a barbell with a force a 450 N at a height of 0 7 meters but Blue did the work in just 9 seconds If Sky was able to do the work in 11 seconds prove that Blue is more powerful