Work, power & energy Questions and Answers

What is the factor by which a runner s kinetic energy is changed if the runner s velocity is ncreased to 10 times their initial velocity a b 5 times 10 times c 20 times d 50 times e none of the above

3 xVo 1 10 J 3 15 J VK M m 4 K M m 10 A body of mass 2 kg is acted upon by two forces 2 N and 5 N in the direction of and k respectively If the body is displaced from 3 2 1 to 1 2 3 Positions are in m then work done is xvo 2 5 2 J 4 20 J 11 OOO III 1 Only 1 3 Only III 15 Power given

I wanted to ask we students are just taught Work force x displacement But isnt work affected by friction or angle of force or thru st Like if I apply a 10N force on an object i n space it will just go straight and straight a nd assuming there is nothing that comes it way wouldnt the displacement become infi nite and so does the work Also on the eart h itself for the same force an object will tra vel much further on ice than on wood So is nt work a very vague concept considering p hysics is the science which doesnt go about things blindly And if work and energy are b asically the same why introduce the concep t of work in the first place

and ss tic and E then energy stored in B will be of equal magnit 1 2EA EA 3 2 stored in spring A is 2 EA 4 4 4EA SECTION D NEET Booster Questions A point mass 1 kg collides elastically with a 1 stationary point mass of 5 kg After their collision the 1 kg mass reverses its direction and moves with a speed of 2 m s For the system of these two masses the KE of the centre of mass is 1 0 75 J 2 0 5 J 3 1 J 4 1 5 J A conservative force in a region is given by from rest at x 0 then its spoed x 12 mis F N 4 10 0 1 10 2 m s X 4 x 8 x 2 20 3 40 m s A pump is required to lift 1 minute from a well 20 m speed of 20 m s The powe 1 6 6 kW 3 2 kW

A conservative force field F is shown below Compute the work done by F to move a particle from 1 1 to 1 1 along the indicated path For scale F 0 0 0 0 2 01 00 0 1 0 2 2 5 CT 1 1 AF X 1 1 O 250 2 2 5 C I 21 0 5

A body of mass m begins to move under the action of time dependent force F ti 21 N where i and are unit vectors along x and y axis respectively The power developed by the force in watt at time t is dmed MHT CET 2020 3 3 t 4t5 3t4 A ed C D 3m 2m 2m 3t3 3m 2m B t m 13 4t5 2m 3m

In the circuit shown use the node analysis method to calculate 3V 0 10 Q 2 A 492 502 222 w V 4 A a The voltage Vo b the power dissipated by the dependent source c If the resistance of 10 ohms is short circuited what would be the value of the voltage Vo What would happen to the current dependent source Explain your reasoning

If on Jupiter unit of force is Tendulkar unit of acceleration is Kohli and unit of time is Rohit such that 1 Tendulkar 10 N 1 Kohli 5 m s 1 Rohit 10 sec If unit of power is Yuvi Find the value of 20 Yuvi O 500 W O O O None 1000 W 10000 W

In the diagram below a solid marble rolls from rest without slipping down a mountain of height h 100 m A Find the linear v 1 and angular speed omega 1 of the marble at the bottom of the hill 100m below top State the equations used and briefly explain your method Hint 1 Use conservation of energy 2 It is not necessary to know the mass M of marble B Find the linear v 2 and angular speed omega 2 of the marble when it lands on the ground in the pit or to the right of the pit State the equations used and briefly explain your method h V V 1 omega 1 W 45 m V1 W Pit 25 m 26m The moment of inertia of a solid sphere is I MR where M is the mass of the marble and R 0 1 m is the radius of the marble V V 2 W omega 2

Light with an energy of 24 W cm falls on a non reflecting surface at normal incidence The surface area is 50 cm What is total momentum delivered to surface for complete absorption in one minute 2 1 x 10 4 kg m s 2 4 x 10 4 kg m s 1 2 x 10 4 kg m s 3 1 x 10 4 kg m s

m 5kg block moving from point A to point B on a 53 inclined surface When it moves downwards in the blocky direction d 4 meters Find how many Joules is the work done by the gravitational force acting on the mass m g 10m s A B C D Question 8 AND 00 120 160 160 200 15009 m Skg k tleli ekildeki blok 6 53 e imli y zey zerinde A noktas ndan B noktas na do ru hareket ediyor Blok 1 nolu y nde asab do ru d 4metre ilerledi inde m k tlesine etki eden yer ekimi kuvvetinin yapt is ka Joule d r bulunuz g 10m sn 4

2 The mass of a bucket full of water is 15 kg It is being pulled up from a 15m deep well Due to a hole in the bucket 6 kg water flows out of the bucket 48 The work done in drawing the bucket out of the well will be g 10m s 1 900 J 3 1800 J 2 1500 J 4 2100 J

a potential energy given by U exerted on it is 1 2 20y 4 Z 20y 20x Z 20v i 20x i 20xY ik 3 20v i 20x 20xv 20x N 3 20xy Z 20xy Z 20xy 2 nas The force

A uniform chain of length L and mass M is lying on 2 of its length is hanging down 3 a smooth table and over the edge of the table If g is the acceleration due to gravity the work done to pull the hanging part on the table is MgL 1 MOL 2 3 MgL 4 2MgL

m A frictionless cart of mass M carries two other frictionless carts having masses m and connected by a string passing over a pulley as shown in figure The horizontal force that must be applied on M so that m and m do not move relative to it will be m1 F M A M m m m m g B M m m m m g C M m m m m g D M m m m m g m A observ wrt Grounal By

The uniform bar shown in the figure weighs 20 lb and when the bar is upright the spring is not deformed Using the Potential Energy Method determine the position s e necessary for equilibrium Study the stability of the system in the equilibrium position s A 3 pies 1 pie

A small bob of mass mis suspended vertically with the help of an ideal inextensible galong the horizontal at lowest string to a rigid support Bob is given a velocity v II point Q Tension in the string at the

A force F Kx acts on a particle at an angle of 60 with the x axis The work done in displacing the particle from to X1 will be 1 kx 3 1 3 x x X2 8 X2 2 1 x x X2 k 4 x x1 O

A stone of mass 100 gm is thrown from ground with a speed of 40 2 m s and at angle of 45 with horizontal at t 0 The average power delivered by gravity between t 1s and t 1s and t 3s is A 20W B 12 5W C 40W D 25W

A particle of mass mis driven by a machine that delivers a constant power kwatts If the particle starts from rest the force on the particle at time t is 0 1 2 2 mkt Imk O Jmk 7 t

Two similar springs P and Q have spring constants Kp and Ko such that Kp KQ They stretched first by the same amount case a then by the same force case b The work done by the springs Wp and Wo are related as in case a and case b respectively Wp Wo Wo Wp O Wp W Wp Wa Wp Wo Wp Wa

45 A 100 g mass is going in a vertical circle of radius 1m What is the minimum speed that mass will reach the top of the circle What is the speed when it is at the Ans 3 13 m s 7 0 ms bottom

planes of lengths and 2s from state of rest as shown in figure The relation between velocities V and V at the bottom of the planes will be V 1 2s tane 3 V 2 BXG V 2 V V 2 god V 1 3 V 28 tane V B GV 2 V V

1 5 J 2 10 J A bullet of mass 50 g moving with 100 m s enters into a horizontal block of thickness 10 m It emerges with kinetic energy equal to 20 of initial kinetic energy The speed of bullet on leaving the block is 1 20 m s 2 20 10 m s 3 20 5 m s 4 20 2 m s particle and displaces it from initial position x 31 47 m to final posit

A The work done by a force is defined by W F It is found that the work done is zero even if F and s are not equal to zero From this we conclude that a F and s are acting in the same direction b F ands are acting in the opposite direction F and and s are acting at right angles c d F and 3 are acting at an angle of 60 s

A certain CI engine consumes No 2 diesel fuel Hg 45 000 kJ kg at the rate of 26 3 kg h while running at a rated speed of 2200 rpm and producing 595 N m of torque Assuming the mechanical efficiency is 0 85 a Calculate the fuel equivalent power b Calculate the brake power c Calculate the indicated power d Calculate the friction power e Calculate the indicated thermal efficiency f Calculate the brake thermal efficiency g Calculate the BSFC

A ring of mass m 30g slides over a smooth vertical rod Attached to the ring is a light string passing over a smooth fixed pulle distance of 0 8 m from the rod At the other end of the string there is a mass M 50 g The ring is held level with the pulley and released see figure Determine the distance by which the mass m moves down before coming to rest for the first time O 1 5m O 0 75m O 5m 005 m

A particle of mass m is tied to one end of a massless inextensible string of length and whirled in a vertical circle Find the maximum tension in the string during particle s motion if the ratio of maximum and minimum tension is 3 2 A B C D 7 mg 14 mg 18 mg 12 mg

Two bars connected by a weightless spring of stiffness and length in the non deformed state rest on horizontal plane A constant horizontal force F starts acting on one of the bars as shown in figure Find th maximum and minimum distances between the bars during the subsequent motion of the system if th masses of the bars are a Equal b Equal to m and m and the force F is applied to the bar of mass m M Mz

A pesky fly mass 5 g is hovering in the air outside your window A sudden gust of wind exerts a force of F 4 0 i 6 0j 10 2 N on the fly a How much work is done by the force of the wind on the fly if the insect undergoes a displacement of Ar 2 0i 2 0 j m Select J b What is the fly s speed at the end of this displacement Assume that the speed is due entirely to the wind Select m s

3 A block starts from rest It is pushed with an applied force for d m It is released and trave over a rough patch Calculate the maximum vertical displacement up the incline a m d 10 m d 3 m F 100 N m 10 kg d 0 d H 0 2

A 7 80 g bullet moving at 690 m s penetrates a tree trunk to a depth of 6 20 cm Use work and energy considerations to find the average frictional force that stops the bullet Assuming the frictional force is constant determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving

A ball is projected with initial velocity u at an angle to the horizontal Then horizontal displacement covered by ball from starting to the time instant when it collides third time to the ground would be if coefficient of restitution is 1 e O O O I N 3u sin 20 2g 7u sin 20 4g u sin 20 2g 5u sin 20 4g X

A crate of mass m 12 4 kg is pulled by a massless rope up a 36 9 ramp The rope passes over an ideal pulley and is attached to a hanging crate of mass m2 16 3 kg The crates move 2 40 m starting from rest Find the final speed of the sliding crate if the frictional force on the sliding crate has magnitude 27 4 N m2 m s m1 0

Two balls of charges q and q initially have exactly same velocity Both the balls are subjected to same uniform electric field for same time As a result the velocity of the first ball is reduced to half of its initial value and its direction changes by 60 The direction of the velocity of second ball is found to change by 90 The electric field and initial velocity of the charged particle are inclined at angle 1 60 3 90 2 30 4 150

Q4 For the figure below the spring is used to stop a 10 kg package If the maximum deflection in the spring is 70 mm a the total work of the system in the figure below is Mk 0 25 8m s 10kg 500m 0 30 K 400N m b The total work when

Three designs are proposed for an engine operating between 500 K and 300 K For 1 kcal of heat input design A claims to produce 3000 J of work design B claims to produce 2000 J of work and design C claims to produce 1000 J of work The design which is possible is a A only c All b B only d C only

Two infinitely long parallel conducting plates having surface charge densities 6 and o respectively are separated by a small distance The medium between the plates is vacuum If eo is the dielectric permittivity of vacuum then the electric field in the region between the plates is AIIMS 2005 a zero c a V m b 0 280 V m d 20 0 V m

C is smalle for the lighter car D depends on the volume of Two objects are moving at a speed of 8m sec and 12 m sec respectively If they are on the same surface then the ratio of their potential energy will be A 4 9 Uttrakhand NTSE Stage 1 2015 D None of the above B 1 1 C 2 3 lift which is moving upwards with a man of on

A ball of mass 5g is thrown downward from point A with certain initial velocity Vo Towards a hard floor Without any loss of energy it rebounds from the floor at point 10m above the original level Thus the initial velocity Vo of the ball is 1 10 m s 3 14 m s 2 50 m s 4 28 m s

In the figure shown find work done by tension in string on 3 kg block in first two second from beginning of motion The system is set free at t 0 g 10 m s Assume pulley and string is ideal GITA A 96 Joule B 48 Joule 2kg 3kg C 24 Joule D 96 Joule

10 kg i Two blocks A and B are connec and a spring the string passes over a frictionless pulley as shown in the figure 2 117 Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C both with the same uniform speed The coefficient of friction between the surfaces of the blocks is 0 2 Force constant of the spring is 1960 N m If the mass of block A is 2 kg calculate the mass of block B and the extension in the spring Take g 9 8 m s t 10 kg 1 cml A Miw Figure 2 117 B

28 Work Energy and P 16 Potential energy of a particle of mass 1 kg moving x along x axis is given by U 4x 12 where 3 x is in meter For this force field consider the following four statements and identify the correct combination of statements 1 i x 2m and x 2m are positions of equilibrium ii x 2m is the position of stable equilibrium iii x 2m is the position of unstable equilibrium iv 21

A moving particle of mass m makes a head on elastic collision with another particle of mass 2m which is initially at rest The percentage loss in energy of the colliding particle on collision is close to B 90 D 67 A 10 C 33

A circular platform is mounted on a frictionless vertical axle Its radius R 2 m and its moment of inertia about the axle is 200 kgm It is initially at rest A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms relative to the ground Time taken by the man to complete one revolution is a S b 3p 2 c 2 S Saat 2012M 319 5296 10 T d s S

4 49 A small disc A slides down with initial velocity equal to zero from the top of a smooth hill of height H having a horizontal portion as shown in figure 4 139 What must be the height of the horizontal portion h to ensure the maximum distance s covered by the disc What is it equal to H h Figure 4 139 S

124 A chain of mass m 0 80 kg and length 1 1 5 m rests on a rough surfaced table so that one of its ends hangs over the edge The chain starts sliding off the table all by itself provided the overhanging of the chain length What will be the total work 3 1 part equals n performed by the friction forces acting on the chain by the moment it slides completely off the table

3 35 An object of mass m is tied to string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases it is pulled extremely slowly so that equilibrium exists at all times until the string makes an angle 0 with the vertical Work done by the force F is A mgL 1 cose C mgL 1 1 L 777 Figure 3 91 B FL sine D FL 1 tane

A force F 51 31 Newton is applied over a particle which displaces it from its origin to the point r 21 11 metres The work done on the particle is MP PMT 1995 KCET 1999 BHU 2001 AIIMS 2001 CBSE PMT 2002 CPMT 2003 RPET 2003 AIEEE 2004 Odisha JEE 2005 RPMT 2006 Kerala PMT 2007 b 13 J d 11J a 7J c 7J

A cylinder having length 10cm and density 0 65 g cm floats half submerged in the liquid shown Pair 1 3 x 10 3 g cm Now pressure of air made 100 time of initial pressure keeping temperature constant Which of the following statement s is are true The cylinder moves upwards The cylinder moves downwards Displacement of the cylinder is 0 56 cm Displacement of the cylinder is 0 60 cm 4