Work, power & energy Questions and Answers

Hailstone at 0 C falls from a height of 1 km on an insulating surface converting whole of its kinetic energy into heat What part of it will melt g 10 m s 1 1 33 2 8 3 1 33 x 10 4 X 4 All of it will melt

An electric dipole of moment placed in uniform electric field E has minimum potential energy The vork done by external agent to rotate this dipole very slowly upto which it has maximum potential energy O PE O2PE OPE 2 O Zero

A 2 7 kg block is moving from point A 0 3 2 2 7 to Point B 3 7 0 0 75 under the action of its weight and the force F 18 6 i 5 1 j 7 5 k Newtons A 0 YA ZA Xu X Za B X8 0 Z The work done by the force F alone during the motion of the block from A to B in Joules is Assume the work done by the force F alone is 109 7J calculate the speed of the block at B if released from rest at A Choose Choose

A uniform sphere of weight W and radius 3 m is being held by a string of length 2m attached to a frictionless wall as shown in the figure The tension in the string will be 1 5 W 4 3 15 W 16 Wall W 2 15 W 4 4 None of these

A block of mass 16 kg is moving on a frictionless horizontal surface and comes to rest after compressing the spring of constant 100 N m by 1 6 m then its velocity will be U A 6 m s 4 m s 8 m s 2 m s

A block whose mass is 5 7 kg slides on horizontal frictionless table top with a constant speed of 5 m s It is brought momentarily to rest by compressing a spring in its path By what maximum distance is the spring compressed spring constant of spring K 1282 5 N m M oooooo 20 cm 28 cm 39 cm 33 cm

A particle of mass 0 5 kg travels in a straight line with velocity v ax3 2 where a work done by the net force during its displacement from x 0 to x 2 m 5 m s What is t

A simple pendulum of length is oscillating with amplitude 0 At some instant it makes angle 0 with the vertical its speed of the bob is v The acceleration of bob will be A g sin 0 B g tan 0 sin 0 G C g sin 0

2 4 A bicyclist comes to a skidding stop in 10 m During this process force on the bicycle due to the road is 200N and is directly opposed to motion The work done by the cycle on the road is a 2000 b 200J c zero Thinking Process d 20 000

25 A long spring when stretched by a distance x has potential energy U On increasing the stretching to nx the potential energy of the spring will be U a n c n U b nu d n c Zero Tim 1 T 2n 177 2 Simple per

A water pump lifts water at the rate of 5 litre per second through an average height of 8 m from a well of depth 12 m Its power will be O 1280 watt O 980 watt O 1180 watt O 1080 watt

d 2 cos it A 3 13 Figure 14 26 a shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end A force F applied at the free end stretches the a mass m at either end Each end of the spring in Fig 14 26 b is stretched by the spring Figure 14 26 b shows the same spring with both ends free and attached to same force F a b k a TTL F F m com time of m k Com b m at nor net bay F Fig 14 26 What is the maximum extension of the spring in the two cases If the mass in Fig a and the two masses in Fig b are released what is the 900 2 plitude

Three charges lie along the x axis The positive charge q1 15 uC is at x 2 0 cm and the positive charge q2 6 0 C is at the origin Where must a negative charge q3 be placed on the x axis so that the resultant electric force on it is zero B Name an application of part A in the real world and draw a diagram

3 4E 3 3R The grid each square of 1 m x 1 m represents a region in space containing a uniform electric field If potentials at point O A B C D E F G H are respectively 0 1 2 1 2 0 1 1 and 0 volts Find the electric field intensity y O C 1 V m 2 1 i V m 3 i 1 V m 4 i i V m CE G A 1m H TI F BX

32 3 9 6 N 3m 1 8N 2 6N 3 3N 4 zero A bicycle is moving with constant acceleration The frictional force on rear wheel is 1 Zero 2 In forward direction 3 Backward direction 4 All of these AJKOT CENTER 0 m 1 mgl sine 2 mgl cos0 3 mgl 1 cose 4 mgl 1 cose Work done to carry bob upto angle 0 with the vertical very slowly from initial vertical position is 12 N 77

9 A particle undergoing simple harmonic motion has time dependent displacement TI given by x t A sin The ratio of kinetic 90 to potential energy of this particle att 210s will be JEE Main 2019 11 Jan Shift 1 a 2 b 1 c 1 2 9 d 3 10 29 pm

nless axis N 0 and n e 3 83 Two blocks of masses m 1 kg and m 2 kg are connected by non deformed light spring They are lying on a rough horizontal surface The coefficient of friction between the blocks and the surface is 0 4 What minimum constant force F has to in be applied in horizontal direction to the block of mass m order to shift the other block Take g 10 m s F m 6oooooooood m A 8N C 10N Figure 3 107 B 15 N D 25 N 2 snoda bila ia

to is of d 0 3 15 A body with mass 2 kg moves in one direction in presence of a force which is described by the potential energy graph If the body is released from rest at x 2 m then its speed when it crosses x 5 m is A Zero C 2 ms U joule 10 1 2 3 3 5 4 4 5 5 x meter Figure 3 83 B 1 ms D 3 ms 1

3 101 The following figure 3 116 illustrates the relation between the position of a particle and force The work done in displacing the particle from x 1 to 5 m is Force in N A 20 joules C 70 joules 20 10 0 10 20 2 3 14 5 Figure 3 116 Xin m B 60 joules D 100 joules

3 80 A block of mass 1 kg is attached to one end of a spring of force constant k 20 N m The other end of the spring is attached to a fixed rigid support This spring block system is made to oscillate on a rough horizontal surface u 0 04 The initial displacement of the block from the equilibrium position is a 30 cm How many times the block passes from the mean position before coming to rest Take g 10 m s B 7 D 15 A 11 C 6

6 A small block A of mass m is given a velocity v in horizontal direction as shown The bigger block B is initially at rest The curved surface of the block B becomes vertical at the top point If M 4m what should be the minimum value of v so that the block A climbs upto the top on B All surfaces are smooth g 10 m s 90 4 m A 1 20 m s m v B M 2 10 m s 4 2 m s

A body constrained to move along y axis is subjected to a constant force F 1 2 3kN The work done by this force in moving the body a distance of 4 m along y axis is b 8 J a 4 c 12 d 24 J

3 39 A block of mass 1 kg slides down a curved track from rest that is one quadrant of a circle of radius 1 m Its speed at the bottom is 2 m s The work done by frictional force is A 8 J C 4J R 1 m Figure 3 93 B 8 J D 4 J P

A stationary body explodes into two fragments each of rest mass 1kg that move apart at speed of 0 6c relative to the original body The rest mass of the original body is A 2 kg B C D 2 5 kg 1 6 kg 2 25 kg

EN 3 Find the compression in spring so that the block travels a distance of 8m before instantaneous come to rest after block is released 1 1 01 m 3 3 03 m x3 9 K 160 N m vooroor 2kg 0 2 2 2 02 m 4 4 025 m

PRACTICE ANOTHER 22 0 kg cannonball is fired from a cannon with muzzle speed of 850 m s at an angle of 40 0 with the horizontal A second ball is fired with the same initial speed at an angle of 90 0 et y 0 at the cannon a Use the isolated system model to find the maximum height reached by each ball m hfirst ball hsecond ball m b Use the isolated system model to find the total mechanical energy of the ball Earth system at the maximum height for each ball Efirst ball Esecond ball TEACHER

Two bars connected by a weightless spring of stiffness k rest on a smooth horizontal plane as shown in figure Bar 2 is shifted a small distance x to the left and then released The velocity of the centre of mass of the system after bar 1 breaks off the wall is x m k m 2 m

2 A raindrop of mass 1 g falling from a height of 1 km hits the ground with a speed of 50 m s If the resistive force is proportional to the speed of the drop then the work done by the resistive force is Take g 10 ms a 10 J c 8 75 b 10J d 8 751 antum of tc de 4

A ball of mass 2 kg is moving with speed 4 m s on horizontal smooth surface collides with a nearly weightles spring of force constant 128 N m as shown in the figure The maximum compression in the spring will be mmmmmm 0 25 m 0 4 m 2 m s 0 15 m 0 5 m

WORK 5 A body is being raised to a height h from the surface of earth What is the sign of work done by applied force and gravitational force respectively a Positive Positive c Negative Positive b Positive Negative d Negative Negative 12

Q17 A particle of mass m starts moving from origin along x axis and its velocity varies with position x as v k x The work done by force acting on it during first t seconds is a b mk4t 4 d mk t 2 mk4t c 8 mk t 4

3 10 A particle of mass m is fixed to one end of a light spring of force constant k and unstretched length 7 The system is rotated about the other end of the spring with an angular velocity w in gravity free space The increase in length of the spring will be A B C mw 1 k mo 1 k mo mw 1 mo k mo 2 2 Heeeeeeeeeeeeee Figure 3 82 D None of these m C 3

4 One mole of a monoatomic gas is carried along process ABCDEA as shown in the diagram The net work done by gas is 0 x J Find value of x B C p N m 4 2 T 1 A Di 2 E 3 4 V m

86 Figure shows a man of mass 55 kg standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 ms The net force acting on the man is a 35 N b 45 N d 65 N c 55 N 2000

Two cylindrical vessels of equal cross sectional area A contains water upto height h and h The vessels are interconnected so that the levels in them become equal The work done by the force of gravity during the process is Option A Zero 2 B PA g Rate this qu

11 g 90 A body of mass 120 kg and density 600 kg m floats in water What additional mass could be added to the body so that the body will just sink a 120 kg b 100 kg d 20 kg c 80 kg Odisha J E E 2006

c 3x 2 A spring of stiffness k is kept compressed by applying horizontal force on m by a length x mg K If the force Fis withdrawn suddenly the block oscillates and finally stops In consequence frictional loss is equal to 50 of the initial ptential energy stored in the spring The coefficient of friction the between block and the ground is a c 1 vor v vo vo vo vo m b 2 3 F Xo

nas overal forces acting on it One force is aryj a force in the negative y direction those magnitude depends on the position of the pol The constant is a 2 60 N m Consider the isplacement of the tool from the origin to the point 3 90 m y 3 90 m Part B Calculate the work done on the tool by Fif the tool is first moved out along the x a the point z 3 90 m y 0 and then moved parallel to the y axis to 3 90 m y 3 90 m Express your answer in joules VAZO W 52 5 Submit F Previous Answers Request Answer J

4 6 A circular current loop of magnetic moment M is in an arbitrary orientation in an external magnetic field B The work done to rotate the loop by 30 about an axis perpendicular to its plane is a MB b 5 c MB MB d zero

10 A horse pulls a cart with constant speed of 7 2 km hr with the help of a rope tied to cart making an angle of 60 with the horizontal for 1 minute Calculate the work done by the horse and its power 1 Force 30 N cos 60

More Than One Correct Answer Type Q19 A man of mass m standing at the bottom of the staircase of height L climbs it and stands at its top a Work done by all forces on man is equal to the rise in potential energy mgl b Work done by all forces on man is zero c Work done by the gravitational force on man is mgl d The reaction force from a step does not do work because the point of application of the force does not move while the force exists Sal b d When a man of mass m climbs up the staircase of height L work done by the gravitational force

The total work done on a particle is equal to the change in its kinetic energy This is applicable Always Only if the conservative forces are acting or it Only in inertial frames Only when pseudo forces are absent

A stone with weight w is thrown vertically upward into the air from ground level with initial speed vo If a constant force f due to air drag acts on the stone throughout its flight The maximum height attained by the stone is h 11 2g 1 v f 29 1 4 2g 2g 1 2011 W

A force 3i j 2k N acting on a body maintains its velocity ai 2j 4k m s If rate of change of kinetic energy of the body is zero then the value of a will be 01 3 O 1 02

The relationship between force and position is shown in fig in one dimensional case The work done in displacing a body from x 1cm to x 5 cm is dyne 30 20 10 0 10 20 2 3 4 5 6 7 8 I O 20 O erg O 60 erg 70 erg 700 erq x in cms

An object has displacement from position vector i 2j m to 2 21 3j m under the effect of a force F 3xi yj N The work done by this force will be O 14 J 07J 05 J 10 J

Consider the following statements Work is not done when Consider the work done either by the gravitational force or by the man or the earth 1 2 3 A man is walking on a horizontal road Moon is revolving round the earth A man with a load on his head is walking on a horizontal road

D Tangential force for the motion F mg sin 0 This force retards the motion ii Results A a Tension at the lowest point A inse TA Here 0 0 TB mv mu TA mg 1 b Tension at point B TB 1 c050 U Tc C mg mvB mu c Tension at point C mvc To mg 5mg 0 180 mu 2mg 2 Here 0 90 Thus we conclude that TA TC TB and also TA TB 6 mg TA Tc 3 mg Tc TB 3 mg iii Cases a If u 5gr In this case tension in the string will not be zero at any of the point which implies that the particle will continue the circular motion

A curved road with radius of curvature 200 m is banked with banking angle equal to tan 0 2 The optimum speed of a car is 20 m s 40 m s 80 m s 10 m s

20 A helium atom mass 4u travels with non relativistic speed v normal to the surface of a certain material makes an elastic collision with an essentially free surface atom and leaves in the opposite direction with speed 0 6 v The atom on the surface must be an atom of O Hydrogen mass 1 u O Helium mass 4 u Carbon mass 12 u Oxygen mass 16 u Silicon mass 28 u