Work, power & energy Questions and Answers

The diagram shows an elevator moving 1 1 up with a constant velocity The work done by the elevator is zero Elevator negative none of the above positive

An object of mass 5 kg is projected with a velocity of 20 m s at an angle of 60 to the horizontal At the highest point of its path the projectile explodes and breaks up into two fragments of masses 1 kg and 4 kg The fragments separate horizontally after the explosion which releases internal energy such that K E of the system at the highest point is doubled Find the separation between the two fragments when they reach the ground a 11 m b 22 m c 44 m d 66 m

A pump ejects 12000 kg of water at speed of 4 m s in 40 second Find the average rate at which the pump is working 12000 kg si 4 m s 0 aradan A B 2 4 W C 2 4 KW D 24 W 0 24 KW Your Answer

A molecule of a substance has electric dipole moment of 29 Cm A mole of this substance is polarised by applying strong electric field of magnitudes 107 Vm 1 The direction of field is changed by an angle of 60 The heat released by the substance in aligning its dipole along the new direction of field is O 60 J 0 12 J O 15 J 30 J

The circuit shown in figure has resistance R 20 2 R 302 At what value of Ro will the thermal power P generated in it be practically independent of small variations of that resistance The voltage dP between A and B is constant Hint 0 dRo A www R R R

Which of the following statements are correct Somerto a Centre of mass of a body always coincides with the centre of gravity of the body b Central of mass of a body is the point at which the total gravitational torque on the body is zero c A couple on a body produce both translational and rotation motion in a body d Mechanical advantage greater than one means that small effort can be used to lift a large load 1 a and b 2 b and c 3 c and d 1 b and d

A massless spring of spring constant k initially in its natural length has two ends P and Q as shown in the figure End Q is being pulled by person B with constant speed u towards right End P is being pushed by person A with constant acceleration a towards right starting from rest Both start simultaneously Choose the correct options at the instant when B appears to be at rest with respect to A mooooo S O work done by B work done by A ku4 3a work done by B 5ku4 24a work done by A 5ku4 24a ku4 8a A P B 4 4

When a spring is stretched by 2 cm its potential energy is U If the spring is stretched by 10 cm The potential energy stored in it will be Question Type Single Correct Type 125 U 2 U 5 3 5 U

A variable horizontal force F 25t acts on a block of mass 10kg kept on al rough horizontal surface Co efficient of static and kinetic friction are H 0 6 0 4 What is the velocity of the block at t 4 second A 1 6 m s B 3 2 m s C 5 m s D 6 4 m s

5 2 points A spring has a natural length of 3 m It takes 10 N of force to stretch the spring to a total length of 5 m How much work is done in stretching the spring from a total length of 4 m to a total length of 6 m Be sure to write the units for your answer

OPTIONS CLEAR SELECTION MARK FOR REVIEW A Only in conservative field OB Only in non conservative field As the positive work done by conservative force

A uniform rope of linear mass density dand length is hanging from the edge of a table The work done in pulling the rope on to the table is OPTIONS CLEAR SELECTION dgl A 2 OB dgl dal MARK FOR REVIEW

A block of mass m moving at speed v compresses a horizontal mounted spring through a distance d before its speed becomes zero The spring constant of the spring is OPTIONS CLEAR SELECTION A mv d MARK FOR REVIEW

roblem 5 Find the work done by the force F direction 6yi 6x j along one loop of the curve r sin 90 in the positiv

Two springs have their force constants k and k and they are stretched to same extension If k k work done is OPTIONS CLEAR SELECTION O A O B MARK FOR REVIEW More in spring having force constant k More in spring having force constant k2

A body of mass 2 kg is projected vertically up with velocity of 20 m s If the energy spent in over coming air resistance is 100 J the maximum height attained by it is g 10 m s OPTIONS CLEAR SELECTION OA 15 m OB 20 m MARK FOR REVIEW

Heater 1 takes 10 minutes to increase temperature of liquid A of mass 2kg by 20 C when connected with 200 V supply Heater 2 takes 20 minutes to increase temperature of liquid B of mass 4 kg by 20 C when connected with 400 V supply Given Specific heat of liquid A 6000 J kg C Specific heat of liquid B 12000 J kg C Select correct option s A The power of heater 1 is 400 watt B The resistance of heater 2 is 200 C If both heaters are connected in series to a 300 V supply then time taken to increase temperature of liquid A by 30 C is 20 min D If both heaters are connected is parallel to a 300 V supply then time taken to increases temperature of liquid B by 27 C is 16 min

A block of mass m moving with velocity vo on smooth horizontal surface strikes with a spring fixed in vertical wall as shown in the figure If maximum compression in the spring is xo then spring constant of the spring will be Vo 00000 m OPTIONS CLEAR SELECTION MARK FOR REVIEW

A ball released from a height of 20 m hits the ground and rebound to a height of 16 m The coefficient of restitution of the collision will be OPTIONS MARK FOR REVIEW CLEAR SELECTION A 4 49

A man weighing 60 kg climbs up a staircase with 20 kg weight on his head The staircase has 20 steps each being 15 cm high If he takes 10 s to climb then the power is g 10 m s A 24 W B 180 W C 240 W D 320 W

A particle of mass m released from top position on one side of a smooth semicircular surface of radius r in the vertical plane Maximum power generated by gravity is when e is 20

A body of mass 10 kg is raised from certain depth If work done in raising it by 10 m is 1600 J its velocity at this position will be g 10 m s OPTIONS CLEAR SELECTION OA 30 m s MARK FOR REVIEW OB 4 30 m s

When a spring is compressed by a distance x the potential energy is U When it is further compressed by a distance 2x the potential energy is U The ratio of U U is OPTIONS CLEAR SELECTION OA 1 3 B 1 9 MARK FOR REVIEW

A motor pump lifts water from an average depth of 10 m at the rate of 5 kg per second If the water is coming out of the pump with velocity 2 m s the power of the motor is g 10 m s OPTIONS MARK FOR REVIEW CLEAR SELECTION OA 1020 W O B 600 W C 510 W

A car stops to slide in 10 m During this process the force on the car due to road is 200 N opposite to the motion The work done by the road on the car will be OPTIONS CLEAR SELECTION MARK FOR REVIEW OA A 2000 J O B 1000 J

A transistor is connected in common emitter configuration supply is 8 V and voltage drop across a resistor of 800 Q in collector circuit is 0 5 V If the current gain factor 24 then base current will be O 20 A O 26 A O 32 A 24 A

g 20 A weight of 200 kg is repeatedly dropped freely from a height of 10 m on the head of a pole of mass 50 kg to K push it into the ground For every impact the pole pen etrates 7 cm into the ground Find the average resis tance of the ground Ans 223 440 N

Figure shows a block of mass m projected with velocity vo towards a wedge Consider all the surfaces to be smooth Block does not have sufficient energy to negotiate over come wedge Mark the correct option s m 4 H M When block is at the maximum height on wedge block and wedge have velocity equal to velocity of centre of mass of block wedge system Wedge acquires maximum speed with respect to ground when block returns to lowest point on wedge Momentum of wedge and block in horizontal direction is conserved at all times

A B D A 0 5 kg block slides from the point A on a horizontal track with an initial speed 3 m s towards a weightless horizontal spring of length 1m and force constant 2N m 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 2 respectively If the distance AB and BD are 2m and 2 14 m respectively find the to distance through which the block moves before it comes to rest complete g 10m s rrrrrrrr

Q 21 The potential energy of a particle under a conservative force field is given by U 10 x 4 2 where x is in meter At x 6 m K E of particle is 10 J The maximum kinetic energy of particle is 8 0 84

Solve the problem Find the work done by a force of F 101 12j newtons in moving an object along a line from the point 1 2 to the point 8 6 distance in meters 166 100 731

series with an AC source is constant F in series with a ce 4 9mH and a hat the maximum fP and Q at this respectively pedance 1002 0 2cm Ans 7 5 x 10 N A 596 a distance gle a to the tected at the des without cal field R 5 23 A periodic voltage wave form has been shown in figure 5 337 10 V in volt 11 100 200 t in ms Figure 5 337 Determine a Frequency of the wave form b Average value of the voltage Ans a 10Hz b 5V 5 29 A re field B ac to pull it calculat

A circular coil of 100 turns and effective diameter 20 cm carries a current of 0 5 A It is to be turned in a magnetic field B 2T from a position in which 0 equals zero to 0 equals 180 The work required in this process is x J value of x ix

A particle of mass 3 kg is moving under the action of a central force whose potential energy is given by U r 10r joule For what energy and angular momentum will the orbit be a circle of radius 10 m Calcu late the time period of this motion

2 Three liquids of densities p P2 and p3 with P P2 P3 having the same value of surface tension T rise to the same height in three identica capillaries The angles of contact 0 02and 0 obe 3 NEET 2 a 0 0 03 20 T b 0 0 0 03 2 90 mesia c 0 0 03 T 2 d 0 0 0 03

5 A Draw a diagram to show the energy changes in an oscillating simple pendulum Explain how the total mechanical energy in it remains constant during the oscillation 3 B Describe positive and negative work with the help of one illustration of each 4 C Two bodies of masses m and m are moving with same kinetic energy Calculate 3 i Ratio of their momentum ii Ratio of their velocity

Consider the condition shown in the figure Pulley is massless and frictionless springs are massless Both the blocks are released with the springs in their natural lengths Choose the correct options Ruffa A Maximum elongation in the spring S is B Maximum elongation in the spring S is 4m m g K m m 4m m g K m m reeeeeee eeeeeee m both the blocks will come to instantaneous rest simultaneously C If m m D If K K both the blocks will come to instantaneous rest simultaneously m gan

0 A block of mass 500 g and attached to one end of a spring of spring constant K 450 Nm 1 The friction is also present which dissipate energy and damping constant of system is 25 g s What is time taken for its amplitude of oscillation to drop to half of its initial value NCERT Pg 352 1 18 73 s 2 27 72 s 3 32 2 s 4 6 52 s Which of the following example does not 4 1 0 157 s 3 0 314 s 13 The acceleration du surface of moon is period of oscillation a the surface of moon surface of earth is 2s 1 4 8 s 3 1 8 s ATM

c 51 Among the four graph shown in the figure there i d Both a and b over only one graph for which average velocity time interval O T can vanish for a suitably chosen T Which one is it a X x t b d 2 X t Exempl ad is just ab

Velocity of a body of mass 2 kg moving in xy plane 21 4t m s where t is the time is given by in second The power delivered to the body by the resultant force acting on it at t 5 sec is 1 80 W 2 160 W 3 40 W 4 100 W

Potential at a region is given by U x x 2 5x A particle at rest initially at origin moves under the influence of the potential field Kinetic energy of the particle at x 3 is A 2J

An electron moves in in the field produced by a charged sphere of radius 10 cm along the radius connecting the points separated by 12 and 15 cm from the centre of the sphere The velocity of the electron changes thereby from 2 x 105 to 2 x 106 m s Determine the surface charge in nC m density of the sphere Mass of electron 9 1 x 10 31 kg

c T 12 79 The variation of PE of harmonic oscillator is as shown in figure The spring constant is U joule a 1 10 Nm c 2 10 Nm 1 0 04 0 01 0 20 x mm b 1 5x 102 Nm d 3 10 Nm 1 on

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 1 The ratio of their nuclear sizes will be A 21 3 1 B 1 3 1 2 X

SHOULD NT THE ANS BE ZERO AS WORK DONE IN BOTH THE LIMBS IS OPPOSITE direction of displacement is zer PLS EXPLAIN IN DETAIL 7 Two cylindrical vessels of equal cross sectional area A contain water upto heights h and h The vessels are interconnected so that the levels in them become equal Calculate the work done by the force of gravity during the process The density of water is p

this force during a displacement from X A particle of mass 0 5 kg travels in a straight line with velocity v ax3 2 where a 5 m 1 2 What is the 0 to x 2 m work done by the net force during its displacement from x 1413 ation of forc

73 In SHM potential energy of a particle at mean position is E and kinetic energy is E2 then a E E asda olemely van vad 100 3A 3E is E 4 b total potential energy at x 2 c total kinetic energy at x 3A 2 d total kinetic energy at x is A E2 4 2 is 3E2 4 do of 20

17 Figure gives the acceleration of a 2 0 kg body as it moves from rest along x axis while a variable force acts on it from x Om to x 9m The work done by the force on the body when it reaches i x 4m and ii x 7 m shall be as given below 6 6 NIM 1 21 J and 33 J respectively 2 21 J and 15 J respectively 3 42 J and 60 J respectively 4 42 1 and 30 J respectively x m

Y 0 9520 515 530 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 510 505 500 495 490 480 485 540 470 0 1460 0 550 5604 570 580 590 1600 610 Equal energy point 650 620 HIF 400 0 1 0 2 0 3 0 4 0 5 0 6 0 7 700

A uniform rope of linear mass density and length 1 is coiled on a smooth horizontal surface One end is pulled up with constant velocity v Then the average power applied by the external agent in pulling the entire rope just off the ground is