WORK, ENERGY AND POWER NCERT

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1 Exemplar Problems Physics Chaper Six WORK, ENERGY AND POWER MCQ I 6.1 An elecron and a proon are moving under he influence of muual forces. In calculaing he change in he kineic energy of he sysem during moion, one ignores he magneic force of one on anoher. This is because, (a) he wo magneic forces are equal and opposie, so hey produce no ne effec. (b) he magneic forces do no work on each paricle. (c) he magneic forces do equal and opposie (bu non-zero) work on each paricle. (d) he mageneic forces are necessarily negligible. 6.2 A proon is kep a res. A posiively charged paricle is released from res a a disance d in is field. Consider wo experimens; one in which he charged paricle is also a proon and in anoher, a posiron. In he same ime, he work done on he wo moving charged paricles is 38

2 Work, Energy and Power (a) same as he same force law is involved in he wo experimens. (b) less for he case of a posiron, as he posiron moves away more rapidly and he force on i weakens. (c) more for he case of a posiron, as he posiron moves away a larger disance. (d) same as he work done by charged paricle on he saionary proon. 6.3 A man squaing on he ground ges sraigh up and sand. The force of reacion of ground on he man during he process is (a) consan and equal o mg in magniude. (b) consan and greaer han mg in magniude. (c) variable bu always greaer han mg. (d) a firs greaer han mg, and laer becomes equal o mg. 6.4 A bicyclis comes o a skidding sop in 10 m. During his process, he force on he bicycle due o he road is 200N and is direcly opposed o he moion. The work done by he cycle on he road is (a) J (b) 200J (c) zero (d) 20,000J 6.5 A body is falling freely under he acion of graviy alone in vacuum. Which of he following quaniies remain consan during he fall? (a) Kineic energy. (b) Poenial energy. (c) Toal mechanical energy. (d) Toal linear momenum. 6.6 During inelasic collision beween wo bodies, which of he following quaniies always remain conserved? (a) Toal kineic energy. (b) Toal mechanical energy. (c) Toal linear momenum. (d) Speed of each body. 6.7 Two inclined fricionless racks, one gradual and he oher seep mee a A from where wo sones are allowed o slide down from res, one on each rack as shown in Fig Which of he following saemen is correc? (a) Boh he sones reach he boom a he same ime bu no wih he same speed. (b) Boh he sones reach he boom wih he same speed and sone I reaches he boom earlier han sone II. Fig

3 Exemplar Problems Physics Fig. 6.2 (c) Boh he sones reach he boom wih he same speed and sone II reaches he boom earlier han sone I. (d) Boh he sones reach he boom a differen imes and wih differen speeds. 6.8 The poenial energy funcion for a paricle execuing linear SHM 1 2 is given by V( x) = kx where k is he force consan of he 2 oscillaor (Fig. 6.2). For k = 0.5N/m, he graph of V(x) versus x is shown in he figure. A paricle of oal energy E urns back when i reaches x =± xm. If V and K indicae he P.E. and K.E., respecively of he paricle a x = +x m, hen which of he following is correc? (a) V = O, K = E (b) V = E, K = O (c) V < E, K = O (d) V = O, K < E. 6.9 Two idenical ball bearings in conac wih each oher and resing on a fricionless able are hi head-on by anoher ball bearing of he same mass moving iniially wih a speed V as shown in Fig (a) Fig. 6.3 If he collision is elasic, which of he following (Fig. 6.4) is a possible resul afer collision? (b) (c) (d) Fig

4 Work, Energy and Power 6.10 A body of mass 0.5 kg ravels in a sraigh line wih velociy v = a x 3/2 where a = 5 m 1/2 s 1. The work done by he ne force during is displacemen from x = 0 o x = 2 m is (a) 1.5 J (b) 50 J (c) 10 J (d) 100 J 6.11 A body is moving unidirecionally under he influence of a source of consan power supplying energy. Which of he diagrams shown in Fig. 6.5 correcly shows he displacemen-ime curve for is moion? (a) (c) (a) Fig Which of he diagrams shown in Fig. 6.6 mos closely shows he variaion in kineic energy of he earh as i moves once around he sun in is ellipical orbi? K.E (b) (d) (b) (c) Fig. 6.6 (d) 41

5 Exemplar Problems Physics 6.13 Which of he diagrams shown in Fig. 6.7 represens variaion of oal mechanical energy of a pendulum oscillaing in air as funcion of ime? E E E (c) (a) h PE KE (a) Fig A mass of 5 kg is moving along a circular pah of radius 1 m. If he mass moves wih 300 revoluions per minue, is kineic energy would be (a) 250π 2 (b) 100π 2 (c) 5π 2 (d) A raindrop falling from a heigh h above ground, aains a near erminal velociy when i has fallen hrough a heigh (3/4)h. Which of he diagrams shown in Fig. 6.8 correcly shows he change in kineic and poenial energy of he drop during is fall up o he ground? E h PE (b) (d) h/4 KE (b) 42

6 Work, Energy and Power h PE h KE (c) 6.16 In a shopu even an ahlee hrows he shopu of mass 10 kg wih an iniial speed of 1m s 1 a 45 from a heigh 1.5 m above ground. Assuming air resisance o be negligible and acceleraion due o graviy o be 10 m s 2, he kineic energy of he shopu when i jus reaches he ground will be (a) 2.5 J (b) 5.0 J (c) 52.5 J (d) J KE Fig Which of he diagrams in Fig. 6.9 correcly shows he change in kineic energy of an iron sphere falling freely in a lake having sufficien deph o impar i a erminal velociy? K.E K.E deph (a) K.E deph (b) (d) K.E PE deph (c) Fig. 6.9 deph (d) 43

7 Exemplar Problems Physics 6.18 A cricke ball of mass 150 g moving wih a speed of 126 km/h his a he middle of he ba, held firmly a is posiion by he basman. The ball moves sraigh back o he bowler afer hiing he ba. Assuming ha collision beween ball and ba is compleely elasic and he wo remain in conac for 0.001s, he force ha he basman had o apply o hold he ba firmly a is place would be MCQ II (a) 10.5 N (b) 21 N (c) N (d) N 6.19 A man, of mass m, sanding a he boom of he saircase, of heigh L climbs i and sands a is op. (a) Work done by all forces on man is equal o he rise in poenial energy mgl. (b) Work done by all forces on man is zero. (c) Work done by he graviaional force on man is mgl. (d) The reacion force from a sep does no do work because he poin of applicaion of he force does no move while he force exiss A bulle of mass m fired a 30 o he horizonal leaves he barrel of he gun wih a velociy v. The bulle his a sof arge a a heigh h above he ground while i is moving downward and emerges ou wih half he kineic energy i had before hiing he arge. Which of he following saemens are correc in respec of bulle afer i emerges ou of he arge? (a) The velociy of he bulle will be reduced o half is iniial value. (b) The velociy of he bulle will be more han half of is earlier velociy. (c) The bulle will coninue o move along he same parabolic pah. (d) The bulle will move in a differen parabolic pah. (e) The bulle will fall verically downward afer hiing he arge. (f) The inernal energy of he paricles of he arge will increase Two blocks M 1 and M 2 having equal mass are free o move on a horizonal fricionless surface. M 2 is aached o a massless spring as shown in Fig Iniially M 2 is a res and M 1 is moving oward M 2 wih speed v and collides head-on wih M (a) While spring is fully compressed all he KE of M 1 is sored as PE of spring.

8 Work, Energy and Power VSA (b) While spring is fully compressed he sysem momenum is no conserved, hough final momenum is equal o iniial momenum. (c) If spring is massless, he final sae of he M 1 is sae of res. (d) If he surface on which blocks are moving has fricion, hen collision canno be elasic A rough inclined plane is placed on a car moving wih a consan velociy u on horizonal ground. A block of mass M ress on he incline. Is any work done by force of fricion beween he block and incline? Is here hen a dissipaion of energy? 6.23 Why is elecrical power required a all when he elevaor is descending? Why should here be a limi on he number of passengers in his case? 6.24 A body is being raised o a heigh h from he surface of earh. Wha is he sign of work done by (a) applied force (b) graviaional force? 6.25 Calculae he work done by a car agains graviy in moving along a sraigh horizonal road. The mass of he car is 400 kg and he disance moved is 2m A body falls owards earh in air. Will is oal mechanical energy be conserved during he fall? Jusify A body is moved along a closed loop. Is he work done in moving he body necessarily zero? If no, sae he condiion under which work done over a closed pah is always zero In an elasic collision of wo billiard balls, which of he following quaniies remain conserved during he shor ime of collision of he balls (i.e., when hey are in conac). (a) Kineic energy. (b) Toal linear momenum? Give reason for your answer in each case Calculae he power of a crane in was, which lifs a mass of 100 kg o a heigh of 10 m in 20s. Fig

9 Exemplar Problems Physics 6.30 The average work done by a human hear while i beas once is 0.5 J. Calculae he power used by hear if i beas 72 imes in a minue Give example of a siuaion in which an applied force does no resul in a change in kineic energy. x L C A m Fig B 6.32 Two bodies of unequal mass are moving in he same direcion wih equal kineic energy. The wo bodies are brough o res by applying rearding force of same magniude. How would he disance moved by hem before coming o res compare? 6.33 A bob of mass m suspended by a ligh sring of lengh L is whirled ino a verical circle as shown in Fig Wha will be he rajecory of he paricle if he sring is cu a SA (a) Poin B? (b) Poin C? (c) Poin X? 6.34 A graph of poenial energy V ( x ) verses x is shown in Fig A paricle of energy E 0 is execuing moion in i. Draw graph of velociy and kineic energy versus x for one complee cycle AFA. V(x) A B E o C Fig A ball of mass m, moving wih a speed 2v 0, collides inelasically (e > 0) wih an idenical ball a res. Show ha (a) For head-on collision, boh he balls move forward. (b) For a general collision, he angle beween he wo velociies of scaered balls is less han Consider a one-dimensional moion of a paricle wih oal energy E. There are four regions A, B, C and D in which he relaion beween poenial energy V, kineic energy (K) and oal energy E is as given below: Region A : V > E Region B : V < E Region C : K > E Region D : V > K Sae wih reason in each case wheher a paricle can be found in he given region or no. D F x 46

10 Work, Energy and Power 6.37 The bob A of a pendulum released from horizonal o he verical his anoher bob B of he same mass a res on a able as shown in Fig If he lengh of he pendulum is 1m, calculae (a) he heigh o which bob A will rise afer collision. (b) he speed wih which bob B sars moving. Neglec he size of he bobs and assume he collision o be elasic A raindrop of mass 1.00 g falling from a heigh of 1 km his he ground wih a speed of 50 m s 1. Calculae (a) he loss of P.E. of he drop. (b) he gain in K.E. of he drop. (c) Is he gain in K.E. equal o loss of P.E.? If no why. -2 Take g =10 m s 6.39 Two pendulums wih idenical bobs and lenghs are suspended from a common suppor such ha in res posiion he wo bobs are in conac (Fig. 6.14). One of he bobs is released afer being displaced by 10 o so ha i collides elasically head-on wih he oher bob. (a) Describe he moion of wo bobs. (b) Draw a graph showing variaion in energy of eiher pendulum wih ime, for 0 2T, where T is he period of each pendulum Suppose he average mass of raindrops is kg and heir average erminal velociy 9 m s -1. Calculae he energy ransferred by rain o each square mere of he surface a a place which receives 100 cm of rain in a year An engine is aached o a wagon hrough a shock absorber of lengh 1.5m. The sysem wih a oal mass of 50,000 kg is moving wih a speed of 36 km h -1 when he brakes are applied o bring i o res. In he process of he sysem being brough o res, he spring of he shock absorber ges compressed by 1.0 m. If 90% of energy of he wagon is los due o fricion, calculae he spring consan An adul weighing 600N raises he cenre of graviy of his body by 0.25 m while aking each sep of 1 m lengh in jogging. If he jogs for 6 km, calculae he energy uilised by him in jogging assuming ha here is no energy loss due o fricion of ground and air. Assuming ha he body of he adul is capable of convering 10% of energy inake in he form of food, calculae he energy equivalens 1m Fig Fig B m m A 47

11 Exemplar Problems Physics of food ha would be required o compensae energy uilised for jogging. 30 o m F Fig On complee combusion a lire of perol gives off hea equivalen o J. In a es drive a car weighing 1200 kg. including he mass of driver, runs 15 km per lire while moving wih a uniform speed on a sraigh rack. Assuming ha fricion offered by he road surface and air o be uniform, calculae he force of fricion acing on he car during he es drive, if he efficiency of he car engine were 0.5. LA 6.44 A block of mass 1 kg is pushed up a surface inclined o horizonal a an angle of 30 by a force of 10 N parallel o he inclined surface (Fig. 6.15).The coefficien of fricion beween block and he incline is 0.1. If he block is pushed up by 10 m along he incline, calulae (a) work done agains graviy (b) work done agains force of fricion (c) increase in poenial energy (d) increase in kineic energy (e) work done by applied force A curved surface is shown in Fig The porion BCD is free of fricion. There are hree spherical balls of idenical radii and masses. Balls are released from res one by one from A which is a a slighly greaer heigh han C. A B Fig Wih he surface AB, ball 1 has large enough fricion o cause rolling down wihou slipping; ball 2 has a small fricion and ball 3 has a negligible fricion. (a) For which balls is oal mechanical energy conserved? (b) Which ball (s) can reach D? (c) For balls which do no reach D, which of he balls can reach back A? C D 48

12 Work, Energy and Power 6.46 A rocke acceleraes sraigh up by ejecing gas downwards. In a small ime inerval Δ, i ejecs a gas of mass Δm a a relaive speed u. Calculae KE of he enire sysem a + Δ and and show ha he device ha ejecs gas does work = ( ) Δ mu in his ime inerval (neglec graviy) Two idenical seel cubes (masses 50g, side 1cm) collide head-on face o face wih a speed of 10cm/s each. Find he maximum compression of each. Young s modulus for seel = Y= N/m A baloon filled wih helium rises agains graviy increasing is poenial energy. The speed of he baloon also increases as i rises. How do you reconcile his wih he law of conservaion of mechanical energy? You can neglec viscous drag of air and assume ha densiy of air is consan. 49

IB Physics Kinematics Worksheet

IB Physics Kinematics Worksheet IB Physics Kinemaics Workshee Wrie full soluions and noes for muliple choice answers. Do no use a calculaor for muliple choice answers. 1. Which of he following is a correc definiion of average acceleraion?