Sec: Sr. Inter/XII Completed/Target Batch/LT VARIABLE MASS .

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TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8Sec: Sr. Inter/XII Completed/Target Batch/LTVARIABLE MASS SYSTEM & CIRCULAR MOTION REVISIONDPA-8DATE: 13.04.2020PHYSICSSECTION – I(SINGLE CORRECT ANSWER TYPE)This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for itsanswer, out of which ONLY ONE option can be correct.Marking scheme: 4 for correct answer, 0 if not attempted and -1 if not correct.1.A cyclist riding with a speed of 27kmph. As he approaches a circular turn on the road of radius 80m, heapplies breaks and reduces his speed at the constant rate of 0.50 m/s every second. The net accelerationof cyclist on the circular turn isA) 0.5m/s22.B) 0.87m/s 2C) 0.56m/s 2D) 1m/s 2A particle moves in a circle of radius 20 cm. its linear speed is given by v 2t where t is in s and v inm/s . Then1) The radial acceleration at t 2s is 80 ms 22) Tangential acceleration at t 2s is 2 ms 23) Net acceleration at t 2s is greater than 80 ms-24) Tangential acceleration remains constant in magnitude.3.A) Only 1, 2, 3 are correctB) Only 1, 2, 4 are correctC) Only 1, 3, 4 are correctD) All 1, 2, 3, 4 are correctA particle of mass m is suspended from the ceiling through a string of length L. The particle moves in ahorizontal circle of radius r . The speed of the particle isA)rgL2 r 2B)r g L2 r12 4 r gC) L2 rPage 112 2 D)mgL1 L2 r 2 2

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-84.Kinetic energy of a particle moving along the circle is ax 2 . If R is the radius of the circle, the radialforce on the particle is12ax 2A)R5. 1 x 2 2B) 2 R C) 2axD) 2aR 2xTwo particles of same mass 'm' each tied to different strings of Lengths L1 &L2 are whirled in ahorizontal circles, The angles made by each string with vertical are 300 & 600 respectively. Then the ratioof lengths of the strings so that they complete their circular path with equal time periods isA)6.32B)13C) 1D)3A small coin of mass 80g is placed on the horizontal surface of a rotating disc. The disc starts from rest2and is given a constant angular acceleration 2rad / s . The coefficient of static friction between thecoin and the disc is s 3 / 4 and coefficient of kinetic friction is k 0.5 . The coin is placed at adistance r lm from the centre of the disc. The magnitude of the resultant force on the coin exerted bythe disc just before it starts slipping on the disc isA) 0.2 N7. d 2 v2B)8C) 420B) 400D) 1 ND) None22 s, the angle made by him with theD) 480A particle is moving with a uniform speed in a circular orbit of radius R in a central force inverselyproportional to the nth power of R. If the period of rotation of the particle is T, thennA) T R3/ 2 for any n B) T R 210. d 2 v2C)6A cyclist goes round a circular path of circumference 34.3 m invertical will beA) 4509.C) 0.4 NWater of density 'ρ flows with a linear speed ' v ' through a horizontal rubber tube having the form of aring of radius ‘R’. If the diameter of the tube is ‘d’ (d R). Then the tension developed in the rubbertube is d 2 v2A)48.B) 0.3 N 1C) T R n 1 / 2D) T R n / 2Two particles revolve concentrically in a horizontal plane in the same direction. The time required tocomplete one revolution for particle A is 3 min, while for particle B is 1 min. The time required for A tocomplete one revolution relative to B isA) 2 minB) 1.5 minC) 1 minPage 2D) 1.25 min

11.TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8A rocket having mass of 5 10 kg. and it contains fuel of mass 5 106 kg is ejecting gas with velocity64000 m/s relative to rocket. Then what will be the velocity of rocket when entire fuel finishes?A) 2727 m/s12.C) 2772 m/sD) 4000 m/sA very flexible chain of mass M and length L is suspended vertically in a lift so that its lower end is justtouching the surface of the floor. When the upper end of the chain is released it falls with each linkcoming to rest instantaneously. Find the force exerted by the floor of the lift on the chain at the momentwhen one fourth of the chain has already landed on the floor. Assume the lift is moving up withacceleration g/2A)13.B) 2277 m/s9Mg8B)Mg8C)5Mg4D)3Mg4A rocket of initial mass 6000 kg ejects mass at a constant rate of 16 kg/s with constant relative speed of11km/s. what is the acceleration of the rocket a minute after the blast. g 0 A) 35ms -214.B) 34.92ms 2C) 24.92ms -2D) 25ms -2A flat car of mass m 0 starts moving to the right due to a constant force F. sand spills on the flat car froma stationary hopper. The velocity of loading is constant and equal to µ kg/s. Find the time dependence ofthe velocity of the flat car. (Neglect friction)A)15.Ftm0 µB)Ftm0 t µC)Fm0 µtD)Ftm0 µtA car has total mass 50kg. Gases are ejected from its backwards with relative velocity 20 m/sec . The rateof ejection of gas is 2 kg/s. Total mass of gas is 20 kg. Coefficient of friction between the car and road is 0.1 . Then car will start moving after time t sec. g 10ms 2 A) 416.B) 10C) 5D) 8A car is moving in a circular horizontal track of radius 10m with a constant speed of 10 ms-1 . A plumbbob is suspended from the roof of car by a light rigid rod of length 1m. The angle made by rod with thetrack is g 10 ms -2 A) 30017.B) 450C) 600D) 370A rocket of mass 6000kg is set for vertical firing. If the exhaust speed is 1000 m/s . The rate of mass ofgas ejected to supply a thrust needed to give the rocket an initial upward acceleration of 20.2ms -2 is.A) 180 kg/sB) 190 kg/sC) 200 kg/sPage 3D) 170 kg/s

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-818.A hopper drops gravel at a rate of 75 kg/s onto a conveyor belt moving at a constant speed 2.20 m/s ,determine the force needed to keep the conveyor belt moving.A) 85N19.B) 95NC) 165ND) 75NWater jet coming out of a hose pipe strikes a wall at an angle 450 with the normally with a speed 40m/sand returns back elastically. It the area of cross section of the pipe is 1cm 2 , The force on the wall isA) 160N20.B) 220NC) 216.24ND) 226.24NA disc of mass 0.5kg is kept floating horizontally in mid air by firing bullets of mass 5g each, verticallyat n bullets per sec, and the bullets drop dead. If speed of the bullet striking the disc is 100 ms -1 then findnumber of bullets striking the disc per sec.A) 10B) 5C) 8D) 12SECTION-II(Numerical Value Answer Type)This section contains 5 questions.The answerto each question is aNumerical value. If the numericalvaluehasmore than twodecimalplaces, round-off the value ofTwo decimalplaces. Answer to each question will beevaluated according to the following marking scheme:Marking scheme: 4 for correct answer, 0 in all other cases.21.A car is driven round a curved path of radius 18m without the danger of skidding. The coefficient offriction between the tyres of the car and the surface of the curved path is 0.2. What is the maximumspeed in kmph of the car for safe driving? g 10 ms 2 22.A stone is thrown horizontally with a velocity of 10m / sec. the radius of curvature of it’s trajectory at theend of 3s after motion began is g 10m / s 2 n 10m then n value is23.A weightless thread can bear a tension upto 3.7 kg-wt. A stone of mass 500g is tied to it and revolved ina circular path of radius 4m in a vertical plane. If g 10 ms 2 ,then the maximum angular velocity of thestone will be in rads-1 24.A rocket with an initial mass of 1000kg is launched vertically upward from rest under gravity. The10kg/sec . The burnt matter is ejected vertically downwards with a speedrocket burns fuel at the rate ofof 2000 m/s relative to the rocket. Find the velocity of the rocket after 1 min of start in km/sec Take g 10m/s25.2& ln 2.5 0.92 and length ' l ' is coiled on a smooth horizontal surface one endA uniform rope of linear mass densityis pulled up with constant velocity . If the average power applied by the external agent in pulling theentire rope just off the ground is a a l b gthen 2bPage 4

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8KEY1C11C2121.6Q NokeyQ NoKeyQ NoKey2D12A221003B13B2344A14D241.245B15C253HINTS1.a a 2c a 2r2.mv2 2ax 2f RRat dv 2ms -2dta a c2 a t2 80ms-23.fmg rL2 -r 24.1mv 2 ax 22Radical force: f 5.Tan mv2 2ax 2 RRrw2gbut r L sin L g1 L cos cos 2L1 cos 2 cos 60 01 0L2 cos 1 cos 3036.Namg , f s mgPage 56D16B7A17A8A18C9C19D10B20A

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8Resultant reaction by disc to theCoin B F N 2 f 2 mg 1 s2 1N7.At equilibrium: 2Tsinθ 2T T 8. u220 2 R p4R d 2 pv 242 r 34.3 r v dmν 2R34.3e 2 r 2 r T22 2 Angle of banking : Tan 1 450 rg 9.F mw2 RGiven F 1k F nnRR2k4 2 m n 1 2 2 n m R T R Rk T T Rn 12T1T23 1 1.5minT2 T1 3 110.t 11.m0 5 106 5 10 6 10 10 6 kgm m0 m fuel 5 106 kgv r 4000m/sPage 6

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8 m V vr ln 0 m 10 106 4000 ln 6 5 10 4000 ln 2 4000 0.693 2772 m/secM g 9Mg Mg 4 2 812.f 13.m0 6000kg ,vr 11dm 16kg / s, t 60secdtkm.10s 11000m/smass of rocket after t 1min is dm m m0 t dt 6000 16 60 5040kg acceleration of rocket a a 14.Fexternal vrWherev r dm gm dt 11000 16-0 34.92 m/s 25040dmdv m 1 dtdtdm , vr 0 v vdt 1 F v m0 t dvdtdvdt F v m0 tOn integration, we getPage 7

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8Ftv m0 t15.Car mass M 50kgGas mass m 20kgdm 2kg / secdtvr 20ms 1 , 0.1Thrust force on car F vrdm Right dtF 20 2 40 NNow friction acts Left.At Time t:Ejected gas mass m 2 t Total mass of system M total 50 m Friction f N M total gf 0.1 50 2t 10If car start moving: F f 40 50 2t t 5sec16.a v 2 102 10r10Tan 17.a 10 1 450g 10 m M g a 4 t 6000 9.8 20.2 m 1000tPage 8

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-8m 180kg/st18. V rel V gravel V belt V rel 0 V Along horizontalV gravel 0 VNow Fexternal MdvdM Vreldtdt 0 V dMdM VdtdtFexternal 2.2 75 165N19.F 2 Ap 2 cos 2 2 10 4 103 40 cos 450 226.24N20.Mg n mu tn0.5 10 t 5 10 3 100n 10t21.Maximum speedv Mgrv 21.6 km / hq22.Radius of curvature R and Tanθ vyvxV 2 tangentg sinθat t 3secPage 9

TARGET JEE MAIN & ADV 2020 PROGRAMME-2 ASSIGNMENT DPA-823.Tmax mg mrw23.7 10 0.5 10 0.5 4w2w 4 rad/sec24. m v gt ln 0 vr m 1000 v 10 60 ln 2000 400 600 2000 ln 2.5 600 1840v 1240 m/s v 1.24km/s25. v 0 F xg dx dt F xg v 2R Fdxpave w pave t 0 l / l g 32 pave v3 But p a lvg2 l bga 3 32b lPage 10

TARGET JEE MAIN & ADV _2020_PROGRAMME-2 ASSIGNMENT_DPA-8 Page 2 4. Kinetic energy of a particle moving along the c

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