NLM & FRICTION 2.37 Exercise - 1 Objective Problems | JEE Main Section A- String Constrained, Wedge $. Find velocity of ring B (V,) at the instant shown, Constrained Find the velocity ofthe hanging blockitthe velocities of the free ends of the rope are as indicated in the figure (A) 322 mis? (B) 32 nis 4 (©) 12 ws? (D) 12 ms L 2mis limis Find velocity of block 'B' at the instant shown in figure (A) 25 mis (B) 20 mis (©) 2 ms (D) 30 mis In the figure shown the velocity of different blocks is shown. The velocity of Cis (A) 6 ms (B)4 ms © oms (D) none of these ‘The velocity of end ‘A’ of rigid rod placed between two smooth vertical walls moves with velocity “u’ along vertical direction. Find out the velocity of end “BY ofthat rod, rod always remains in constant with the vertical walls, A (A) wtan 26 (B) ucot 0 (© utan 0 (D) 2utan o The string is taut and inextensible: ay dos 1 2) mis ©; (D) mvs The 50 kg homogencous smooth sphere rests on the 30? incline A and bears against the smooth vertical wall B, Calculate the contact forces at A and B. 1000 so, 8 Ne 1000 00 Nn, gon eNom . Ny 300 ON= BN NA 1000 50 (N= FR NN = BN Three blocks 1,2 and 3 are arranged as shown in the figure. The velocities of the blocks v,, v, and ¥, are shown in the figure, What is the relationship between v, v, and v,? )a,+% Ov, +2¥, (Dy None of these2.38 Theory and Exercise Book Section B - Newton's Law theory Que: 10, u 2 ‘The ratio of acceleration of pulley to the acceleration of the block is (string is inextensible) wos (B)2 ol m (Dy None ofthese When forceli, FF. act on a particle, the particle remains in equilibrium, IF, snow removed then acceleration of the particle is, You are on a friction less horizontal plane, How can you get off if no horizontal force is exerted by pushing against the surface ? (A) by jumping (©) by rolling your body on the surface (B)by spitting or sneezing (D) by running on the plane A particle moves in the xy plane under the action of «force F such that the value of ts linear momentum (P) at any time tis, P,= 2 cost, P, = 2 sint, The angle 0 between Pand F at that time t will be - ayo (B)30° ©90° (Dy 180° You fall in the forward direction when a moving bus apply brakes to stop and fall backward when it accelerates from rest because of. (A) Newton’s First law (B) Newton's Second law (©) Newton’s Third law (D) E = m 1B. 4. 15. 16, ‘According to Newton’s third law action is always equal to thereaction, a horse can pull a cart because it applies a, (A) Force on cart (C) Both of than(D) None of these (B) Force on ground Which ofthe Newton’s law explain difficulty fora fireman to hold a hose pipe, which ejects large amounts of water at high velocity. (A) Newton's First law (B) Newton’s Second law (©) Newton’s Third law (D) E ne? ‘When a carpet is beaten with a stick, dust comes out of it. Explains by (A) Newton’s First law (B) Newton’s Second law (C) Newton's Third law (D) E = me* ‘As an inclined plane is made slowly horizontal by reducing the value of angle @ with horizontal, The component of weight parallel to the plane ofa block resting on the inclined plane- (A) decreases (B) remains same (C) inereases (D) increases if the plane is smooth Section C - Equillibrium Questions (Normal 17, and Tension), Problems with Acceleration (F=ma) ‘Two blocks of masses 2.9 kg and 1.9 kg are suspended froma rigid supports bytwo inextensible wires each of length 1 m, The uppet wire has negligible mass and the lower wire has a uniform mass of 0.2 kg/m. Thewhole system of block, wire and support have an upward acceleration of 0.2 mvs?, 29.8 mis, The tension a the mid-point of lower wire (AION (B)20N (30N (B)50.N18, 19. 20, a. NLM & FRICTION 2.39 ‘The forces acting on an object are shown in the fig Ifthe body moves horizontally at a constant speed of $ mis, then the values ofthe forces P and S are, respectively ve5mis (AON ON 300N-—[_M P (B) 300 N, 200 N (©) 300 N, 1000 N s|s (D) 2000 N, 300. 2000N A body of mass 5 kg is suspended by the strings making angles 60° and 30° with the horizontal - (a)T,=25N ()T,=25 f5N ab Oecd ‘A mass M is suspended by a rope from a rigid support at A as shown in figure, Another rope is tied at the end B, and its pulled horizontally with a force F, Ifthe rope AB makes an angle 0 with the vertical in equilibrium, then the tension in the string AB (AF sin 8 (B) Fisin 0 (©)F eos (D) Fieos 0 Three block are connected as shown, on a horizontal frictionless table and pulled tothe right with a force 0, Hem, = 10 kg, m, = 20 kg and m, = 30 kg, the tension T, is- m, ™) 7. aaa T, “ (A) 10N. (B)20N (C)30N (D)60N 2. 24, A weight can be hung in any of the following four ‘ways by string of same type. In which case is the ing most likely to break ? “ ®) © W] w} (0) w WA mec (B) B (py ‘An aeroplane, which together with its load has a ie with Ifa part of the load equal to m kg be thrown out, the aeroplane will begin to rise with an leration of a= 5 mis Find the value of m? (ay 6400 (B) 6450 (©) 6600 () 6700 n acceleration of A stretching force of 1000 Newton is applied at one end ofa spring balance and an equal stretching force is applied at the other end at the same time. The reading of the balance will be (A) 2000N. (B) Zero, (©) 1000 N. (D) 500 N Section D - wedge problems 25, 26. Body A is placed on frictionless wedge making. an angle O with the horizon, The horizontal acceleration towards left to be imparted to the wedge forthe body Ato fively fall vertically, is — (A) g sind (B) gos (© gtand (D) geot0 A wolley is accelerating down an ineline of angle 0 with acceleration gsin®. Which ofthe following correct (4. is the constant angle made by the string with vertical)2.40 Theory and Exercise Book 7. 28. (Wa=0 @Ba-0 (€) Tension in the sting, T= mg (D) Tension in the string, T = mg see 0 A body of mass 1 kg lies on smooth inclined plane. The block of mass m is given force F = 10 N horizontally as shown, The magnitude ofnet normal reaction on the block is oy (A) 10V2N Oy (C)10N (D) none of these In the figure shown ‘P* is a plate on which a wes B is placed and on B a block A of mass mis placed, ‘The plate is suddenly removed and system of B and A is allowed to fall under gravity. Neglecting any force dueto air on A and B, the normal force on A D> P me wos (By mg cosd as py 2m (€) zer0 Oe ao 29, Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass Mas shown in the figure. The magnitude of force P is (A) (Mém)g tan B (B) gtan B | (Orme cos B (D) (Me+m)g coses fi 30. A block of mass m is kept on a wedge of mass M Initially the systems held @ Atcertain time the sytstem is released and the wedge is observed to move with accelertion A on inclined aN surface as shown. There is no anywhere, The acceleration of block (m) ‘with respect to wedge (M) willbe (A) A rightward (B) Acos 0 rightward (CA cos leftward (D) none of these Section E- Pulley Block system 31, ‘Three blocks A, B and Care suspended as shown in the figure, Mass of each blocks A and C is m, If system is in equilibrium and mass of B is M, then (A)M=2m (B)M<2m (M>2m (D)M=m 32, Two masses are hanging vertically over frictionless pulley. The acceleration of the two masses is ™ in? m, (B) ™, olism)33. NLM & FRICTION 2.41 Inthe given arrangement, n number ofequal masses 36. are connected by strings of negligible masses. The tension in the string connected to n* ma im} fm}—fm}—fm}-fm] a. mMe () maM ®) tmM mMg © mg ©) aNeM Inthe given figure, pulleys and strings are massless, For equilibrium of the system, the value ofa is~ (A) 60° (B)30° (90° 38: (0) 120° The pulley arrangements shown in figure are identical the mass of the rope being negligible. In ease I the mass m is lited by attaching a mass 2m tothe otherend ofthe rope In case I, the mass mis lifted by pulling the other end of the rope with cosmtant downward force F = 2mg, where g is acceleration due to gravity. The ae in ease Lis 2», “ i) (A) zero (B) more than that in case Il (C) less than that in ease I (D) equal to that in case I ‘A particle of small mass mis joined to a very heavy body by a light string passing over a light pulley. Both bodies are free to move. The total downward force in the pulley is (Aymg (C)4mg (B)2mg (D)can not be determined ‘Three equal weights A, B,C of'mass 2 kg each are ‘hanging on a string passing overa fixed frictionless pulley as shown in the fig, The {ension in the string connecting ‘weights B and C is- (A) ze10 (B) 13 Newton (©)3.3 Newton (D) 19.6 Newton Section F - Spring force and spring cutting problems ‘Two masses of 1 kg and 5 kg are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in figure, The masses start moving luring this intervals the reading of spring balance will be: (A) more than 6 kg, (B) less than 6 ke (C) equal to 6 kg (D) none of the above ‘A system consists of two cubes of masses m, and 1m, respectively connected by a spring of force constant k. The force (F) that should be applied to the upper cube for which the lower one just lifts after the force is removed is- (Aymg (B) ©im,+ mg Omg2.42 Theory and Exercise Book 40. a A block of mass? ke is hanging with two identical 43. massless springs as shown in figure, The acceleration ofthe block at the moment, the right spring breaks is(g= 10 ns!) (A) 10 m/s? (B) S m/s? (C) 25 mis? (D) 4 mvs? 4“ Section G- Pseudo force, Weighing Machine Aliflis going up. The total mass of the lift and the passengers 1500 ky The variation in the speed of the lift is as given in the graph, The tension in the rope pulling the lift at t= 11th see will be # ‘ 45. et z 1012 (A) 17400 N (B) 14700N (C) 12000 N (D) Zero 4. 2. Figure shows a man of mass 50 kg standing on a light weighting machine kept in a box of mass 30 kg, The box is hanging from a pulley fixed to theceiling throughta light rope, the other end of which is held by the man himself, Iftheman manages to keep the box at rest, the weight shown by the machine is. (A) 10N (B) 100N (©) 800N (0) 200 N With what acceleration ‘a’ should the hox of figure moving up so that the block of mass M exerts a force 7 Mg/4 on the floor of the box? Ag Ber k (C)3g4 4g A triangular block of mass M with angle 30°, 60°, 90° rests 30° 90° side on a horizontal smooth fixed table, A cubical block of ‘mass mrests on the 60° - 30° side of the triangular block. What horizontal acceleration a must M have relative to the stationary table so that m remains stationary with respect to the triangular block with its [M=9 kg, m=1 kg] (A) 2.8 mys? (B) 5.6 nvs* (C84 mise (D) Zero Which of the following statement is absolutely correct ubout mass (A) More the mass of abody connected with spring balance more will be elongation in spring balance (B) More the mass of body kept in one pan of beam balance more the mass has to be kept on the other pan to keep beam-horizontal (C) More the mass of a body, lesser will be its acceleration for a given force (D) All In the arrangement shown, the pulleys are fixed and ideal, the strings are light, m, > m,and 8 isa spring balance which is itself massless. The reading of S (in unit of mass) is s oor &) H(m.+m,) aes )7. Section H - Static friction, Kinetic fri 49. NLM & FRICTION 2.43 A block of mass m resting on a wedge of angle ® as shown in the figure. The wedge is given an accel- eration a, What is the minimum value ofa so that the mass m 4 falls freely ? Ag +r (B) gos 0 ©) georo B c (D)gtano Find out the reading of the weighing machine in the following cases (A) 103 (B) 10y2 © 2093 (D) 303) ion ‘The maximum value of the block m, for which the system will remain in equilibrium (coefficient of friction between block m, and plane sur Pulley are mass less) is —t (D) 2um, ce isp wry (©) am, Ifthe coefficient of ft ction between A and B is p, the maximum horizontal acceleration of the wedge ‘Aor which B will emain at rest wart the wedge is one) 8 Aug ©) {) Ow si. 52. 53. IF'the coefficient of friction between an insect and bow! is 4 and the radius of the bowl, is r, the ‘maximum height to which the insect can crawl in the bow! is, r “Jap © nine ©) fier -1 A block is placed on a rough floor and a horizontal force F is applied on it. The force of friction fby the floor on the block is measured for different values of F and a graph is plotted between them - (a) The graphris a straight line of slope 45° (b) The graph is straight line parallel to the F axis (6) The graph isa straight line of slope 45° for small F and astraight line parallel to the F-axis for langeF. (d) There is small kink on the graph (Aye.d (Byad ab ya Mark the correct statements about the friction between two bodies (a) static friction is always greater than the kinetic friction (b) coefficient of static friction is always greater than the coefficient of kinetic friction (6) limiting friction s always greater than the kinetic friction (4) limiting friction is never less than stati friction (Abed Babe Cac (D)a,b.d44 Theory and Exercise Book 54, A body is placed on a rough inclined plane of inclination 0. As the angle 0 is increased from 0° to 90° the contact force between the block and the plane (A) remains constant (B) first remains constant then decreases (©) first decreases then increases (D) first increases then decreases 55. A block of mass 2kg rests on a rough inclined plane ‘making an angle of 30° with the horizontal, The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is— (A) 0.7 «9.8 Newton (B)9.8 Newton (©)0.7 *9.8,J3 Newton (D) 9.8 * Jj Newton 56. A body of mass m moves with a velocity v on a surface whose friction coefficient is u. Ifthe body ‘covers a distance s then v will be (A) Pes 8) Ji © ngs? (©) Snes Section I- Direction of friction, Pulley Block system on horizontal plane 57. A box 'A’ is lying on the horizontal oor of the ‘compartment of a tain running along horizontal rails from left to right, At time W, it decelerates. Then the reaction R by the floor on the box is given best by R R w—L4 @ 14 Toor Toor RY (c) A (D) wy floor Toor 58. ol. A wooden block of mass m testing on a rough horizontal table (coefficient of fiction = y) is pulled bya force F as shown in figure, The acceleration of the block moving horizontally is Fos on uFsind M (B) (D)none A cart of mass M has a block of mass m attached to it as shown in figure. The coefficient of fiction between the block and cart is yt. The minimum acceleration of the eart so thatthe block does not fall is? eu (8) we Cue (D) Mpgim In the arrangement as shown, block A of mass3 kg moves towards left with velocity 10 ms, Initially block A is 100 m from pulley on a smooth surface. Black B iscf mass2 kg (g= 108) (A) ALL = 1 see, velocity A of Awill be 6mis towards «| left (B)A will stop at t= 4.5 see (©) Block A will be at @ distance 108 m from pulley at t= 5s (D) Block A will again be a distance of 100 m from pulley at t= 10s Toom) CB A body is projected up a 45° rough incline. Ifthe coefficient of friction is 0.5, then the retardation of the block is ws 3g ORo. ‘Mass of upper block and lower block kept over the tuble is 2 kg and 1 kg respectively and coefficient of fiction between the blocks is 0.1. Table surface is smooth, The maximum mass M for which ll the three blocks move with same acceleration is (= 10 nv) - (A) kg. we0d (B) 2/3 kg. re (C18 kg (D) 3/4 kg, mn Abody A of mass I kg rests on a smooth surface. Another body B of mass 0.2 kg is placed over A as shown. The coetficient of static friction between A and B is 0.15. B will begin to slide on A, if A pulled with a force greater than (A) 1.764 (B)0.1764N ©03N (D) it will ntslide forany F In the figure shown, blocks A, B and C weigh 3 kg, 4 kgand 8 kg respectively. The coefficientof sliding friction between any two surfaces is 0.25. A is held at rest bya massless rigid rod fixed to thewall while Band C are connected by a string passing round a frictionless pulley. Find the force needed to drag C along the horizontal surface toleft at constant speed. Assume the arrangement shown in figure is, ‘maintained all through. (= 10 mis") ayis (ss (B) 80 (Dy None of these NLM & FRICTION 2.45 Section J- Pulley Block system on inclined plane 65. Twomasses M, and M, are attached to the ends of 67. light string which passes overa masslesspulleyattached to the top ofa double inclined smooth plane of angles of inclination cand The tension in the stringis M(sina)g M+M, MM. (sin +sina)g © MM, (D) zero ‘Two masses M, and M, are attached to the ends of a string which passes over a pulley attached to the top of an inclined plane, Theangle of inclination of the plane is 30° and M, = 10 kg. M,=5 kg, What is the acceleration of mass M, ? (A) 10 mist (B) Smit (©) Zero (D) Data insutficient ft Inclined plane is moved towards right with an acceleration of Sms" as shown in figure, Find force in newton which block of mass 5 kg exerts on the inctine plane. (All surfaces are smooth) &p i Smee (A) 50N (B)60N (C)55N (D) 70 N2.46 Theory and Exercise Book 70. A block of mass 5 kg resting on a horizontal surface is connected by a cord, passing over a light fFietionless pulley toa hanging block of mass 5 kg. ‘The coefficient of kinetic ition between the block and tne surice is 0.5. Tension in the cord is (g=9.8 mvs!) (Ayaon A (B) Zero (€)36.75 N (0) 12.75 Inthe arrangement as shown, when mass of block A ism, and mass of block B is m,, time taken by m, to reach maximum height is 3 times the time taken by 1m, to reach maximum height, when block A is of ‘mass m, and block B is of mass m,. All ropes and pulleys are smooth and massless ~ (A) The ratio of acceleration in first to second ease is2, (B) The ratio of acceleration in first to second case is9. (C) The ratio of (my/m,) is (19/11) (D) The ratio of (m/m,) is (4/3) ‘Two blocks are connected over a massless pulley as shown in figure, The mass of block A is 10 kg and the coefficient of kinetic friction is 0.2. Block A sliders down the incline atconstant speed. The mass of block B in kg is (aya LT 33 ® a2 ‘ ib (V6.8 1. n 2B. 4. The value(s) of mass m for which the 100 kg block does not move upward (A) 39 kg, (B) 40 kg (C)83 kg (D)85 ke For the arrangement shown in the figure the tension in the string is [Given: tan (0.8)= 39°], (AON (B)64N (C)0AN (D)ze10 m=ikg, NK - Two Block system, Two Block on Inclined plane ‘Three blocks A, Band C of equal mass mare placed ‘ona smooth surface as shown, Coefficient of fiction between any block A, Band Cis yt. The maximum value of mass D so the block A, B & Cmove without slipping over each other is= 3mm + ial A @) ain(l+40) jm On" ow» ‘Two masses 40 kg and 30 kg connected by a massless string passing over a frintionless light pulley as shown in the figure. The tension (almost) in the string will be : (All surfaces are frictionless) (A) 188 N. (B) 368 N (C) 288 N (D) 168 N.16. 7. 10 m/s"), Acceleration of 2 kg. eri8h (A)2 misec? (B) 4 mise? (©) 6 msec? (D)8 msec? ‘A block placed on a rough inclined plane of inclination (0= 30°)can justbe pushed upwards by applying a force “F” as shown, If the angle of inclination of he inclined plane is increased to (= 60°), the same block can just be prevented from sliding down by application of a force of same ‘magnitude, The coefficient of friction between the block and the inclined plane is, Bat OB 2y3-1 ® a B-1 © War (D) none of these A fixed wedge with both surface inclined at 45° to the horizontal as shown in the figure. A particle Poof ‘mass mis held on the smooth plane by a light string ‘which passes over a smooth pulley A and attached to aparticle Q of mass 3m which rests on the rough plane, The system is released from rest. Given that the acceleration of each particle is of magnitude g yo then, the tension in the string is (A) me ing O 5h oF oy 7B. 9. NLM & FRICTION 2.47 A block of mass 15 kgis testing on arough inclined plane as shown in figure, The block is tied up by a horizontal string which has a tension of 50 N. The coetlicient of fiction between the surfaces of contact is (g= 10 mis wr (B)28 34 & % horizontal Figure shows two blocks in contact sliding down an inclined surface of inclination 30°, The friction coefficient between the block of mass 2.0 kg, and the inclines y,, and that between the block of mass 4.0 kg and the incline isp, Calculate the acceleration of the 2.0 kg block if p,= 0.30 and g= 10 mis (A)2 mvs? (B)2.7 ws ame (D) 24 ws ‘Two blocks connected by a massless string slide down an inclined plane having angle of inclination 37°, The masses of the two blocks are M, = 4 kg and M, = 2 kg respectively and the coefficients of friction 0.75 and 0.25 respectively — (A) The common acceleration of the two masses is 1.3 ms* (b) The tension in the string is 14.7 N (c) The common acceleration of the two masses 2.94 ms (4) The tension in the string is 5.29 N Wad Bed (bd (D)b,¢