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PHYSICS, , Daily Practice Problems, Class:XI, Q.1, , Discussion: 07-08/09/2015 Time: 35 Min., , Target JEE, M.M.: 30, DPP. NO.-64, , Blocks A& B of mass m each are connected with spring of constant k. Both blocks lie on frictionless, ground and are imparted horizontal velocity v as shown when spring is unstretched. Find the maximum, stretch of spring., [3], (A) v, , m, k, , (B) v, , m, 2k, , (C) v, , 2m, k, , (D) none, , Q.2, , A gun of mass M at rest on a smooth surface fires a shell of mass m. The ratio of kinetic energy of the, shell and gun after firing is : (Assume that shell is fired horizontally)., [3], (A) m/M, (B) M2/m2, (C) m2/M2, (D) M/m, , Q.3, , A machinist starts with three identical square plates but cuts one corner from one of them, two corners, from the second, and three corners from the third. Rank the three plates according to the x-coordinate, of their centers of mass, from smallest to largest., [3], y, , y, , y, , x, , x, , [1], , [2], , (A) 3, 1, 2, (C) 3, 2, 1, Q.4, , [3], , (B) 1, 3, 2, (D) 1 and 3 tie, then 2, , A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at 3m/s as, shown. After the sack rests on the flatcar, the speed of the flatcar is:, [3], , (A) 0.6m/s, Q.5, , x, , (B) 1.2m/s, , (C) 1.8m/s, , (D) 2.4m/s, , (E) 3.6m/s, , Two blocks Aand B of masses 2kg and 3kg respectively are connected by a compressed spring placed, on a smooth horizontal surface. When the system is released, two blocks seem to be moving as shown, below. Select the true statement from the following, [3], 6 ms, A, , –1, , 5 ms, , –1, , B, , (A) Irrespective of the velocities ofAand B, the centre of mass of the system will remain stationary, (B) the centre of mass moves with velocity 0.6 ms–1 away from A, (C) The centre of mass moves with velocity 0.6 ms–1 away from B, (D) The centre of mass moves with velocity 5.4 ms–1 away from A, PAGE # 1

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Question No. 6 to 10 (5 questions), Two persons of mass m1 and m2 are standing at the two ends A and B, respectively, of a trolley of mass M as shown., Q.6, , When the person standing at Ajumps from the trolley towards left with urel with respect to the trolley,, then, [3], m1u rel, (A) the trolley moves towards right, (B) the trolley rebounds with velocity, m1  m 2  M, (C) the centre of mass of the system remains stationary, (D) all the above, , Q.7, , When only the person standing at B jumps from the trolley towards right while the person at A keeps, standing, then, [3], m 2 u rel, (A) the trolley moves towards left, (B) the trolley moves with velocity, m1  m 2  M, (C) the centre of mass of the system remains stationary, , (D) all the above, , Q.8, , When both the persons jump simultaneously with same speed then, (A) the centre of mass of the system remains stationary, (B) the trolley remains stationary, (C) the trolley moves toward the end where the person with heavier mass is standing, (D) None of these, , Q.9, , Whenboththepersonsjumpsimultaneouslywithurel withrespecttothetrolley,thenthevelocityofthetrolleyis, [3], | m1  m 2 | u rel, m1u rel, m 2 u rel, | m  m 2 | u rel, (A) m  m  M, (B) 1, (C) m  M  m  M (D) none of these, M, 1, 2, 2, 1, , Q.10, , Choose the incorrect statement, if m1 = m2 = m and both the persons jump one by one, then, (A) the centre of mass of the system remains stationary, (B) the final velocity of the trolley is in the direction of the person who jumps first, , mu rel ,  mu rel, , (C) the final velocity of the trolley is , , M, , m, M, , 2, m, , , , (D) none of these, , [3], , [3]

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PHYSICS, , Daily Practice Problems, Class:XI, Q.1, , Discussion: 09-10/09/2015 Time: 35 Min., , Target JEE, M.M.: 30, DPP. NO.-65, , The force acting versus time graph of a rocket is shown in figure. The mass of the rocket is 1200 kg. The, velocity of rocket 16 seconds after starting from rest will be (neglect gravity) :, [3], , F(KN), 20, 2, (A) 50 m/s, Q.2, , t(s), , 10, , (B) 100 m/s, , 16, (C) 200 m/s, , (D) 300 m/s, , In a gravity free space, two particles (of masses 8m and m) separated by 3m are at rest. The particles, are connected by a massless string of length 5 cm. If the particle of mass m is imparted velocity v along, y-axis, velocity of the particle of mass 8m, just after the string becomes taut, is, [3], y, massless string, 8m, , m, , x, , 3cm, , (A), Q.3, , v, 3, , (B), , v, 5, , (C), , 4v, 45, , (D), , v, 30, , In the given figure an impulse J is given to the block of mass m in the downward direction.As a result of, the impulse, [3], , (A) both the blocks start moving with, , J, in opposite directions, 3m, , (B) both the blocks start moving with, , J, in opposite direction, m, , (C) both blocks start moving with, , J, in opposite direction., 2m, , (D) the system is not moving., , PAGE # 3

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Q.4, , A projectile is moving at 60 m/s at its highest point, where it breaks into two equal parts due to an internal, explosion. One part moves vertically up at 50 m/s with respect to the ground. The other part will move, at, [3], (A) 110 m/s, , Q.5, , (B) 120 m/s, , (C) 130 m/s, , (D) 10 61 m/s, , Two blocks sit on a horizontal frictionless surface connected to an ideal spring. Initially everything is at, rest and there is a string compressing the mass-spring system from equilibrium.At some time after the, string is cut, the block of mass 2M reaches its maximum kinetic energyK. What maximum kinetic energy, does the block of mass M attain in terms of K ?, [3], String, 2M, , (A), Q.6, , 1, K, 4, , (B), , 1, K, 2, , M, , (C) K, , (D) 2K, , A man pulls a bucket of water from a well of depth h. If the mass of the uniform rope and bucket full of, water are m and M respectively. The value of work done by the man is, [3], (A) (m+M) gh, , m, , (B)   M  gh, 2, , , mM,  gh, (C) ,  2 , , (D) None of the above, , Q.7, , An insect of mass m is initially at one end of a stick of length L and mass M, which rests on a smooth, floor. The coefficient of friction between the insect and the stick is k. The minimum time in which the, insect can reach the other end of the stick is t. Then t2 is equal to, [3], (A) 2L/kg, (B) 2Lm/kg(M+m), (C) 2LM/kg(M + m) (D) 2Lm / kgM, , Q.8, , Two blocks of same mass (4 kg) are placed according to diagram. Initial velocities of bodies are 4 m/s, and 2 m/s and the string is taut. Find the impulse on 4 kg when the string again becomes taut, [3], 4 m/s, 4kg, , 4kg, , (A) 24 N-s, Q.9, , (C) 4 N-s, , (D) 2 N-s, , A square of side L/2 is removed from one corner of a square sandwich that has sides of length L. The, center of mass of the ramainder of the sandwich moves from C to C'. The displacement of the xcoordinate of the center of mass (from C to C') is, [3], (A), , Q.10, , (B) 6 N-s, , 2 m/s, , 2, L, 12, , (B), , 1, L, 12, , (C), , 1, L, 6, , Sand falls vertically at a rate of 50 kg/s from a stationary hopper on a, horizontal conveyor belt moving at a speed of 1 m/s as shown in fig. If, belt is perfectly inelastic, then what is the minimum power output of the, engine which drives the belt with speed v = 1m/s, [3], (A) 50 watt, (B) 25 watt, (C) 100 watt, (D) none of these, , (D), , 2, L, 8

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PHYSICS, , Daily Practice Problems, Class:XI, , Discussion: 11-12/09/2015 Time: 45 Min., , Target JEE, M.M.: 50, DPP. NO.-66, , Q.1, , An enclosed ideal gas Ahas its pressure P as a function of its volume V as P = P0  V2, where P0 & , are constants . Find the physical dimensions of  ., [5], , Q.2, , A particle of mass 10 kg moves in x-y plane such that its position is given by (3 sin t, 4 cos t). where t is, the time find, its momentum vector at time t =  sec., (ii), net force acting on it at this time, [5], , (i), Q.3, , Aparticleismovingonastraightline.Its displacement fromtheinitial position, is plotted against time in the graph shown. What will be the velocity of the, particle at 2/3 sec? Assume the graph to be a sine curve., [5], , Q.4, , A particle P is projected horizontally, with speed V, from a point O on a plane which is inclined at an, angle  to the horizontal. The particle hits the plane at a point A which is on the line of greatest slope, through O. (a) Find the time of flight. (b) Find the tangent of the acute angle between the horizontal and, the direction of motion of P when P reached A.A second particle Q is projected from O, with speed V,, in a direction perpendicular to the plane. (c) Find the time taken for Q to return to the plane and, (d) show that Q hits the plane at A., [5], , Q.5, , Two blocks A and B of mass 2 kg and 4 kg are placed one over the other as shown in, figure.Atime varying horizontal force F = 2t is applied on the upper block as shown in, figure. Here t is in second and F is in newton. Draw a graph showing accelerations ofA, and B on y-axis and time on x-axis. Coefficient of friction betweenAand B is =1/2, and the horizontal surface over which B is placed is smooth. (g =10 m/s2 ) [5], , Q.6, , Two monkeys Ronit and Yatin of equal mass 'm' can climb strings of a pulley arrangement as shown in, figure. Find magnitude of acceleration (in m/s2) of Ronit with respect to rope so that block remains, stationary. It is given that Yatin is just holding the string. Assume pulley is frictionless and string is, massless and inextensible., [5], , Ronit, Yatin, 5m, , Q.7, , A smooth strip of metal is formed into a thin hoop of radius r and fastened to a rough horizontal surface., Aparticle of mass m is now launched with an initial speed v, so that it travels in a circle around the inside, of the hoop. Because of friction , after one complete circle the speed was reduced to 0.8v. (a) Find the, coeffcient of kinetic friction between the particle and the horizontal surface. (b) What total number of, additional revolutions will the particle make before coming to rest?, [5], , PAGE # 5

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Q.8, , The essential elements of one form of simple speed governor are as shown: to a, vertical shaft a horizontal rod is mounted symmetrically and on the horizontal rod are, freely sliding brake shoes. When the shaft turns at a frequency of rotation f = 10 Hz,, the brake shoes press against the inner surface of a stationarycylindrical brake drum., If the brake shoes are each of mass m = 1kg, and their thickness dimension is negligible, compared to the inner radius of the brake drum r =0.1 m, and the coefficient of, sliding friction between the shoes and the drum is = 0.5, find the, power required in watt to turn the governor shaft., [Take: 2 = 10] [5], , Q.9, , A particle of mass m approaches a region of force starting from r = + . The potential energy function is, given by, [5], , (a), (b), , K, K, (3a 2  r 2 ), for |r| < a ;, =, for |r| > a, 3, | r|, 2a, Derive the force F(r) and determine whether it is repulsive or attractive., With what velocity should the particle start at r =  to cross over to r = – , , (c), , If the velocity of the particle at r =  is, , Q.10, , A 5kg block is attached to an unstretched ideal spring of constant K=, 2kN/m. The coefficient of static and kinetic friction between the block and, , plane are 0.6 and 0.4 respectively. If a horizontal force F is slowlyincreased, to the block until the tension in spring reaches 90N then suddenlyremoved., Find, [5], Velocity of block as it returns to its initial position., Position of block where it will have maximum velocity., , U(r) =, , (a), (b), , 2K / am , describe the motion.