1-MACHANICS-PART TEST - 1

PART TEST - 1 (PT-1) TOPIC : MECHANICS (PHYSICS) Duration : 1 Hour Max. Marks : 90 GENERAL INSTRUCTIONS 1. This Question Paper contains 30 objective type questions. 2. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct. 3. For each question, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. Straight Objective Type This section contains 30 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 2. An automobile enters a turn of radius R. If the road is banked at an angle of 450 and the coefficient of friction is 1, the minimum and maximum speed with which the automobile can negotiate the turn without skidding is : (A) and (B) rg and 2 (C) rg and 2 (D) 0 and infinite 2 3. Figure shows the roller coaster track. Each car will start from rest at point A and will roll with negligible friction. It is important that there should be at least some small positive normal force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the minimum safe value for the radius of curvature at point B is (g = 10 m/s2) : (A) 20 m (B) 10 m (C) 40 m (D) 25 m 4. Two masses m1 and m2 which are connected with a light string, are placed over a frictionless pulley. This set up is placed over a weighing machine, as shown. Three combination of masses m1 and m2 are used, in first case m1 = 6 kg and m2 = 2 kg, in second case m1 = 5 kg and m2 = 3kg and in third case m1 = 4 kg and m2 = 4 kg. Masses are held stationary initially and then released. If the readings of the weighing machine after the release in three cases are W 1, W 2 and W 3 respectively then : (A) W1 > W2 > W3 (B) W1 < W2 < W3 (C) W1 = W2 = W3 (D) W1 = W2 < W3 Weighing Machine 5. The ratio of work done by the internal forces of a car in order to change its speed from 0 to V and from V to 2V is (Assume that the car moves on a horizontal road) - (A) 1 (B) 1/2 (C) 1/3 (D) 1/4 6. A weightless rod of length 2𝑙 carries two equal masses 'm', one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is : (A) (B) (C) (D) 7. Power versus time graph for a given force is given below. Work done by the force upto time t( t ). (A) First decreases then increases (B) First increases then decreases (C) Always increases (D) Always decreases 8. A motor car is going due north at a speed of 50 km/h. It makes a 90º left turn without changing the speed. The change in the velocity of the car is about (A) 50 km/h towards west (B) 50 km/h towards south-west (C) 50 km/h towards north-west (D) zero 9. A body is thrown horizontally with a velocity from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is (A) h (B) h 2 2h (C) 2h (D) 3 10. A train is standing on a platform , a man inside a compartment of a train drops a stone . At the same instant train starts to move with constant acceleration . The path of the particle as seen by the person who drops the stone is : (A) parabola (B) straight line for sometime & parabola for the remaining time (C) straight line (D) variable path that cannot be defined 11. P is a point moving with constant speed 10 m/s such that its velocity vector always maintains an angle 60° with line OP as shown in figure (O is a fixed point in space). The initial distance between O and P is 100 m. After what time shall P reach O. (A) 10 sec. (B) 15 sec. (C) 20 sec. (D) 20 sec 12. A mosquito with 8 legs stands on water surface and each leg makes depression of radius ' a'. If the surface tension and angle of contact are ' T ' and zero respectively , then the weight of mosquito is : (A) 8 T . a (B) 16  T a (C) T a (D) 8 T a 16  13. The work done in increasing the size of a rectangular soap film with dimensions 8 cm × 3.75 cm to 10 cm × 6 cm is 2 × 10–4 J. The surface tension of the film in N/m is : (A) 1.65 × 10–2 (B) 3.3 × 10–2 (C) 6.6 × 10–2 (D) 8.25 × 10–2 14. The property of surface tension is to : (A) increase the volume (B) decrease the volume (C) increase the surface area (D) decrease the surface area 15. Two uniform rods of equal length but different masses are rigidly joined to form a Lshaped body, which is then pivoted about O as shown. If in equilibrium the body is in the shown configuration, ratio M/m will be: (A) 2 (B) 3 (C) (D) 16. A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side 'L' at a depth '4y' from the top and the other is a circular hole of radius 'R' at a depth ‘y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, 'R' is equal to : L (A) (B) 2L (C) . L (D) 2 17. A stationary body explodes into two fragments of masses m1 and m2. If momentum of one fragment is p, the energy of explosion is : p2 p2 p2(m  m ) p2 (A) 2(m1  m2 ) (B) (C) 1 2 2m1m2 (D) 2(m1  m2 ) 18. A shell of mass 2 m projected with a speed ' u ' at an angle  to the horizontal explodes at the highest point of its motion into two pieces of mass ' m ' each. If one piece whose initial speed is zero, falls vertically, the distance at which the other piece will fall from the gun is given by : (A) 3 u2 sin 2 g (B) 3 2 u2 sin 2 g (C) u2 sin 2 g (D) none of these 19. A man of 80 kg attempts to jump from a small boat of mass 40 kg on to the shore. He can generate a relative velocity of 6 m/s between himself and boat. His velocity towards the shore is : (A) 4 m/s (B) 8 m/s (C) 2 m/s (D) 3 m/s 20. A block of mass m slides along the track with coefficient of kinetic friction . A man pulls the block through a rope which makes an angle  with the horizontal as shown in the figure. The block moves with constant speed V. Power delivered by the man is : (A) TV (B) TV cos  (C) (T cos    mg) V (D) zero 21. A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown in the figure. C is the pivot, O is the centre of the circle in which the → pendulum bob moves and  the constant angular velocity of the bob. If L is the angular momentum about point C, then - → → (A) L is constant (B) only direction of L is constant → (C) only magnitude of L is constant (D) none of the above. 22. A sphere of mass m and radius r is projected in a gravity free space with speed v. If coefficient of viscosity is 1 6 , the distance travelled by the body before it stops is : mv (A) 2r (B) 2mv r (C) mv r (D) none of these 23. Two same masses are tied with equal lengths of strings and are suspended O at the same fixed point. One mass is suspended freely whereas another is kept in a way that string is horizontal as shown. This mass is given initial velocity u in vertical downward direction. It strikes the freely suspended L mass elastically that is just able to complete the circular motion after the collision about point of suspension O. Magnitude of velocity u is : m L m u (A) (B) (C) (D) 24. A ring attached with a light spring is fitted in a smooth rod. The spring is fixed at the outer end of the rod. The mass of the ring is 3kg & spring constant of spring is 300 N/m. The ring is given a velocity ‘V’ towards the outer end of the rod and the rod is set to be rotating with an angular velocity . Then ring will move with constant speed with respect to the rod if : (A) angular velocity of rod is increased continuously (B)  = 10 rad/s (C) angular velocity of rod is decreased continuously. (D) constant velocity of ring is not possible. 25. A force → = 3 t ˆi  5 ˆjN acts on a body due to which its position varies as → = 2 t2 ˆi  5 ˆj. Work done by F s this force in initial 2 seconds is : (A) 23 J (B) 32 J (C) zero (D) can't be obtained 26. A partical A is projected with speed VA from a point making an angle 60º with the horizontal. At the same instant, a second particle B is thrown vertically upwards from a point directly below the maximum height point of parabolic path of A , with velocity VB. If the two particles collide then the ratio of VA/VB should be : (A) 1 (B) 2 / (C) /2 (D) 27. A uniform rod of density , and length ‘l’ is having square cross-section of side ‘a’. It is placed in a liquid of equal density  vertically along length in a tank having sufficient height of liquid. The surface tension of liquid is ‘T’ and angle of contact is 120º. Then : (A) rod will float completely immersed inside the liquid (B) rod will sink to bottom of the tank (C) rod will float partially submerged with height 4T ag above liquid (D) rod will float partially submerged with height 2T ag above liquid. 28. A rigid body undergoing uniform pure rolling encounters horizontal tracks AB and BC as shown in the figure AB is a smooth layer of ice and BC is a rough surface with  = 1. Both AB and BC are rigid tracks. Which of the following statements are correct : (1) the body will slow down over BC (2) the body will start slipping on AB (3) the body remains in pure rolling over the whole stretch AC (4) the angular velocity of the body remains constant over the whole stretch AC. (A) 1 and 2 (B) 1 and 3 (C) 2 and 4 (D) 3 and 4 29. A disc of mass m0 rotates freely about a fixed horizontal axis through its centre. A thin cotton pad is fixed to its rim, which can absorb water. The mass of water dripping onto the pad is  per second. After what time will the angular velocity of the disc get reduced to half of its initial value? (A) 2m0  (C) m0  (B) 3m0  (D) m0 2 30. A uniform cylinder of mass M and radius R rolls without slipping down a slope of angle  to the horizontal. The cylinder is connected to a spring constant K while the other end of the spring is connected to a rigid support at P. The cylinder is released when the spring is unstretched. The maximum distance that the cylinder travels is 3 Mgsin Mgsin (A) 4 K (B) K 2Mgsin 4 Mg sin (C) K (D) 3 K A nswers 1. (C) 2. (D) 3. (A) 4. (B) 5. (C) 6. (C) 7. (C) 8. (B) 9. (C) 10. (C) 11. (C) 12. (B) 13. (B) 14. (D) 15. (D) 16. (C) 17. (C) 18. (B) 19. (C) 20. (B) 21. (C) 22. (C) 23. (D) 24. (B) 25. (B) 26. (B) 27. (D) 28. (D) 29. (D) 30. (C) PART TEST - 2 (PT-2) TOPIC : MECHANICS (PHYSICS) Duration : 1 Hour Max. Marks : 88 GENERAL INSTRUCTIONS 1. This Question Paper contains 24 questions. 2. For each question in Section I , you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 3. For each question in Section II , you will be awarded 4 Marks if you give the correct answer. There is no negative marking. 4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded : (i) 1 Mark for correct answer in one row. (ii) 2 Marks for correct answer in two rows. (iii) 4 Marks for correct answer in three rows. SECTION - I Straight Objective Type This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. The spring block system lies on a smooth horizontal surface. The free end of the light spring is being pulled towards right with constant speed v0 = 2m/s. At t = 0 sec, the spring of spring constant k = 100 N/cm is unstretched and the block has a speed 1 m/s to left. The maximum (A) 2 cm (B) 4 cm (C) 6 cm (D) 8 cm 2. The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume V in the cube as shown. This chamber is completely 4 filled by m kg of water. Water leaks through a hole H. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is : (A) 1 2 5 (C) 8 3 mg a (B) 8 1 mga (D) 8 mg a mga 3. Two blocks ‘A’ and ‘B’ each of mass ‘m’ are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on the two blocks ‘A’ and ‘B’ respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is : (A) F (B) F/2 F (C) (D) 3F 4. A coin is released inside a lift at a height of 2 m from the floor of the lift. The height of the lift is 10 m. The lift is moving with an acceleration of 11 m/s2 downwards. The time after which the coin will strike the lift is : (A) 4 s (B) 2 s (C) s (D) s 5. The extension in a uniform rod of length l, mass m, cross section radius r and young’s modulus Y when it is suspended at one of its end is : (A) mg𝑙 r2Y (B) mg𝑙 2r2Y (C) 2mg𝑙 r2Y (D) mg𝑙 4r2Y 6. A spherical soap bubble of radius 1.0 cm is formed inside another of radius 2 cm. If a single soap bubble is formed which maintains the same pressure difference as inside the smaller and outside the larger bubble, the radius of this bubble is - (A) 0.005 m (B) 0.05 m (C) 0.0067 m (D) 0.067 m 7. Block ‘ A‘ is hanging from a vertical spring and is at rest. Block ‘ B‘ strikes the block ‘A’ with velocity ‘ v ‘ and sticks to it. Then the value of ‘ v ‘ for which the spring just attains natural length is : (A) (B) (C) (D) None of these 8. A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities  and  ( > ) fill half of the tube as shown.  is the angle which the radius passing through the interface makes with the vertical.        (A)  = tan–1   (B)  = tan–1                 (C)  = tan–1     (D)  = tan–1          SECTION - II Multiple Correct Answers Type This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE may be correct. 9. A ball tied to the end of a string swings in a vertical circle under the influence of gravity (A) when the string makes an angle 90º with the vertical, the tangential acceleration is zero amd radial acceleration is somewhere between maximum and minimum (B) when the string makes an angle 90º with the vertical, the tangential acceleration is maximum and radial acceleration is somewhere between maximum and minimum (C) at no place in the circular motion, tangential acceleration is equal to radial acceleration (D) throughout the path whenever radial acceleration has its extreme value, the tangential acceleration is zero. 10. A particle moves along the X-axis as x = u(t – 2) + a(t – 2)2 (A) the initial velocity of the particle is u (B) the acceleration of the particle is a (C) the acceleration of the particle is 2a (D) at t =2s particle is at the origin. 11. Which of the following is not possible ? (A) (B) (C) D) 12. Two particle P and Q are in motion under gravity. Then : (A) their relative acceleration is constant but not zero (B) their relative velocity is constant (C) their centre of mass has constant velocity (D) their centre of mass has constant acceleration. SECTION - III Reasoning Type This section contains 4 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 13. Statment–1 : Steady flow can be maintained in compressible liquids. Statment–2 : Steady flow means all physical parameters related to the flow being constant with time though they may vary with position. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 14. Statment–1 : In a circular motion, the force must be directed perpendicular to the velocity all the time. Statment–2 : A centripetal force is required to provide the centripetal acceleration in a circular motion. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 15. Statment–1 : The centre of gravity and centre of mass of a body may be at different positions. Statment–2 : If the mass is uniformly distributed then only the centre of mass and centre of gravity of a body will be at the same place. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 16. Statment-1 : Consider an object that floats in water but sinks in oil. When the object floats in water, half of it is submerged. If we slowly pour oil on top of water till it completely covers the object, the object moves up. Statment-2 :As the oil is poured in the situation of statement-1, pressure inside the water will increase everywhere resulting in an increase in upward force on the object. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True SECTION - IV Comprehension Type This section contains 2 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Comprehension (For Q.No. 17 to 19) Consider a star and two planet system. The star has mass M. The planets A and B have the same mass m, radius a and they revolve around the star in circular orbits of radius r and 4r respectively (M > > m, r > > a). Planet A has intelligent life and the people of this planet have achieved a very high degree of technological advance. They wish to shift a geostationary satellite of their own planet to a geostationary orbit of planet B. They achieve this through a series of high precision maneuvers in which the satellite never has to apply brakes and not a B single joule of energy is wasted. S1 is a geostationary satellite of planet A and S2 is a geostationary satellite of planet B. Neglect interaction between A and B, S1 and S2, S1 and B & S2 and A. 17. If the time period of the satellite in geostationary orbit of planet A is T, then its time period in geostationary orbit of planet B is : (A) T (B) 4T (C) 8 T (D) Data insufficient  m 1/ 3 18. If the radius of the geostationary orbit in planet A is given by rG = r  M  , then the time in which the   geostationary satellite will complete 1 revolution is I. 1 planet year = time in which planet revolves around the star II. 1 planet day = time in which planet revolves about its axis. (A) I (B) II (C) both I and II (D) neither I nor II. 19. If planet A and B, both complete one revolution about their own axis in the same time, then the energy needed to transfer the satellite of mass m0 from planet A to planet B is - (A) Gmm0 4r (B) GMm0 4 r (C) 3GMm0 8 r (D) Zero Comprehension (For Q.No. 20 to 22) In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x- coordinate. The particle moves under the effect of this conservative force along the x-axis. 20. If the particle is released at the origin then : (A) it will move towards positive x-axis. (B) it will move towards negative x-axis. (C) it will remain stationary at the origin. (D) its subsequent motion cannot be decided due to lack of information. 21. If the particle is released at x = 2 +  where   0 (it is positive) then its maximum speed in subsequent motion will be : (A) m/s (B) 5 m/s (C) 5 2 m/s (D) 7.5 m/s 22. x = – 5 m and x = 10 m positions of the particle are respectively of (A) neutral and stable equilibrium. (B) neutral and unstable equilibrium. (C) unstable and stable equilibrium. (D) stable and unstable equilibrium. SECTION - IV Matrix - Match Type This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column-I and four or five statements (p,q,r, s or p,q,r, s,t) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B- s, C-r, C-s, D-q and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t. 23. A particle is taken to a distance r (> R) from centre of the earth. R is radius of the earth. It is given → velocity V which is perpendicular to r . With the given values of V in column I you have to match the values of total energy and path of particle in column II. Here 'G' is the gravitational constant and 'M' is the mass of the earth. Column I (Velocity) Column II (A) V = GM/ r (p) Total energy Negative (B) V = 2GM/ r (q) Total energy Positive (C) V > 2GM/ r (r) Total energy Zero (D) GM/ r < V < 2GM/ r (s) Path is circular (t) Path is elliptical 24. An arrangement of the pipes is shown in the figure. The flow of water (incompressible and nonviscous) through the pipes is steady in nature. Three sections of the pipe are marked in which section 1 and section 2 are at same horizontal level, while being at a greater height than section 3. Correctly match order of the different physical parameter with the options given. Column I Column II (A) volume flow rate (p) same everywhere (B) kinetic energy per unit mass (q) same at 2 and 3 (C) pressure in the sections. (r) maximum at 1 (D) flow speed in sections (s) minimum at 1 (t) maximum at 3 A nswers 1. (C) 2. (C) 3. (D) 4. (A) 5. (B) 6. (C) 7. (B) 8. (A) 9. (B), (D) 10. (C), (D) 11. (A), (C), (D) 12. (B), (D) 13. (A) 14. (D) 15. (C) 16. (A) 17. (D) 18. (C) 19. (C) 20. (B) 21. (B) 22. (D) 23. (A) p,s (B) r (C) q (D) p, t 24. (A) p,q (B) q,r (C) s,t (D) q,r PART TEST - 3 (PT-3) TOPIC : MECHANICS (PHYSICS) Duration : 1 Hour Max. Marks : 88 GENERAL INSTRUCTIONS 1. This Question Paper contains 22 questions. 2. For each question in Section I, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 3. For each question in Section II, you will be awarded 4 Marks if you give the correct answer. There is no negative marking. 4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded : (i) 1 Mark for correct answer in one row. (ii) 2 Marks for correct answer in two rows. (iii) 4 Marks for correct answer in three rows. 7. For each question in Section VI, you will be awarded 6 Marks if you give the correct answer. There is no negative marking. SECTION - I Straight Objective Type This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass m at a point A is in horizontal direction, find the tangential force at this point in terms of tension T and mg. (A) mg (B) mg T mg T (C) T (D) mg (mg)2  T2 2. Hailstones falling vertically with a speed of 10 m/s, hit the wind screen (wind screen makes an angle 30° with the horizontal) of a moving car and rebound elastically. The velocity of the car if the driver finds the hailstones rebound vertically after striking is : (A) 10 m/s (B) 20 m/s (C) 10 m/sec (D) m/sec 3. A water tank stands on the roof of a building as shown. Then the value of 'h' for which the distance covered by the water 'x' is greatest is - (A) 0.5 m (B) 0.67 m (C) 1 m (D) none of these 4. A U-tube of base length “𝑙” filled with same volume of two liquids of densities  and 2 is moving with an acceleration “a” on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height h is given by: a (A) 2g 𝑙 3a (B) 2g 𝑙 a (C) g 𝑙 5. A particle A of mass 10 7 2a (D) 3g 𝑙 kg is moving in the positive direction of x. Its initial position is x = 0 & initial velocity is 1 m/s. The velocity at x = 10 is: (use the graph given) (A) 4 m/s (B) 2 m/s (C) 3 m/s (D) 100/3 m/s 6. The string of a step rolling wheel is pulled by applying force F with different lines of action in two situations as shown. The wheel starts rolling without slipping due to application of the force : (A) The wheel rolls to the right in situation  and to the left in situation . (B) The wheel rolls to the left in situation  and to the right in situation  (C) The wheel rolls to the right in both situations. (D) The wheel rolls to the left in both situations. 7. Two particles start together from a point O and slide down straight smooth wires inclined at 30º & 60º to the vertical & in the same vertical plane as in figure. The relative acceleration of second with respect to first will be (in magnitude & direction) as : (A) g 2 g in the vertical direction (B) g 3 2 at 45º with vertical (C) inclined at 60º to vertical (D) g in the vertical direction 8. Two points A & B on a disc have velocities v1 & v2 at some moment. Their directions make angles 60° and 30° respectively with the line of separation as shown in figure. The angular velocity of disc is : (A) 3v1 (B) v 2 d (C) v2  v1 d v 2 (D) d SECTION - II Multiple Correct Answers Type This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE may be correct. 9. In the figure shown ADB & BEF are two fixed circular paths. A block of mass m enters in the tube ADB through point A with minimum velocity to reach point B. From there it moves on another circular path of radius R . There it is just able to complete the circle. (A) velocity at A must be (B) velocity at A must be (C) R 2 R = 3 (D) the normal reaction at point E is 6 m g 10. The displacement of a body from a reference point is given by, t in seconds. This shows that the body : (A) is at rest at t = 3/2 (B) is accelerated = 2 t  3, where ' x ' is in metres and (C) is decelerated (D) is in uniform motion 11. If the resultant force on a system of particles is non-zero, then : (A) The linear momentum of the system must increase. (B) The velocity of the centre of mass of the system must change. (C) The distance of the centre of mass may remain constant from a fixed point. (D) kinetic energy of all particles must either increase simultaneuosly or decrease simultaneously. 12. A painter is applying force himself to raise him and the box with an acceleration of 5 m/s2 by a massless rope and pulley arrangement as shown in figure. Mass of painter is 100 kg and that of box is 50 kg. If g = 10 m/s2, then : (A) tension in the rope is 1125 N (B) tension in the rope is 2250 N (C) force of contact between the painter and the floor is 375 N (D) none of these SECTION - III Reasoning Type This section contains 2 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 13. Statement-1 : For a disc undergoing fixed axis rotation, the magnitude of angle between velocity and acceleration vector of any moving point on disc at a particular instant of time are same. Statement-2 : Each moving point on a disc undergoing fixed axis rotation has same angular speed and same angular acceleration at an instant of time. Hence the ratio of magnitude of tangential acceleration and magnitude of centripetal acceleration is same for all moving points at an instant of time. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. 14. Statement-1 : The equation of distance travelled by a particle moving in a straight line with constant a acceleration in nth second is S = u + (2n – 1) 2 , where letters have usual meaning, is dimensionally incorrect. Statement-2 : For every equation relating physical quantities to be true, it must have dimensional homogenity. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. SECTION - IV Comprehension Type This section contains 1 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Question Nos. 15 to 17 Figure shows block A of mass 0.2 kg sliding to the right over a frictionless elevated surface at a speed of 10 m/s. The block undergoes a collision with stationary block B, which is connected to a nondeformed spring of spring constant 1000 Nm–1. The coefficient of restitution between the blocks is 0.5. After the collision, block B oscillates in SHM with a period of 0.2 s, and block A slides off the left end of the elevated surface, landing a distance 'd' from the base of that surface after falling height 5m. (use 2 = 10; g = 10 m/s2) Assume that the spring does not affect the collision. 15. Mass of the block B is (A) 0.4 kg (B) 0.8 kg (C) 1 kg (D) 1.2 kg 16. Amplitude of the SHM as being executed by block B-spring system, is - (A) 2.5 10 cm (B) 10 cm (C) 3 17. The distance 'd' will be equal to - cm (D) 5 cm (A) 2m (B) 2.5 m (C) 4m (D) 6.25 m SECTION - V Matrix - Match Type This section contains 1 questions. Each question has four statements (A, B, C and D) given in Column-I and five statements (p,q,r, s and t) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s, D-q and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t. 18. A uniform disc of mass M and radius R lies on a fixed rough horizontal surface at time t = 0. Initial angular velocity o of each disc (magnitude and sense of rotation) and horizontal velocity v0 of centre of mass is shown for each situation of column-I. Match each situation in column-I with the results given in column-II. Column-I Column-II (A) (p) The magnitude of angular speed keeps on decreasing till the disc starts rolling without slipping. It is given that v0 = 2R0 (B) (q) After the disc starts rolling without slipping, the angular velocity is nonzero and in clockwise sense. It is given that 2v0 = R0 (C) (r) After the disc starts rolling without slipping, the velocity of centre of disc is towards right. It is given that v0 = 2R0 (D) (s) After the disc starts rolling without slipping, the kinetic energy of disc is less than its initial value. It is given that 2v0 = R0 (t) The magnitude of angular speed keeps on increasing till the disc starts rolling without slipping. SECTION - VI Integer value correct Type This section contains 4 questions. The answer to each question is a integer type. 19. Two particles are projected simultaneously with the same speed v in the same vertical plane with angles of elevation  and 2 , where  < 45º . At what time will their velocities be parallel. 20. A man can swim in still water with a speed of 3 m/s. x and y axis are drawn along and normal to the bank of river flowing to right with a speed of 1 m/s. The man starts swimming from origin O at t = 0 second. Assume size of man to be negligible. Find the equation of locus of all the possible points where man can reach at t = 1 sec. 21. In the figure shown a small block ‘B’ of mass ‘m’ is released from the top of a smooth movable wedge ‘A’ of the same mass ‘m’. ‘B’ ascends another movable smooth wedge ‘C’ of the same mass. Neglecting friction any where find the maximum height attained by ‘B’ on ‘C’. 22. A cylinder rotating at an angular speed of 50 rev/s is brought in contact with an identical stationary cylinder. Because of the kinetic friction, torques act on the two cylinders, accelerating the stationary one and decelerating the moving one. If the common magnitude of the acceleration and deceleration be one revolution per second square, how long will it take before the two cylinders have equal angular speed ? A nswers 1. (B) 2. (A) 3. (C) 4. (B) 5. (A) 6. (A) 7. (A) 8. (D) 9. (B), (C) (D) 10. (A), (B) 11. (B), (C) 12. (A), (C) 13. (A) 14. (D) 15. (C) 16. (A) 17. (B) 18. (A)  q,r,s; (B)  p,s; (C)  q,r,s,t ; (D)  p,q,r,s v     3  19. cos  cosec   g 2 2 20. (x – 1)2 + y2 = 9     21. h = h 22. 25 s 4