Tiêu đề IIT-JAM PHYSICS MECHANICS_CLASS TEST_29-09-2023.pdf ✅

1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT-JAM PHYSICS TEST : MECHANICS Time : 60 Minutes Date : 29-09-2023 M.M. : 40 INSTRUCTIONS:  Part-A contains 10 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c) and (d), for its answer, out of which ONLY ONE is correct. For each correct answer you will be awarded 2 marks. For each incorrect answer 0.5 mark will be deducted.  Part-B contains 5 Multiple Select Questions (MSQ). Each question has 4 choices (a), (b), (c) and (d) for its answer, out of which ONE or MORE than ONE is/are correct. For each correct answer you will be awarded 2 marks, there is no negative marking in this section.  Part-C contains 5 Numerical Answer Type (NAT) questions of 2 Marks each, and there is no negative marking. PART-A [Multiple Choice Questions] 1. A long wire has linear mass density . A particle of mass m moves around the wire in circular path. Kinetic energy of the particle is (a) m G (b) 2 m G (c) 2m G (d) 4 m G 2. Two particles each of mass M are fixed at x a y    , 0 . A particle of mass m moves along y axis. Maximum acceleration of m is (a) 2 2 3 GM a (b) 2 4 3 3 GM a (c) 2 2 3 3 GM a (d) 2 3 3 GM a 3. Two planets each of mass M and radius R are separated by centre to centre distance 16R. With what minimum speed should a particle be projected from one planet towards the other so that it reaches the other planet? (a) 41 30 GM R (b) 49 30 GM R (c) 43 30 GM R (d) 31 30 GM R 4. Two particles of equal mass m move in circle of radius R under their mutual gravitational attraction. Total energy of system is (a) 2 Gm R  (b) 2 2 Gm R  (c) 2 4 Gm R  (d) 2 8 Gm R 
2 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 5. Assume earth is a sphere of radius R and mass M. A satellite of mass m is taken from surface of earth and set into a circular orbit of radius 4R around earth. Energy required for this mission is (a) 4 GMm R (b) 2 GMm R (c) 3 4 GMm R (d) 4 4 GMm R 6. In figure shown moment of inertia about the axis is maximum for m x 2m d (a) 2 d x  (b) 2 3 d x  (c) 3 d x  (d) 3 4 d x  7. A hollow sphere is rolling on the wedge as shown in figure. Value of F required to keep the wedge at rest is  F wedge R m (a) 2 sin 5 mg  (b) 2 sin cos 5 mg   (c) 5 sin 7 mg  (d) 5 sin cos 7 mg   8. A sphere rolls on horizontal surface. Ratio of magnitude of acceleration of lowest and highest points is (a) zero (b) 1 (c) 2 (d) 4 9. From a disc of mass m and radius r a circular portion of radius 2 r is cut as shown in figure. R/2 4 1 2 3 Moment of inertia is maximum about axis (a) 1 (b) 2 (c) 3 (d) 4 10. A bead of mass is embedded into smooth horizontal wire. Initially bead is at distance r 0 from fixed end of wire. When wire is rotated with constant angular speed  bead slides on wire. Normal reaction between the rod and wire varies with time as m g=0 (a) 2 0 mr t   cos (b) 2 0 mr t   sin (c) 2 0 mr t   cosh (d) 2 0 mr t   sinh
3 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 PART-B [Multiple Select Questions] 11. A planet moves around the Sun in elliptical orbit of eccentricity e with time of revolution T as shown in figure. Which of the following is/are correct? D C B A (a) ABC CDA t t  (b) DAB BCD t t  (c) CD BC t t  (d) 2 2 DAB e t T      12. A rod of mass m and length l lying on smooth horizontal table is hinged at one end, about which it is free to rotate. A force F is applied at free end. F is always parallel to the rod. As a function of time t which of the following statements is/are true? (a) Kinetic energy of rod is 2 2 3 2 F t m (b) Acceleration of centre of rod is 3 2 F m (independent of t) (c) Force due to hinge is 2 F (independent of t) (d) Rate of change of angular momentum is constant 13. At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct ? (a) The mass of the brass ball on this planet is a quarter of its mass as measured on earth. (b) The weight of the brass ball on this planet is a quarter of the weight as measured on earth. (c) The brass ball has the same mass on the other planet as on earth. (d) The brass ball has the same volume on the other planet as on earth. 14. A mass m is placed a distance d away from an infinite plane with surface mass density  . (a) The gravitational force on the mass is 2 2Gm d . (b) The gravitational force on the mass is 2Gm . (c) The gravitational force on the mass is not dependent on d. (d) The gravitational field on the mass is 4G .
4 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 15. At the moment t = 0, the force F kt  is applied to a small body of mass m resting on smooth horizontal plane (k is constant). The permanent direction of this force forms an angle  with the horizontal. Which of the following option(s) is/are correct ? m  F (a) The body will break off the plane at sin mg t k   . (b) The velocity of the body at the moment of its breaking off the plane will be 2 2 cos 2 sin mg v k         . (c) The distance travelled by the body upto the moment of its breaking off the plane will be 2 3 2 3 cos 6 sin m g s k    . (d) The distance travelled by the body upto the moment of its breaking off the plane will be 2 3 2 3 cos 3 sin m g s k    . PART-C [Numerical Answer Type] 16. Water ( = 103 kg/m3 ) is filled in a tank upto height 5 metre. There is an opening of area 1cm2 at the bottom of tank. Rate at which liquid flows out of opening is ____________ kg/s [Integer] 17. A ball of mass 0.25 kg is thrown with initial velocity ˆ ˆ v i j   (3 4 )  m/s. Gravity acts in –y direction. Impulse on the ball due to gravitational force during its flight from ground to ground is ______ kgm/s [Integer] 18. In figure shown coordinates of centre of mass of uniform triangle is ( , ) X Yc c value of c c X Y is ____ [Integer] 2a a X Y 19. A particle moves in 3-D space in a central potential ( )  n V r kr , where k is a constant. The angular frequency  for a circular orbit depends on its radius R as 2 , then     n R is equal to _________. [Integer] 20. A horizontal circular platform rotates with a constant angular velocity 4 rad/sec directed vertically upwards. A man shoots a bullet of mass 2 kg horizontally with speed 3m/sec from the centre. The acceleration of the bullet in the reference frame of the man is 10 4  x , then value of x is _________. [Integer]